i (UK*
AJRi A l,
!' '"' ;
ENTARY
AND BROOKS
IN MEMORIAM
FLOR1AN CAJORI
EATIONAL
ELEMENTARY ARITHMETIC
GEORGE W. MYERS, Ph.D.
PROFESSOR OF THE TEACHING OF MATHEMATICS AND ASTRONOMY
SCHOOL OF EDUCATION, THE UNIVERSITY OF CHICAGO
AND
SARAH C. BROOKS
PRINCIPAL OF THE TEACHERS' TRAINING SCHOOL, BALTIMORE, MARYLAND
CHICAGO
SCOTT, FORESMAN AND COMPANY
1906
COPYRIGHT 1898, 1899, 1905
BY SCOTT, FORESMAN AND COMPANY
BOBT. O. X<AW CO.. nUiraVKB AND H1NDHUH, OHIOA8O.
PREFACE.
Many and substantial gains have been made in
GENERAL. the last decade in both theory and practice in elemen-
tary education, and arithmetic has gained largely from
this general advance. We have learned much of late as to practical
ways of securing in the teaching of the elements of mathematical science
the larger and the more significant educational aims strengthening
the judgment and the will, the power to think and to do.
The writer of an arithmetic who cuts himself off from these ad-
vances and satisfies himself with mere "figuring/' or the mere meeting
of an existing "consensus," cheapens his effort by denying the higher
purposes of education and renounces his opportunity to help even
the makers of programs by pointing the direction whence improve-
ment must come. Without neglecting either of these two important
requirements, the authors of this book have striven to make the arith-
metic work more thoughtful, and even the drill purposeful and
educative.
There is no school subject in which foreshortened
PLACE FOR views and distorted perspective work more harm than
FORMAL in elementary mathematics. Children as well as adults,
STUDY. learn new ideas by meeting them first in simple forms,
intermingled with familiar ideas arid fairly well-under-
stood uses of the new ideas.
After a little, the new idea makes itself felt as something new.
This is the time to differentiate it for formal study, to learn what it
really is. This is the stage for the study of process and for drill
enough to fix it and to make its use easy and facile.
The learner then desires to experience the added power the
mastery of the process has given him, and this calls for the applica-
tion stage. The treatment of new ideas, processes and topics in this
book is accordingly arranged on this three-fold plan of (1) its in'
iii
it PREFACE
formal use, (2) its formal study, and (3) its application. Examples
of this plan may be seen in the teaching of the tables.
The arrangement of number work for the grades
ORDER OF must be in accordance with the natural unfolding of
DEVELOP- the child's mind. Too often this important fact is
MENT. lost sight of in the logic of the subject itself. Strictly
speaking there can be no contradiction between the
demands of the child's mental development and the logical require-
ments of the subject. It is nly wLen 1 gic is construed to mean the
procedure of adult mind that the .emends ~f logic become mischievous
in the elementary school. Rightl^ understooa, logic means the nat-
ural procedure of the learning mind in mastering a subject. The
recent work of experimental psychologists has proved conclusively
that one law of human development is that what is best for the learner
at a given stage of his development is also best for him ultimately.
In the language of biological science, what is best for the tadpole
while he is a tadpole is also best for him when he is a frog.
This doctrine, now generally accepted by all students of educa-
tion, has done much toward the general accrediting of childhood at
its true worth and has given flat and final denial of the right to quarrel
with the child because he is not something else, by attempts of the
teacher to force upon him the logic of the adult. This modern doc-
trine is also accepted by this book and it is believed it has unified
the interests of logic with those of the child by making its logic the
logic of the learner at the stage he has reached.
Two things must be carefully provided for in an
MOVEMENT arithmetic for children. There must be continuous
AND UNITY. and progressive movement through the subject and
there must be Organic unity of parts. Too often
sequence of processes and grading f exercises have wrought havoc
with the essential integrity of arithmetic as a whole. The child looks
through a narrow slit at the passing column, but fails to see the proces-
sion as a whole or even any important part of it. Divers attempts
merely to make arithmetic easy, to make play of what must be work
and work of what ought to be play, to tell number stories when there
PREFACE v
is no story, which have gotten into recent texts, are open to the charge
of having lost the unities of the subject in a confusion of irrelevant
not to say remote associations.
Other writers, in the struggle for scientific unification and pro-
portion of parts, have secured a sort of unity and balance at a great
cost of practicability. The latter is a danger that leans toward
"virtue's side," but the danger is real and serious and must be avoided.
It is largely avoided by teaching nothing not even a partial notion
which is sometimes necessary in such a way at one stage that it
must be unlearned by the pupil at a later stage. How to secure both
economic movement and essential unity has been the most earnest
struggle of the authors of the RATIONAL ARITHMETICS. The task has
not been easy and the teaching public will say how well they have
succeeded.
The ideas of number and of the numerical proc- I
MATERIAL. esses must be derived from the concrete. Form and
number are the two main developments of quantity^
The process of numbering in its varied aspects is very closely paral- j
leled in the physical world by the process of measuring in its varied !
applications. This does not imply that numbering and measuring
are one and the same process, or set of processes. What it does imply
is that numbering is the mental side of the same problem of adjust-
ment of activity that has its physical expression in measurement. It
means that measurement is the most direct and certain route to cor-
rect notions of number, for one who has not yet acquired them.
That the theory of number has no necessary connection with
measurement is witnessed by the fact that perfectly sound and ade-
quate theories, constructed altogether on the basis of counting, are
familiar to all students of advanced mathematics. The continuum
of quantity can be constructed with perfect logical rigor out of the
elementary number discreta. But this mode of evolution of the num-
ber system and processes is neither the more economical nor the more
fruitful mode for the immature learner. The physical acts of the
measuring processes run so closely parallel to the mental acts of the
numbering processes, the one-to-one correspondence of steps in the
vi PREFACE
processes is so complete and so natural, that the child glides succes-
sively and with perfect ease and certainty into and through correct
ideas of the unit, of the assemblage, of times, of parting and dividing,
of fractioning, of ratio and proportion, and of valuation, to the idea
of continuous positive and negative magnitude and number. The chief
advantage to the child of making measurement fundamental to number
is that motor, tactual, auditory, and visual sensations serve powerfully
to re-enforce and to sharpen number impressions at every turn The
whole being thus engages in the struggle for mastery of the difficulties
of number and number process "The whole boy goes to school."
Without abating energy on the symbolical phases and processes, this
book seeks through joining, dividing, and measuring lines, surfaces,
and solids, weights, etc., to fill symbols with meaning and processes
with purpose.
The appeal to the concrete involves the use of certain materials,
and any book based on this method of instruction must provide
these within its pages. This the RATIONAL ELEMENTARY ARITHME-
TIC does in great variety; e.g., lines, squares, and surfaces, cubes,
and solids, pp. 1, 2, 4, 12, 20, 60, 100, 198, 204, etc., the construction
of figures for linear and square measure on pp. 2, 4, 173, and 184,
the visual presentation of fractions on pp. 158, 159, 161, 252, and 256.
By means of these the child is also led to make use of other material
which will aid him in grasping the principles involved. >He learns to
seize quantitative questions by the handle.
There are numerous lists of problems involving
USE OF real measurement, and incidentally also counting at its
MATERIAL. best. These lists are carefully graded and the teacher
is urgently recommended at all times to have pupils
solve all they can orally. The pencil and paper should be used only
when the difficulties of the problem make it too hard for the pupil
orally. Different pupils will show very different degrees of aptitude
for rapid oral work No plan of isolating the oral from the written
work can suit the varying needs of different pupils, and every pupil
has a right to the best sort of training of which he is capable. The
problems of life are handled in this way and the pupil should early
PREFACE vii
form the habit of using his head as much as possible and his pencil
only as an aid to his head.
It is also recommended that teachers follow the
CHOOSING . . . .. 11 i
practice of having pupils work rapidly through many
of the lists of problems, indicating the processes called
AND I** i i
tor and giving and recording estimates of about what
FORMING * t 7 f\ .
the answers must be, before any figuring is done.
Then the problems should be worked through and the
correct results compared with the estimates. This work
is of high value as training of judgment and as aiding the pupil to know
when, as well as how, to add, subtract, multiply, or divide.
One of the gains that accrue from basing number
THE TABLES, teaching on measurement is that by associating parts
of the multiplication table with certain facts of the
denominate number tables, both sets of facts may be learned at once,
and more easily than either may be learned alone. For example, the
2's may be based on the fact, 2 pt. = l qt.; the 3's on 3 ft.= l yd.;
the 4's on 4 gi. = l pt.; 4 pk.= l bu.; 4 qt. = l gal.; the 5's on 5c~
1 nickel, 5 nickels =1 quarter, on the divisions of the clock-face, the
number of school days in a week, etc. In this way the most common
denominate number facts are learned and at the same time they fur-
nish a concrete background and purpose for learning the multiplica-
tion table. The space idea is utilized in building the tables, so that
the products of the multiplication tables are abo seen to be mensu-
ration facts. This incidental use of form is of no mean value. It
is indeed one great reason why we need a multiplication table.
The problems from beginning to end deal with
PROBLEMS. realities, and appeal strongly to the child's environ-
ment and experience. This gives to the work a genuine
interest which cannot otherwise be secured, and cultivates the powers
of observation and of inference, and the ability to apply numbers to
the situations of every-day life and experience, and at the same time
strengthens the ability to see and make problems on one's own account
from the raw materials of quantitative situations. Every new idea
comes to the child in the form of a problem, and through the agency
viii PREFACE
of real problems he can be most easily made to feel the genuineness
and usefulness of arithmetical knowledge. The RATIONAL ELEMEN-
TARY ARITHMETIC works out the elementary ideas of arithmetic
through the agency of real problems.
The work of the first 5 pages includes a review and
THE PLAN summary of the 2's and 3's, which pupils will have
OF THE learned before the third grade. Then follow the intro-
BOOK. " duction of halves and fourths through a study and use
PART i. of the foot-rule, then the teaching of the tables, begin-
ning with the 4's, through the use of those standards of
measure which call for the several factors to be taught and tabulated,
and largely by aid of the mensurational facts involving these factors,
see pp. 11, 12, 19, 20, 49, 50, etc. The tables are developed through
the use of the 4, 5, 6, etc., as multiplicand, because this is the most
natural way to teach them, but in the final form for reference the 4, 5,
6, etc., are put into the relation of multiplier. In consequence of the
two-fold aspect of every number, the unit and the multiplicity (the
times), the products are most easily built up and grasped by keeping
the more difficult element, the multiplicity, as small as possible. One
6, two 6's, etc., are much easier than 6 ones, 6 twos, etc. Thus the
6's , for example, are first developed in the form
1X0= G
2X6=12
3X6=18
etc.
But these products are, speaking strictly, not the 6's at all, since the
6's are those products in which 6 enters as a multiplier. So that for
final reference the table is written in the form of The Sixes, thus
6X1= 6
6X2=12 (Seep. 61)
6X3=18
etc.
PREFACE ix
The same system is followed in the rest of the tables, up to and includ-
ing the 10's in Part I. Many uses of the 11 's and 12's are given in
Part I, but the final treatment and formulation of the ll's and 12's are
reserved for Part II. Ample drills, short and frequent, are given to
fix and make flexible the tabular facts taught.
Part II includes the final treatment of the ll's and
PART n. 12's, easy scale-drawing, further use of denominate
number tables, the teaching of the four fundamental
operations, many unified lists of problems, promiscuous as to process
but unified as to some central and interesting thought. See pp. 104,
105, 121, 132, 133, 146, 167, 168, etc., and considerable easy work
calling for simple fractions. The demands of form are met through
many useful problems in the mensuration of simple figures.
The last part of the book carries forward through
PART m. the fifth ffrade the application of the fundamental proc-
esses to an extended range of practical problems
calling often for more than one process , the development of the prod-
ucts by 12, 15, 16, and other factors of frequent occurrence in
business and the industries; it includes the mensuration of boxes,
scale-drawing, a fairly complete treatment of common and decimal
fractions, denominate numbers, together with percentage and interest.
These latter features will commend themselves to teachers who de-
sire to do as much as possible for the boys and girls who are unable
to go on with their school work beyond the fifth year.
Exercises and problems for practice are to be
DRILL. found frequently throughout the book and they every-
where stand in organic relations to what precedes
and follows. This book does not "teach by drill," but everywhere
puts the drill feature in such relations to interesting and useful work
as to make the drill both purposeful and interesting. Drill should
always be for the purpose of fixing facts that have already been
taught and for the sake of establishing right habits of work. Even
in the army the manual of arms and the manoeuvres are first care-
fully taught and the drill is kept up to make correct procedure
habitual and natural. Something like this is the correct mode in
x PREFACE
number teaching. Judicious and intelligent drill constitutes an im-
portant feature of this book. The drill-master must live up to his
reputation of being a master of drill.
A fairly well-rounded elementary treatment of
FRACTIONS, the essentials of common and decimal fractions, of
PERCENTAGE, percentage, and of interest is given at the close of
INTEREST. Part III. The attempt has been to give only a fairly
complete first view, rather than fullness and finality.
As a means of recapitulating and bringing out more clearly the con-
nections and meaning of the fundamentals than could be done in
the earlier grades, this will be recognized at once as a feature no
less valuable to the pupil who goes on to the more mature work of
the grammar school, which builds on these fundamentals, than to
the pupil who is forced to leave school at the end of the fifth year,
and is very considerably benefited by a knowledge of these practi-
cal subjects.
The pleasant task now remains to the authors to make acknowl-
edgment of their indebtedness to many superintendents, principals,
and teachers who have assisted in perfecting the book by suggestions
and corrections both in the manuscript and the proofs. To Mr. F.
W. Buchholz, Professor of Mathematics in the Chicago Normal
School, the authors are under especial obligations for the great pains
and efficient service so kindly bestowed upon the proofs. His insight
and broad experience as a mathematical teacher and supervisor have
wrought wholesale improvement in the form, no less than in the sub-
stance of this book.
Chicago, Sept,, 1905. THE AUTHORS.
CONTENTS.
PART I.
MEASURING LENGTH 3
SURFACE MEASURE-MULTIPLES 5
ADDITION AND SUBTRACTION REVIEWS 7
TABLE OP FOURS.
USES, LIQUID MEASURE 9
USES, DRY MEASURE 11
BUILDING TABLE. 13
APPLICATION, WEIGHT 15
TABLE OP FIVES.
USES, U. S. MONEY 17
USES, TIME 21
BUILDING TABLE . .... 23
REVIEW PROBLEMS 25
EXERCISES FOR PRACTICE 27
FUNDAMENTAL OPERATIONS.
ADDITION 29
SUBTRACTION 33
MULTIPLICATION 37
DIVISION 41
LAUNDRY BILLS 45
DRAWING TO A SCALE 47
TABLE OF SIXES
USES, LINEAR MEASURE 49
BUILDING TABLE 51
APPLICATION 58
BOX MAKING 55
SCHOOL GARDEN 57
TABLE OF SEVENS.
USES, TIME 59
BUILDING TABLE 61
APPLICATION 63
AREA OF TRIANGLES 65
TABLE OF EIGHTS.
USES, DRY MEASURE 67
BUILDING TABLE 69
APPLICATION 71
MEASURING SOLIDS 73
BUILDING SOLIDS 75
CONTENTS OP BOXES 77
xl
xii CONTENTS
REVIEW. 79
TABLE OF NINES.
USES, SQUARE MEASURE 81
BUILDING TABLE 83
DRILL ON NINES 85
APPLICATION 87
WEIGHT 89
TABLE OF TENS.
BUILDING TABLE 91
APPLICATION, U. S. MONEY 93
FUNDAMENTAL OPERATIONS IN U. S. MONEY ; 95
USES OF ELEVENS AND TWELVES. 97
COST OF MEALS 99
PART II.
MEASURING A FLOWER GARDEN 101
PURCHASES AND WAGES 103
PROBLEMS ON CANDY RULES 105
TABLE OF ELEVENS.
BUILDING TABLE AND DRILL 107
TABLE OF TWELVES.
USES, LINEAR MEASURE 109
BUILDING TABLE Ill
APPLICATION 113
FIVES, SIXES, SEVENS, AND TWELVES 115
WRITING AND READING NUMBERS 117
THREES, SIXES, NINES, ELEVENS, TWELVES 119
SCALE DRAWING OF TILING 121
TWOS, FOURS, AND EIGHTS 123
MEASURES OF WEIGHT 125
THE DOZEN 127
FUNDAMENTAL OPERATIONS.
EXERCISES IN ADDITION 129
PROBLEMS IN ADDITION 131
FURNISHING A HOME 133
PROBLEMS IN ADDITION 135
EXERCISES IN SUBTRACTION 137
PROBLEMS IN SUBTRACTION 139
DRILL IN FUNDAMENTAL OPERATIONS. 141
MULTIPLICATION 143
PROBLEMS IN MULTIPLICATION 145
DIVISION LONG. 149
PROBLEMS IN DIVISION. 151
EXERCISES IN DIVISION 153
PROBLEMS OF SALE 155
MISCELLANEOUS PROBLEMS 157
FRACTIONS 159
MIXED NUMBERS 161
PROBLEMS IN FRACTIONS 168
MISCELLANEOUS PROBLEMS 165
PROBLEMS IN TIME 107
BUYING GROCERIES.... 169
CONTENTS xiii
EXERCISES FOR PRACTICE 171
MEASURES OF LONG DISTANCES.. 173
MEASURES OF DISTANCE 175
TWELVE AND A HALF 179
TIME AND DISTANCE 181
REVIEW PROBLEMS 183
PART III.
MKASURING SURFACES 187
APPLICATION OF SQUARE MEASURE 189
PROBLEMS OF DIVISION 191
PROBLEMS IN VALUES RATIO 193
PRODUCTS BY 14 195
TRIANGLES 197
AREAS 199
MISCELLANEOUS PROBLEMS 201
PROBLEMS IN TIME 203
SOLIDS AND CAPACITY 205
TABLE OF CUBIC MEASURE 209
PRODUCTS BY 15 211
APPLICATIONS OF LIQUID MEASURE. 213
PRODUCTS BY 16 215
APPLICATIONS OF DRY MEASURE. 217
PRODUCTS BY 16% 219
READING AND WRITING NUMBERS 221
EXERCISES IN ADDITION AND SUBTRACTION 223
PROBLEMS IN MULTIPLICATION , 225
PROBLEMS IN DIVISION 227
PRODUCTS BY 20 229
PROBLEMS IN WEIGHING .'.... 231
PROBLEMS IN TIME 233
MISCELLANEOUS PROBLEMS 235
COUNTING PAPER 237
MISCELLANEOUS PROBLEMS 239
DENOMINATE NUMBER EXERCISES 243
DENOMINATE NUMBER PROBLEMS 245
BILLS AND ACCOUNTS. 247
PROBLEMS IN FRACTIONS 251
EXERCISES IN FRACTIONS 253
PROBLEMS IN FRACTIONS 255
ADDING AND SUBTRACTING FRACTIONS 257
MULTIPLYING AND DIVIDING FRACTIONS 259
DECIMAL FRACTIONS 261
MULTIPLYING DECIMALS
PERCENTAGE 265
PROBLEMS IN INTEREST .'. 269
PRINCIPLES OF INTEREST 273
SCALE DRAWING OF MANTEL ^
TABLES OF WEIGHTS AND MEASURES 277
PART FIRST.
O
A boy made a cardboard house, one end the size of this drawing.
Without measuring write what you think are these distances:
1. The width. The greatest height. Length of the slant of
the roof. Height to the lowest point of the slant.
2. Width and height of the lower window and of the door.
3. The distance between the right side of the house and the
door; between the door and the lower window; between
the lower window and the left side of the house; be-
tween the sill of the lower window and the floor.
4. Measure each of these distances with your ruler and com-
pare them with what you thought they would be.
l
RATIONAL ELEMENTARY ARITHMETIC.
E
FG
1. Find the lines A, B, C, D, E, F, G.
2. Which is longer, A or B? C or D? D or E? E
or F? F or G?
3. How many lines like A will make one like C? B?
E? D? F? G? F and G?
4. Measure each line with your ruler.
5. How many inches long is A? B? C? D? E? F? G?
6. How many inches long are A and B together?
7. A, B, and C together are as long as which line?
8. F and G are together how many inches long?
9. What is the name for the measure which is as
long as F and G together?
10. How many inches are there in one foot?
11. What is a measure 3 feet long called?
12. Hold your hand a yard from the floor.
13. How many feet high are you? How many yards
high? How many inches high?
14. How many inches do you measure around your
chest?
15. Stretching your arms straight sidewise, how many
yards and inches is it from the tips of the rin-
gers of one hand to those of the other?
16. How many feet can you reach upward from the
floor when standing close to the wall?
MEASURING LENGTH. 3
1. How many inches long is the front edge of your desk?
2. How many inches high is your desk?
3. How many feet high is a window sill in your schoolroom?
4. How many feet wide is the window?
5. Your schoolroom is how many feet long? How many
yards long?
6. Your schoolroom is how many feet wide? How many
yards wide?
7. How long, in feet, is one end of your schoolroom? How
long are the two ends? How long is one side? How
long are the two sides? How many feet are there around
the walls of your schoolroom?
8. Measure a strip of the blackboard 3 yards long; 5 feet long;
15 inches long; 2 yards 1 foot long; 2 feet 10 inches long.
9. Step off or walk 5J yards.
10. How many inches in one foot? In 2 feet? In 3 feet?
TABLE
1 yard = - feet?
1 foot = inches?
11. How many feet in 36 inches? In 24 inches?
12. A blackboard 6 feet long is how many yards long?
13. A box that is 2 yards long is how many feet long?
14. A room 12 feet wide is how many yards wide?
15. 3 and 2 are 5 \
or 2 added to 3 equals 5 ( Thege ftll haye the game mea ning.
3 plus 2 equals 5 I
3 + 2 = 5
16. 3 + 4=? 6 + 2=? 4+2=? 6+1 = ? 5+2=?
8+1=? 3+5=? 5+4=? 7+2=? 4+3=?
17. Add:
6 pounds 8 dollars 6 feet 6 cents 7 yards 7 bushels
5 pounds 2 dollars j? feet 4^ cents 2_ yards 5_bushels
RATIONAL ELEMENTARY ARITHMETIC.
SURFACE MEASURE MULTIPLES.
1. Draw the line a one inch long. Draw
b, c, and d as in the figure A.
2. What kind of a figure have you made?
3. How long is a? bf c? df How long,
then, is each side of the square?
Then what kind of a square may it
be called?
4. How much space (surface) does A cover?
5. Find a surface (space) on page 4 which is equal to A.
6. On page 4, find a surface equal to two times A. What is
it marked? How long is it? How wide? What kind of
a figure is it? How many square inches are in it, or,
what is its area? Draw an oblong the same size as B.
7. Draw an oblong as long as A and B (page 4) together.
8. How long is the oblong (rectangle) you have drawn?
How wide? What is its area?
9. Find on page 4 a rectangle (oblong) the same size as the
one you have just drawn.
10 On page 4, A and C together form a rectangle how long?
How wide? What is its area?
11. Make a square equal to A and C together. What kind
of a square is it called?
12. 2 twos equal 4 \
or 2 multiplied by 2 = 4 I Thege ^ haye thft game meaning<
2 times 2 = 4 I
2X2 = 4
Which is the shortest way to make this statement?
13. 2X3=? 2X7=? 2X 9=? 2X11=? 3X 9=?
3X2=?
3X3=?
3X 6=?
4X12=?
4X 9=?
3X4=?
4X4=?
4X 6=?
4X11 = ?
3X10=?
2X6=?
2X8=?
2X10=?
2X12=?
3X11 = ?
5X2=?
3X5=?
3X 7=?
3X 8=?
3X12=?
2X4=?
4X5=?
4X 7 = ?
4X 8=?
4X 1 = ?
6 RATIONAL ELEMENTARY ARITHMETIC.
1 INCH
Yz
[ /4
1. How many inches are there in a foot?
2. Using the drawing on this page for a measure, cut a piece
of stiff paper the same width and three times as long,
for a rule.
3. Divide your rule into half inches. How many half inches
will you have on your rule?
4. Divide it into quarter inches. How many quarter inches
are there?
5. Draw a rectangle that is 5 inches long and contains 10
square inches. How wide is it?
6. Draw "a rectangle that is 3 inches long and contains 9
square inches. How wide is it? What figure is it?
7. Multiply:
2 5 7 3 6 8 4 9 12 11 10
22222222222
2
3
5
3
7
3
3
3
6
3
8
3
4
3
9
3
12
3
11
3
10
3
8. How many 2's in 4? In 2? 8? 6? 10? 12?
9. How many 3's in 6? In 12? 3? 9?
10. What is one-half of 4? Of 8? 2? 6? 10? 12? 14? 16? 18? 20?
11. What is one-third of 6? Of 12? 9? 15? 18? 21?
12. Count by 2's to 50; by 3's to 48.
13. Two is one-half of what number? One-fourth of what
number? One-third of what number?
ADDITION AND SUBTRACTION REVIEWS. 7
1. On page 2 which is the shortest line? The next in length?
What is the difference between them?
2. C is how much longer than B? D than A? F than C?
3. F and G together are how much longer than D? Than E?
4. Draw a line twice as long as E. Name it H. Mark off
a part of H equal to C on page 2. What is the length
of the rest of H?
5. Draw a line 12 inches long. Mark off 3 inches. How
many inches remain?
6. Draw a line 14 inches long. Mark off 6 inches. How
much remains?
7. Find D on page 4. If a square equal to A were taken
away, how many square inches would remain?
8. In square inches what is the difference between B and D?
E and D? E and F? D and F?
9. What is the difference between F and the whole rectangle?
10. A 3-inch square contains how many more square inches
than a 2-inch square?
11. A rectangle containing 12 square inches is how much
greater than one containing 5 square inches?
6 less 2 = 4 j These all have the same meaning.
or 2 subtracted from 6 = 4 ( which ig the shortest way to make thi ,
6 minus 2 = 4 statement?
6 2=4
12. 8-4-? 7-2-? 10-3 = ? 8-5-? 9-5-?
11-5-? 10-8-? 12-7-? 9-7=? 8-6-?
13. Subtract:
6 7 8 9 10 11 12 7 8 9
5 5 6_i_4J[_7J_3J>
4 5 6 7 8 9 10 11 12 5
2323537552
8
RATIONAL ELEMENTARY ARITHMETIC.
1. What is measured by the quart?
2. By measuring, find how many pints in a quart.
3. Two quarts equal how many pints?
4. One pint equals what part of a quart?
5. Measure and find how many gills in a pint.
6. Four pints equal how many quarts?
7. What is measured by the gallon?
8. Measure and find how many quarts in a gallon. How
many pints are there in a gallon?
9. What part of a gallon is one quart? What part of a gal-
lon are 2 quarts? 3 quarts?
1 gallon =
1 quart
1 pint =
Quarts.
Pints.
Gills.
LIQUID MEASURE USES OF FOURS 9
Answer all you can orally.
1. At 12 cents a quart, how much will a pint of oil cost?
2. How much will a gallon of milk cost at 6 cents a quart?
3. How much will a quart of cream cost at 4 cents a gill?
4. A can holds twelve quarts; how many gallons will it hold?
5. How many quarts does a three-gallon jug hold?
6. How many quarts of milk are there in sixteen pints? In
twenty pints? In twenty-four pints?
7. A boy bought two gallons of mineral water, and sold four
pints of it. How many pints had he left? How many
gallons?
8. If a gallon of molasses costs 48 cents, what will a quart
cost?
9. If a gallon of molasses costs 48 cents, what will 5 quarts
cost?
10. At 48 cents a gallon, what will 1 pint of molasses cost?
What will 3 pints cost?
11. Allen and Harold kept a lemonade stand at a picnic. At
20 cents a gallon, what did it cost them to make 2 gal-
lons of lemonade?
12. They sold 8 half-pint glasses at 5 cents a glass. How
many pints did they sell in this way? How much did
they receive for them?
13. They sold 4 pint glasses at 8 cents a glass. How much
did they receive for these?
14. They sold to 2 persons each 1 quart at 15 cents a quart.
What part of a gallon did they sell in this way? How
much did they receive for it?
15. At 20 cents a gallon, what would it cost them to make
one quart of lemonade?
16. What was the gain on the first quantity sold? The
second? The third?
17. How much did they have left?
10 RATIONAL ELEMENTARY ARITHMETIC.
1. What is sold by the bushel?
2. Find by measuring how many pecks there are in a bushel.
3. One peck equals what part of a bushel?
4. One-half of a bushel equals how many pecks? One-
fourth of a bushel equals how many pecks? Three-
fourths equal how many pecks?
5. How many pecks are there in one and one-half bushels?
6. Find by measuring how many quarts there are in one
peck.
7. Put four quarts into the peck measure. Tell what part
of the measure is filled.
8. Two quarts equal what part of a peck?
9. How many quarts are there in one and one-half pecks?
10. How many quarts fill a bushel measure?
11. One-eighth of a bushel is how many quarts?
12. One-fourth of a bushel is how many quarts?
13. Three-fourths of a bushel equals how many quarts?
Pecks. Quarts. Pints.
1 bushel = ? ? -?
Ipecl: ? -?
1 quart = ?
DRY MEASURE USES OF FOURS. 11
1. At 9 cents a quart, what will 4 quarts of strawberries cost?
2. A bushel of peaches contains how many pecks?
3. There are 2 pecks of shelled corn in a box and 8 quart?
are taken out. How many quarts are left in the bin?
How many pecks?
4. A man put in the bin a peck of oats at one time and a
half bushel at another time. How many pecks were
there then in the bin? How many quarts?
5. At 8 cents a quart, what will 4 quarts of cranberries cost?
6. If cherries cost 10 cents a quart, what will one-half of a
peck cost?
7. A boy picked one and one-half bushels of cherries. He
sold them by the peck; how many pecks did he sell?
How many dollars did he receive for them at one-half
dollar for a peck?
8. How many bags holding one bushel each would be required
to hold twenty-four pecks of corn? How many hold-
ing two bushels each would be needed?
9. At 4 cents a quart what will a peck of beans cost? What
will three-fourths of a peck cost?
10. If there are two bushels of wheat in a bin and seven
pecks are taken out, how many pecks are left? How
many quarts are left?
11. A man can dig five bushels of potatoes in one hour. How
many bushels can he dig in two hours? How many pecks?
12. If oats cost 30 cents a bushel, what will two pecks cost?
13. A can holds sixteen quarts of berries. Ten pints of ber-
ries are taken out; how many pints are left?
14. At 1 dollar a bushel, what will 1 peck of apples cost?
15. If apples are bought at a dollar a bushel and sold at 30
cents a peck, what is the gain on one peck? On one
bushel? On one and one-half bushels? On two
pecks?
12
RATIONAL ELEMENTARY ARITHMETIC.
f
1. How many squares in A? How many rows of 4 squares
each in B? In C? D? E? F? G? H? I? J? K? L?
2. A equals 4, B equals 8. What does C equal? D? E? F?
G? H? I? J? K? L?
BUILDING TABLE OF FOURS. 13
1 A equals what part of B? What part of C? Of D? E?
2. 4 is what part of 8? What part of 12? Of 16? 20?
24? 28? 32? 36? 40? 44? 48?
3. B equals how many A's? What part of D? of F? H? J?
4. 8 equals how many 4's? What part of 16? 24? 32? 40?
48?
5. C equals how many A's? What part of F? I? L?
6. 12 equals how many 4's? What part of 24? 36? 48?
7. D equals how many A's? How many B's? What part of
H? L?
8. 16 equals how many 4's? How many 8's? What part of
32? 48?
9. E equals how many A's? What part of J?
10. 20 equals how many 4's? What part of 40?
11. F equals how many A's? B's? C's? What part of L?
12. 24 equals how many 4's? 8's? 12's? What part of 48?
13. G equals how many A's? 28 equals how many 4's?
14. H equals how many A's? How many B's? How many D's?
15. 32 equals how many 4's? How many 8's? How many 16's?
16. TABLE OF FOURS.
4X1= 4 4X4=16 4X7=28 4X10=40
4X2= 8 4X5=20 4X8=32 4X11=44
4X3=12 4X6=24 4X9=36 4X12=48
17. Multiply
7 10 11 8243561
4 4 44444444
18. 8 contains 4 two times ) These all have the same meaning.
8 divided by 4 = 2 r Which is the shortest way to write this
8-^4 = 2- ) statement?
19. 12-5-4 = ? 32-4-4=? 28+4=? 44+4=? 20+4=?
14
RATIONAL ELEMENTARY ARITHMETIC.
1. What is sold by the pound?
2. One pound equals how many ounces?
3. How many ounces in half a pound? In a fourth of a
pound? In | of a pound?
4. The four-ounce weight equals what part of the pound?
5. The eight-ounce weight and the four-ounce weight to-
gether equal what part of the pound weight?
6. One and three-quarter pounds equal how many ounces?
7. Hold different objects in your hand and tell what you
think the weight of each would be. Weigh each and
compare its weight with what you thought it would be.
1 pound = ? ounces.
J pound =''- - ? ounces.
| pound = - - ? ounces.
APPLICATION OF FOURS WEIGHT. 15
William and Mary went with a camping party and kept a
small grocery store.
They bought for it the following articles:
4 pounds of sugar at 5 cents a pound.
12 pounds of white flour at 4 cents a pound.
10 pounds of Graham flour at 4 cents a pound.
1 pound of tea at 60 cents a pound.
1 pound of coffee at 40 cents a pound.
4 pounds of crackers at 9 cents a pound.
1 pound of cinnamon at 40 cents a pound.
1 pound of black pepper at 32 cents a pound.
12 bars of soap at 4 cents a bar.
1. How much did it cost them to buy all the sugar? The
flour? The Graham flour? The crackers? The soap?
2. They sold the sugar in half-pound packages, charging
3 cents for each package. How much did they receive
for all the sugar? How much did they gain on the sugar?
3. They sold the white flour in lots of 4 pounds each, at
5 cents a pound. How many lots of flour did they sell?
How much did they receive for it? How much did
they gain on it?
4. They sold the Graham flour at 4 cents a pound. How much
did they receive for it? How much did they gain on it?
5 They sold the tea in quarter-pound packages at 20 cents
a package. How much did they receive for it? How
much did they gain on it?
6. The cinnamon was sold in 4-ounce packages, at 12 cents
a package. How much was that for each ounce? How
many packages were there? How much money was
received for all the cinnamon? What was the gain on
one pound?
7. The pepper was sold at 2 cents an ounce. Did they lose
or gain on it and how much?
16
RATIONAL ELEMENTARY ARITHMETIC.
5 nickels
5 cents or 5?
5 dimes
4 quarters
1 dollar or $1
2 half-dollars
Answer all you can orally.
1. How many cents equal a nickel?
2. How many nickels equal a dime? How many cents equal
a dime?
3. How many nickels equal a quarter? How many cents
equal a quarter?
4. How many quarters equal a half-dollar? How many
dimes equal a half-dollar? How many nickels equal
a half-dollar?
5. Which would you rather have, one dollar or 2 half-dollars?
One dollar or 4 quarters? One dollar or ten dimes?
6. What two pieces of money equal a dime?
7. What three pieces of money equal a quarter?
8. What two pieces of money equal seventy-five cents?
What three pieces?
9. What two pieces of money equal a dollar? What three
pieces? What four pieces?
10. To how many quarters are two dollars equal? Four
dollars? Five and one-half dollars?
11. In the shorter way, write: 7 dollars; 9 dollars; 10 dollars;
12 dollars; 19 dollars; 20 dollars; 25 dollars; 5 dollars;
16 dollars; 1 dollar; 4 dollars.
UNITED STATES MONEY AND FIVES. 17
1. A boy bought a top for 25 cents, and paid for it in nickels.
How many nickels did he spend for it?
2. A book worth 30 cents is bought with a half-dollar. How
many dimes are needed to make the correct change?
3. A package of flower seed costs 10 cents. How many
quarters will pay for five packages? How many
dimes?
4. How many 5-cent car fares can be paid with a quarter?
With 15 cents?
5. Harry has 5 dimes in his bank ; John has 1 quarter and 2
dimes in his. Which has the more money? How
much?
6. At 10 cents each, how many balls can be bought for a
quarter, a dime, and a nickel together?
7. A pound of candy costs 50 cents. How much can be
bought for $1? For 25 cents? For 75 cents? For
10 cents?
8. How many 50-cent pieces will pay for a chair that costs
$5? For one that costs $6?
9. A sled costs $1J. How many 25-cent pieces, or quarters,
will be required to pay for it?
10. Joe bought a book for 30 cents, paper for 25 cents, and
two pencils at 10 cents each. How much did he pay
for all? What two pieces of money would pay for
them? What four pieces?
11. If a gill of cream costs a nickel, how many dimes will pay
for a quart?
12. If three dimes pay for a bushel of oats, how many nickels
will pay for two pecks?
13. If one pound of seed costs a dollar, what part of a dollar
will pay for four ounces?
14. If a box of blacking costs a dime, how many boxes can
you buy for 60 cents?
18 RATIONAL ELEMENTAL ARITHMETIC.
1. Name the days of the week.
2. How many days are there in one week? In two weeks i
In three weeks? In four weeks?
3. What part of the week is one day? Two days?
4. How many school days are there in one week? In three
weeks? In five weeks?
5. How many days of the week are not school days?
6. How many days of the week are called working days?
7. How many more working days than school days in five
weeks?
8. How many days are not working days in five weeks?
9. How many weeks are there in a month?
10. One week is what part of a month? Two weeks are what
part? Three weeks are what part?
11. Name the months of the year, beginning with January.
12. How many months are there in the year?
13. What part of the year is one month? Three months?
Six months?
14. The winter months are what part? The spring months?
The summer months? The autumn months?
15. From 7 o'clock one morning to 7 the next morning is
how many hours?
16. What is this number of hours called?
17. From one noon to the next noon is how many hours?
18. A girl walked from half past eleven until half past
twelve. How many hours did she walk?
19. Alice stayed at her grandmother's from 10 o'clock Tuesday
morning to 11 o'clock Wednesday morning. How
many days was that? How many hours over?
20. If you have breakfast at 6 in the morning and dinner at
6 in the evening, how many hours between breakfast
and dinner?
21. How many hours from a 7 o'clock breakfast to a luncheon
at 1 in the afternoon?
USES OF FIVES TIME.
19
1. Draw the face of a
watch, and fasten to
the center two mov-
able hands.
2. Show how far the min-
ute hand moves in
an hour. Show how
far the hour hand
moves in an hour.
3. How many minutes are
there in an hour?
4. How many minutes
are there in half an
hour? How many in one-fourth, or one-quarter, of
an hour?
5. Show where the hands are at one o'clock.
6. Show where the hands are at thirty minutes after one, or
half past one.
7. Show where the hands are at fifteen minutes after one, or
quarter past one.
8. Move the hands to show the time of the opening of school
in the morning; the beginning of recess; the closing of
school at noon; the opening and closing of school in the
afternoon.
9. If recess lasts fifteen minutes, what part of an hour does
it last?
10. If a man works eight hours a day, what part of a day
does he work?
11. George went to school eight months one year. W-hat
part of the year did he attend? . .. .
12. Stephen spent 3 months in Iowa, 3 months in Missouri,
and 3 months in Arkansas. What part of a year did
he spend in each state? In the 3 states?
20
RATIONAL ELEMENTARY ARITHMETIC.
mmmma
1. How many squares in A?
2. A equals 5. How many 5's in B? How many in C? In
D? E? F? G? H? I? J? K? L?
3. A equals 5, B equals 10. To what is C equal? D? E?
F? G? H? I? J? K? L?
BUILDING TABLE OF FIVES. 21
1. A equals what part of B? What part of C? Of D? E?
F? G? H? I? J? K? L?
2. 5 equals what part of 10? What part of 15? Of 20? 25?
30? 35? 40? 45? 50? 55? 60?
3. B equals how many A's? What part of D? F? H? J? L?
4. 10 equals how many 5's? 10 is what part of 20? 30?
40? 50? 60?
5. C equals how many A's? C is what part of F? I? L?
6. 15 equals how many 5's? What part of 30? 45? 60?
7. D equals how many A's? How many B's? What part
of H? L?
8. 20 equals how many 5's? How many 10's? What part of
40? 60?
9. E equals how many A's? What part of J?
10. 25 equals how many 5's? What part of 50?
11. F equals how many A's? How many B's? How many
C's? What part of L?
12. 30 equals how many 5's? How many 10's? What part of 60?
13. G equals how many A's?
14. How many D's equal H?
15. A and B together are what part of F?
5X10=50
5X11=55
5X12=60
10 12 11
A J? J
17. What is one-fifth of 5? Of 15? 10? 20? 25? 40?
18. Divide each of the following numbers by 5: 10; 20;
30; 40; 50; 60; 5; 15; 25; 35; 45; 55.
TABLE
OF
FIVES.
5X1= 5
5X2=10
5X3=15
5X4=20
5X5=25
5X6=30
5X7=35
5X8=40
5X9=45
16.
Multiply :
356
555
812
555
7
5
9 4
5 5
22 RATIONAL ELEMENTARY ARITHMETIC.
1. A train leaves one station at ten minutes after twelve,
and arrives at the next at half past twelve; how many
minutes does it take to go from one station to the other?
What part of an hour?
2. A man closes his store and starts for home at six o'clock.
He walks home in a quarter of an hour. What time is
it when he arrives?
3. A man begins work at eight o'clock, and stops at half
past five. How many hours a day does he work if he
stops an hour at noon?
4. Mary is six years old and Jennie is six and three-fourths
years old. How many months older is Jennie than
Mary?
5. School begins at nine o'clock and closes at half past three.
How many hours are there between the opening and
the closing? An hour and a half are allowed at noon,
and half an hour for recesses; how many hours are the
pupils in school during one day?
6. A farmer owned eighteen horses. He sold six; how many
had he left? What part of 18 had he left?
7. A man mailed nine letters at one time and six at another.
How many did he mail altogether?
8. From a bunch of eighteen bananas, nine bananas were
sold. How many remained on the bunch?
9 There were twenty sheep in one pen, and ten in another.
How many in both? If five were taken out of each
pen, how many remained in the pens?
10. A boy paid a dime for a bat, and a nickel for a ball. How
many cents did he pay for both?
11. A play began at 2 in the afternoon and lasted until 15
minutes after 5. How many hours and what part
of an hour was that?
12. A concert two hours long was how many minutes long?
APPLICATION OF FIVES. 23
1. How long a string will reach around the frame of a slate
that is eight inches long and five inches wide?
2. A box five inches high is twice as wide as it is high. How
wide is it? Its length equals the sum of its width and
height. How long is it?
3. By cleaning walks, Edwin earned a quarter on Monday,
a dime on Tuesday, and a nickel on Wednesday. How
much did he earn in the three days?
4. One jar holds five pints, another holds seven pints. How
many pints do both hold? How many quarts?
5. A ship leaves one port at noon on Monday and arrives
at her next port at noon on Saturday. How many
days was she on the way?
6. In a class of twenty pupils there were five more girls than
there were boys. How many girls were there in the
class? How many boys?
7. A car goes five miles an hour. How many hours will it
take to go ten miles? Twenty miles? Fifteen miles?
Twenty-five miles?
8. Fifteen acres of land are divided into three equal fields.
How many acres are there in each field?
9. When it is a quarter past nine o'clock, how many min-
utes past nine is it?
10. How many pints of oil are there in a can holding fifteen
quarts?
11. A table is four feet long and three feet wide. A leaf
one foot long and as wide as the table can be put in.
How many square feet does the table then contain?
12. A piece of sidewalk seven feet long contains thirty-five
square feet. How wide is it?
13. Henry bought 10 newspapers for 15 cents and sold them
at 3 cents each. How much money did he gain? At
1 cent each, how many papers could he buy with it?
24 RATIONAL ELEMENTARY ARITHMETIC.
1. If a peck of beans costs 40 cents, what will one quart
cost?
2. How many four-quart pails can be filled from seventeen
quarts of milk? How many quarts will be left?
3. A man started for town at ten minutes to nine, and ar-
rived at twenty minutes after nine. How many min-
utes was he on the way? What part of an hour was
he on the way?
4. A garden six yards long is one-half as wide as it is long.
How many yards of fence are needed to inclose it?
5. A grocer bought one tub of butter containing ten pounds,
and another containing five pounds. How many
pounds did he buy? How many jars holding five
pounds each could he fill with the butter?
6. How many dollars are equal to three five-dollar bills? Four
five-dollar bills? Five ten-dollar bills?
7. When 16 cents is paid for twelve eggs, how many cents
must be paid for six eggs?
8. There are twenty days of school in a month. Louis was
absent five days. What part of the school month was
he absent?
9. How many pairs of shoes at $2 a pair can be bought for
$15? How much money will be left?
10. The rent of one house is $30 a month; the rent of
another is one-half as much. What is the rent of the
second house? Of both houses?
11. A signboard contains thirty-six square feet. If the sign-
board is six feet high, how wide is it? If it is nine
feet wide, how high is it?
12. An automobile made a trip at the rate of a mile in
3 minutes. The trip was made in an hour. How
many miles were covered? How far did it run ill I
REVIEW PROBLEMS. 25
1. From a jug holding one gallon of syrup, one quart and
one pint are taken. How much syrup is left in the jug?
2. How many bags holding six pecks each will be required
to hold six bushels of corn?
3. A train leaves one station at fifteen minutes after one
and arrives at the next station half an hour later. At
what time does it reach the second station?
4. What is the weight of three packages, two of which weigh
ten ounces each, and one, five ounces?
5. A rectangular lot containing sixty square yards, is
twelve yards long. How wide is it?
6. If one pound of coffee costs 32 cents, what will four ounces
cost?
7. A boy left home at eight o'clock in the morning and re-
turned at noon. How many hours was he away?
What part of the day was he away?
8. If a rope was cut into four equal parts, and each part was
three feet long, what was the length of the entire rope?
9. In a basket of fruit there are two dozen pears. If half a
dozen are taken out, how many will be left?
10. The glass in a picture frame is two feet wide and three
feet long. How many square feet are there in its sur-
face?
11. A clock is fifteen minutes fast. What is the correct time
when the clock says half past three?
12. With what three pieces bf money can five 3-cent car fares
be paid?
13. If one peck of potatoes costs 25 cents, what will three
pecks cost? Four pecks?
14. There were 12 pages in each chapter and 2 chapters in
each part of a book having 2 parts. How many pages
were in the book? How many pages were in each
part?
26
RATIONAL ELEMENTARY ARITHMETIC.
EXERCISES ON Twos AND THREES
Read each line across the page throughout the table,
read each column from the top downward.
2X4 or 4X2=?
2X3 or 3X2=?
2X2=?
2x5or5x2=?
2X8 or 8X2=?
2X6 or 6X2 = ?
2X9 or 9X2=
2X7 or 7X2=?
2X11 or 11X2=?
2X10 or 10X2=?
2X12 or 12X2=?
2X1 or 1X2=?
3X2 or 2X3=?
3X4 or 4X3=
3X6 or 6X3=?
3X8 or 8X3=?
3X10 or 10X3=?
3X12 or 12X3=
3X3=?
3X5 or 5X3=?
3X7 or 7X3=?
3X9 or 9X3=?
3X11 or 11X3=?
3XJ or JX3=?
Then
9
i
of
8
or
8-2 = ?
1
of 8 or 8-4=?
?
i
of
6
or
6-2=?
of 6 or 6-3=?
i
of
4
or
4-2=?
?
i
of
10
or
10-2=?
i
of 10 or 10-5=?
9
i
of
16
or
16-2=?
1
of 16 or 16-8=?
?
J
of
12
or
12-2=?
i
of 12 or 12-6=?
?
1
of
18
or
18-2=?
i
of 18 or 18-9=?
9
i
of
14
or
14-2=?
4
of 14 or 14-7=?
k rt
i
of
22
or
22-2=?
T Vof22or22-ll=?
5= 9
i
of
20
or
20-2=?
T V of 20 or 20- 10=
9
5= ?
i
of
24
or
24-2=?
f of 24 or 24- 12 =
9
9
of
2
or
2-2=?
:?
i
of
6
or
6-3=?
i
of 6 or 6-2=?
?
i
of
12
or
12-3=?
i
of 12 or 12-4=?
9
|
of
18
or
18-3=?
i
of 18 or 18-6=?
:9
J
of
24
or
24-3=?
i
of 24 or 24-8=?
5=?
i
of
30
or
30-3=?
T V of 30 or 30- 10 = ?
5=?
i
of
36
or
36-3=?
A of 36 or 36- 12=?
4
of
9
or
9-3=?
:?
,>
of
15
or
15-3 = ?
i
of 15 or 15-5 = ?
:?
J
of
21
or
21-3 = ?
i
T
of 21 or 21-7=?
= ?
}
of
27
or
27-3 = ?
^
of 27 or 27-9=?
3=?
Jof
33
or
33-3-?
1
1
I r of33or33+ll =
?
= ?
i
of
3
or
3+3=?
EXERCISES FOR PRACTICE
27
EXERCISES ON FOURS AND FIVES
Read each line across the page throughout the table. Then
read each column from the top downward.
4X3 or 3X4=?
4X9 or 9X4=?
4X5 or 5X4=?
4X4=?
4X2 or 2X4=?
4X6 or 6X4=?
4X8 or 8X4=?
4X12 or 12X4=?
4X7 or 7X4=?
4X11 or 11X4=?
4X10 or 10X4=?
4X1 or 1X4 = ?
5X6 or 6X5=?
5X10 or 10X5=?
5X7 or 7X5=?
5X11 or 11X5 = ?
5x2or2x5=?
5X12 or 12X5=?
5X8 or 8X5=?
5X3 or 3X5=?
5X5 = ?
5X4 or 4X5=?
5X9 or 9X5=?
jXl or 1X5=?
iof 12 or 12-4=? J of 12 or 12-3=?
iof 36 or 36-4=? i of 36 or 36-9=?
iof 20 or 20-4=? i of 20 or 20-5=?
iof 16 or 16-4=?
iof 8 or 8-4=? iof 8 or 8-2=? *
iof 24 or 24-4=? J of 24 or 24-6=?
iof 32 or 32-4=? J of 32 or 32-8=?
J of 48 or 48-4=? T V of 48 or 48- 12=?
iof 28 or 28-4=? $ of 28 or 28-7 = ?
iof 44 or 44-4=? A of 44 or 44- 11 = ?
iof 40 or 40-4=? A of 40 or 40- 10=?
iof 4 or 4-4=?
iof 30
i of 50
iof 35
iof 55
iof 10
i of 60
i of 40
iof 15
-I of 25
I of 20
iof 45
of 5
or 30-5
or 50-5
or 35-5
or 555
or 10-5
or 60-5
or 40-5
or 15-5
or 25-5
or 20-5
or 45-5
or 55
= ? iof 30 or 30-6=?
= ? T V of 50 or 50- 10=?
= ? iof 35 or 35-7=?
T V of 55 or 55- 11 = ?
iof 10 or 10-2=?
T V of 60 or 60- 12=?
Jof 40 or 40-8=?
Jof 15 or 15-3=?
= ? iof 20 or 20-4=?
= ? iof 45 or 45-^9=?
28 RATIONAL ELEMENTARY ARITHMETIC.
1. 25 A tablet cost 25 cents and a reader fifty cents. Find
50 the cost of both.
How many dimes and cents in 75 cents?
2. 25 I sold a peck of apples for 25 cents and a cake for
23 23 cents. How much did I receive for them?
How many dimes and cents in 48 cents?
3. 26 What is the cost of a dozen eggs at 26 cents and one
3 pound of flour at 3 cents?
How many dimes and how many cents in 29 cents?
4 4. 6 What must I pay for a tablet at 6 cents and a pencil
5 at 5 cents?
Eleven cents equals how many dimes and how many
cents?
5. 26 What is the cost of a pound of butter at 26 cents
15 and a peck of apples at 15 cents?
Twenty-six cents equals how many dimes and how
many cents? 15 cents equals how many dimes
and how many cents? 26 cents + 15 cents?
6. 26 = how many tens and how many ones?
15 = how many tens and how many ones?
26 + 15 = how many tens plus how many ones?
7. Write in figures and add:
1 ten + 1 = ? 1 ten + 6 = ? 1 ten + 8 = ?
1 ten + 9 = ? 1 ten + 7 = ? 1 ten + 3 = ?
8. Read the following numbers as ones, and as tens + ones:
21, 32, 44, 56, 27, 49, 45, 64, 73, 75, 78, 87, 89, and 91.
9. Add:
16 inches 18 cents 13 pounds 16 bushels 20 gallons
12 inches 11 cents 14 pounds 13 bushels 16 gallons
20 22 21 56 58 51 64 67
13 11 18 42 31 27 54 91
ADDITION. 29
1. John's bowstring was 19 inches long and William's was
2 inches longer than John's. How long was William's
bowstring?
2. Mary sewed a seam 13 inches long and Kate sewed a seam
18 inches longer than the one Mary sewed. How long
was Kate's seam?
3. Adam made a bench 18 inches long for the porch, and
George made a bench 29 inches long. How long were
the two benches together?
4. Add:
18 14 18 16 17 .16 IS 19 15 13 19
13 17 15 IS 17 17 14 19 19 17 12
5. How many 10's arc there in the answer in each problem
just given? How many 10's are there in the 10's column
of the numbers to be added? Why are there 3 tens in
the answers and only 2 tens in the 10's columns?
6. Add:
14 18 17 16 13 14 15 12 16 18 14
17 16 17 17 19 14 19 18 16 11 17
15 14 15 12 15 17 15 19 16 15 11
7. In each case in problem 6, how many 10's are there in
the answer? Why are there four 10's in the answer
arid only three 10's in the 10's column of the numbers
to be added?
8. Add:
12 14 16 12 18 14 15 14 18 17 17
13 15 18 17 19 15 18 17 18 16 17
9. In each case in problem 8, read the answer as ones and as
tens and ones.
30 RATIONAL ELEMENTARY ARITHMETIC.
1. A lady paid 47 cents for some velvet, 15 cents for straw-
braid, and 34 cents for lace. How much did she pay
for all?
2. There are three mother hens in a barnyard and each has
a brood of little chickens. One has 15, another 14,
and the third 13. How many little chickens are there
altogether?
3. What is the cost of a pound of butter at 28 cents, a dozen
eggs at 16 cents, and a dozen oranges at 35 cents?
4. What is the cost of a box of writing-paper at 35 cents, a
story book at 47 cents and a paper knife at 29 cents?
5. Add from the bottom and from the top:
24 26 27 28 29 29 45 77
13 39 29 38 38 59 15 19
25 17 28 48 27 19 59 19
84 32 76 82 7 96 24 25
19 17 19 9 29 9 59 38
9 58 19 19 79 8 18 49
6. James earned $46; Herman earned $29 and Adam earned
$18. How many dollars did the three together earn?
7. On the first shelf of a bookcase were 58 books, on the
second shelf 27 books and on the third shelf 26 books.
How many books were on the three shelves?
8. In a jeweler's window there were 3 cases of rings. In the
first case there were 27, in the second 59, and in the
third 18. How many rings were in the three cases?
9. Charlie rode on his wheel 24 miles one day, 22 the second
day, and 25 the third. How far did he ride in all?
10. Alice rode her pony 38 miles one week, 36 another week,
and 34 another. How far did she ride in all?
ADDITION. 31
1. A boy had 289 stamps. He bought 195 more and his
father gave him 48. How many stamps had he then?
What is the sum of the ones?
289 How many tens does it contain? (Write
195 the ones.)
48 To what column must the tens be added?
What is the sum of all the tens?
How many hundreds does it contain? (Write the
tens.)
What is the sum of all the hundreds? (Write it.)
2. A miller sold 247 barrels of flour to one man, 256 to
another, and 323 to another. How many barrels of
flour did he sell to all?
3. A newsboy sold 209 papers on Monday, 187 on Tuesday,
193 on Wednesday, 197 on Thursday, 178 on Friday,
and 227 on Saturday. How many did he sell during
the week?
4. Add both upward and downward:
143 354 145 252 178 627 147 397
342 435 514 145 296 192 296 256
235 143 152 243 342 184 499 719
5. A farmer owned 144 sheep, 279 horses, and 298 cows.
How many head of stock did he own?
6. An automobile made a run of 178 miles one day, 164 miles
the next day, and 159 miles the third day. How many
miles were. made in the three days?
7. On three different days a store made sales amounting to
these sums: $175, $186, and $197. What was the sum
of the sales of these three days?
8. Find the entire weight of 4 boxes of freight, weighing:
199 pounds, 134 pounds, 152 pounds, and 181 pounds.
32 RATIONAL ELEMENTARY ARITHMETIC.
1. A farmer kept fifteen sheep in one field, twenty-four in
another, thirty-one in another, and forty-three in an-
other. How many sheep did he have in all the fields?
2. George earned $53 in the winter, $43 in the spring, $25
in the summer, and $34 in the fall. How many dollars
did he earn in the whole year?
3. A girl paid 35 cents for a book, 15 cents for paper, 3 cents
for a ruler, and 23 cents for a box of paints. How much
did she pay for all?
4. A man traveled one hundred thirty-five miles the first
week, two hundred fifty-four miles the second week,
and five hundred forty-one miles the third week. How
far did he travel in the three weeks?
5. I paid $135 for a horse, $154 for a carriage, and $23 for
harness. How much did the horse and carriage cost?
How much did they all cost me?
6. How long a line will it take to go around a house that is
thirty-six feet long and twenty-eight feet wide?
7. George borrowed $31 from his father and paid back $16.
If he saved $3 a week, how many weeks would it take
him to save enough to pay the rest of the debt?
8. Arthur earns $12 in one month and William $10. If
their father earns as much as both of them, how much
does he earn? How much do the three earn?
9. Mr. Stone bought a lot for $354, filled it in at a cost of
$125, and built a fence around it at a cost of $70.
What did the whole cost?
10. In going a journey a man drove 29 miles west, 30 miles
north, 46 miles west again, and 28 miles north. How
long was the journey?
11. The repairs on an automobile cost $14 at one time, $25
at another, $27 at another time, and $52 at another.
How much money was paid for repairs?
SUBTRACTION. 33
1. A boy borrowed $78 from his father and paid back $54.
How much did he still owe?
2. Clara read 42 pages of her book containing 96 pages.
How many pages remained to be read?
3. A girl saved 68 cents (from her allowance of one dollar)
and spent 32 cents. How much more did she save
than she spent?
4. From 78 gallons 89 pounds 97 feet 67 dollars
take 43 " 35 " J>3 " J3 "
5. From 43 54 67 89 354 597 728
takeJJ. 21 34 45 142 423 415
6. From 22 24 28 25 32 43
take JL6 18 19 17 26 38
7. John had 92 cents and gave 38 cents to Albert. How
much had he left?
92 cents ^ 2 cents equals how many dimes and how
38 cents man y cents?
54 cents ^ an ^ ou ta ^ e e *& nt cents from two cents?
If one dime is changed into cents, can you
then take 38 cents from 92 cents?
8. John had 92 marbles and gave away 38 marbles. How
many had he left?
9. From 31 65 42 72 40 53 47 61
take!7 48 24 57 27 27 18 19
10. From 71 94 81 91 84 62 73 82
take 13 45 54 45 25 33 15 56
11. From a spool of thread containing 50 yards, 27 yards
were used. How many yards were left?
34 RATIONAL ELEMENTARY ARITHMETIC.
1. Read each number in the following problems, first as
dimes and cents, then as tens and ones.
From 75 64 83 96 82 97 88 60
take 37^!7755492931
2. Subtract:
41 32 84 71 35 94 43 87 98
191469381667295879
3. Grace bought 37 marbles and gave 19 of them to
Madge. How many had she left?
4. Marion read 25 pages of her book, which had in it
41 pages. How many pages had she yet to read?
5. Elizabeth had 72 cents, 48 of which she earned. The rest
was given to her. How much was given to her?
6. Ethel made 64 fudges and ate 27 of them. How many
were left?
7. John earned 27 cents toward paying for a clock which
will cost 65 cents. How much had he yet to earn?
8. Alice bought 20 ounces of lemon candy and gave away
13 one-ounce packages. How many ounces had she left?
9. Paul planted 58 tomato plants and all but 19 came up.
How many came up?
10. Subtract:
88 76 87 75 86 74 85 73 84 72
29374937583946485934
68 91 82 73 64 95 86 77 67 90
59594939586969485975
11. 27 - 18 = ? 35 - 29 = ? 48 - 29 = ? 34 - 18 = ?
37 _ 19 = ? 42 - 14 - ? 75 - 69 = ? 96 - 58 - ?
SUBTRACTION. 35
1. 48 pounds of flour were taken from a barrel holding 192
pounds. How many pounds remained?
From 192 pounds Add the answer and che lower num-
take 48 " ber (48 pounds). To what other
number is this sum equal?
2. John had $6.22 and he gave $2.55 to Henry. How much
had he left?
$6.22 Can you take 5# from 2^? What, then, must
2.55 you do?
$3.57 How many dimes are left in the dimes'
place in the upper number?
Can you take 5 dimes from one dime? What, then, must
you do?
What remains in the dollars' place of the upper number?
3. Mr. White had 622 books and he sold 255 of them. How
many had he left?
4. From 311 722 416 328 632 345
take 123 499 298 199 594 156
5. A man earned $222 and spent $198 for a horse. How
much money had he left?
6. A farmer sold a lot for $360, which was $171 more than it
cost. What was the cost of the lot?
7. It requires 280 feet of molding for the second story and
192 feet for the third story. How much more is re-
quired for the second than for the third story?
8. Clara's purse contains $3.63. If she spends $2.76 for
books, how much money will there be left?
9. A farmer having 262 sheep, sold 178. How many had he
left? Test.
10. James was flying his kite with 300 feet of string. The
string broke, leaving 234 feet in his hands. How many
feet of string went with the kite? Test.
36 RATIONAL ELEMENTARY ARITHMETIC.
1. Mr. White bought a horse for $175 and sold him for $210.
How much did he gain?
2. It cost Mr. Black $135 to put a new roof on his stable.
He paid all but $39 of this sum. How much did
he pay?
3. A druggist bought 250 boxes of soap. He sold 168 boxes.
How many were left unsold?
4. A man traveled 176 miles of a journey of 360 miles. How
far had he then to travel?
5. A woman owed $275 for a piano. After paying $187,
how much did she still owe?
6. Subtract:
280 311 702 863 524 605 237 800
178 126 345 679 235 517 148 716
790
800
310
671
822
443
924
295
637
518
129
218
213
159
647
167
818
507
686
400
825
727
690
800
729
318
428
217
636
419
528
311
7. John earned $525 a year and his expenses were $347.
How much did he save?
8. A fire was lighted in an old grate and 310 chimney
swallows fell down, blinded by the smoke. When they
were taken to the air 128 of them were able to fly
away, but the rest died. How many died?
9. From a crib containing 213 bushels of corn 136 bushels
were used. How many bushels were left in the
crib?
10. Four hundred fifteen copies of a first reader were bought
by a book store, but only three hundred forty-six
copies were sold. How many were still on hand?
MULTIPLICATION. 37
1. What is the cost of 2 dozen eggs at 23 cents a dozen?
Add 23 Multiply 23 2 times 3 cents =?
^3 by _2 2 times 2 dimes=?
46 46
2. Find the cost of 3 pounds of butter at 22 cents a pound.
3. James has 21 marbles. Henry has 4 times as many.
How many has Henry?
4. Multiply:
34 23 44 32 31 42 62 73
5. How much will 3 yards of cloth cost at 58 cents a yard?
Add 58 Multiply 58 3 times 8 cents equals how many
58 by 3 dimes and how many cents?
^58 3 times 5 dimes equals how
many dimes?
What is the sum of all the dimes?
3 times 58 cents = ?
6. How many pounds of flour in 3 sacks of 58 pounds each?
7. If one-fourth of a barrel of flour weighs 49 pounds, what
does a whole barrel weigh?
8. Multiply:
36 28 57 38 76 41 45 79
_2J*_2_4_3_5_4_2
9. How many ounces in 3 pounds? 4 pounds?
10. At 36 cents a peck, what is the cost of a bushel of
apples?
11. How many feet of fence will it take to inclose a square
lot, one of whose sides is 125 feet long?
12. Four wire ropes, each 243 feet long, are used to hold a
large chimney in place. How many feet of *ope are
used in all?
38 RATIONAL ELEMENTARY ARITHMETIC.
4
1. A gardener set out four rows of trees, putting eighty- two
trees in each row. How many trees did he set out?
2. If a person pays $4 a week for board, how much will
he pay in a year, or fifty- two weeks?
3. There are twenty-four sheets of paper in a quire. How
many sheets are there in five quires?
4. How many bushels of wheat are there in ninety-six bags,
if each bag contains two bushels?
5. What will three pianos cost at $285 each?
6. A family uses thirty-eight quarts of milk in a month.
How much will the milk bill amount to for a month
at 5 cents a quart?
7. Multiply:
325 438 147 235 268 470 138 167 295
325432542
179 489 249 304 169 230 294 157 109
__3_2 _4 _3 _5 _4 _3 _5 _4
8. There are one hundred ninety-six pounds of flour in a
barrel. How many pounds in four barrels?
9. Mr. Gates sold his horse for $87. I sold mine for three
times as much. How much did I receive for my horse?
10. If Mr. Field pays $36 for one month's rent, what will his
rent be for five months?
11. One hundred ninety-six loaves of bread can be made from
a barrel of flour. How many loaves can be made from
five barrels of flour?
12. Dr. Allen pays $75 a year for his telephone. What will it
cost him for four years?
13. At 5 cents each, what will 2 dozen crayon pencils cost?
What will 28 such pencils cost?
14. How many school days in 14 weeks?
MULTIPLICATION. 39
1. Mr. Jones gave each of his 3 children $2.65 to spend for
Christmas. How much did he give them altogether?
2. A boy owned 3 kites, each of them having 155 feet of
string. How much string had the three together?
3. Nellie had four brothers. She bought for each of them
a pair of gloves costing $1.19. How much did they all
cost her?
4. Harry gave a dinner to 4 of his friends. It cost him $1.90
for each person. What was the whole expense of the
dinner?
5. Susan and two of her friends each made 144 chocolate
creams for a party. How many did they all make?
6. Multiply:
248 327 299 185 619 298
_2 _3 _4 5 _2 _3
158 317 192 261 458
34542
196 184 219 313 471
45432
7. A candy store keeper bought 4 barrels of mixed candy,
each weighing 295 pounds. How many pounds did he
buy in all?
8. Herman made a collection of United States stamps, one
of German stamps and a third of mixed stamps. There
were 249 stamps in each collection. How many stamps
had he altogether?
9. Amelia and her three sisters each had 193 buttons on her
button string. How many buttons had they altogether?
10. A baker made 156 ginger cookies on each of the first
five days of the week. How many did he make in all?
40 RATIONAL ELEMENTARY ARITHMETIC.
1. Two boys bought the following to complete their camping
outfit: 2 blankets at 750 each; a frying-pan, a large
pail, and a coffee-pot, each costing 270; 6 yards of
mosquito-netting, at 50 a yard; and 2 large boxes, at
350 each. Find the cost of the blankets; the cooking-
dishes; the netting; the boxes. How much did they
pay for all?
2. Alice and Jane gave a party for which they bought the
following: 5 pounds of candy at 380 a pound; 4 pounds
of mixed nuts at 180 a pound; 3 quarts of ice-cream at
400 a quart; 2 cakes at 500 each. Find the cost of
the candy; the nuts; the ice-cream; the cakes; the
whole cost.
3. John made for his sister a play house out of 4 large store
boxes, each costing 150. They bought for the house
5 yards of curtain calico, at 30 a yard, 3 doll chairs, at
130 each, and a small table at 250. Find the cost of
the boxes; the calico; the chairs. How much did they
spend in all?
4. Alice set 4 hens, giving 13 eggs to each hen. How many
eggs did she give the 4 hens?
5. Amanda counted the -eggs for her father to take to market.
There were 5 baskets, each containing 144 eggs. How
.many eggs were there in all?
6. Henry carried papers 178 days each year for 3 years.
How many days did he carry papers in the 3 years?
At 20 each, how much did he receive for the papers?
7. John bought for his garden 159 tomato plants and the
-same number each of cabbage and celery plants.
How many plants did he buy in all?
8. Herman bought 184 pigeons one year and the next year
he sold 3 times as many. How many pigeons did he
sell?
DIVISION. 41
1. Mr. Blake divided 82 cents equally between his son and
daughter. How much had each child?
Read 82 as dimes and cents.
2)2 One-half of 8 dimes equals how many dimes?
One-half of two cents equals how many cents?
One-half of 82 cents equals how many cents?
2. Fred had 82 stamps and he gave half of them to William.
How many had each then?
3. Find:
4
of
24
2)24
4
of
28
2)28
4
of
60
2)60
4
of
36
3)36
4
of
63
3)63
4
of
39
3)39
i
of
66
3)66
4
of 93
3)93
4
of
96
3)96
i
of
48
4)48
i
of
84
4)84
i
of
44
4)44
i
of
80
4)80
i
of
88
4)88
t
of
120
4)120
i of 55 5)55 i of 50 5)50 i of 155 5)155
4. 5)155 When you divide the 15 by 5 in this problem
where do you write the 3? Why? Where do
you write the 1? Why?
5. 2)124 2)102 3)156 3)129 4)168 4)204
6. Julia divided 126 shells into 3 equal piles. How many
were there in each pile?
7. Elizabeth divided 183 pictures with her 2 sisters, keeping the
same number she gave to each. How many did she keep?
8. Four boys sold 164 newspapers, each selling the same num-
ber. How many did each sell?
9. Max distributed 106 hand bills, an equal number on each
of 2 streets. How many did he leave on each street?
42 RATIONAL ELEMENTARY ARITHMETIC.
1. Mrs. Smith divided 32 cents equally between her two little
girls. How much did each receive?
^ of 3 tens equals how many tens and
2)32=20+12=32 how many over?
10+ 6=16 One ten + 2 ones equals how many
ones? -| of 12 ones = ?
\ of 32 or 32 divided by 2 = ?
2. 2)54 2)38 2)56 2)34 2)36 2)58
3. How many 2's, and how many ones over, in 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 18, and 19?
4. How many 3's, and how many ones over, in 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, and 23?
5. How many 4's, and how many ones over, in 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, and 36?
6. How many 5's, and how many ones over, in 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39?
7. Seventy-five apples are separated into 3 equal piles. How
many are there in each pile?
How many 3's in 7? How many over?
What is this 1? How many ones equal
1 ten and 5 ones? How many 3's in
15? How many 3's in 75?
8. There are 54 books in a case of 3 shelves, the same number
on each shelf. How many are there on each shelf?
9. 3)48 3)78 3)81 3)84 3)243 3)144
4)96 4)84 4)72 4)64 4)184 4)364
DIVISION. 43
1. A boat makes a trip of 840 miles in 5 days, going the same
distance daily. How many miles does it run in one day?
2. A dealer bought five bicycles for $225. What was the
cost cf cne bicycle?
3. In going to school and returning home, Henry has to
walk nine hundred seventy-eight yards. How far does
he live from the schoolhouse?
4. A gardener has eight hundred twenty-eight pounds of
seed, which he puts into four-pound sacks. How many
sacks will be required?
Divisor or number ) _.
.... . r 2)800 Dividend or number to be divided,
to divide by i .-- ~
400 Quotient or answer.
5. Find the quotients:
2)800 2)290 5)150 4)180 5)470 3)987
3)678 5)345 2)178 3)171 4)172 5)175
4)896 3)294 4)188 2)250 5)250 5)215
5)595 4)372 2)636 4)272 3)672 3)648
6. Mary's mother made 215 lemon cookies for the children
to eat while they were camping. They camped 5 days.
How many cookies would they have for each day?
7. Andrew bought a box containing 300 marbles. He
divided them equally among four boys. How many
marbles had each?
8. One fall Allan watched 4 squirrels store acorns in a
hollow tree. On counting the acorns he found there
were 288. If each squirrel carried the same number,
how many acorns did one carry?
44 RATIONAL ELEMENTARY ARITHMETIC.
1. How many 2-cent stamps can be bought for $5.76?
2. At 3 cents a yard, how many yards of ribbon can be
bought for $4.05?
3. There were 640 marbles in 5 boxes, the same number in
each box. How many were there in one box?
4. How many bottles of ink can be bought for $8.05, at
5 cents each?
5. 2)457 How many 2's in 4? How many 2's in
228J 5 and how many over? How many
2's in 17? How many remaining?
Write the remainder thus: J, and place
it to the right of the quotient.
6. Find the quotients:
6. 2)894 2)895 2)962 2)769 2)541
3)217 3)849 3)755 3)314 3)375
4)645 4)474 4)867 4)716 4)419
5)600 5)736 5)598 5)807 5)670
7. How many feet in one side of a square whose perimeter
(distance around) is 588 feet?
8. The perimeter of a rectangle is 586 feet. How many
yards in it?
9. At 4 cents a dozen, how many dozen buttons can you
buy for $3.37?
10. A train traveled 128 miles in 3 hours. How many miles
did it travel each hour?
11. At 4 cents a pound, how many pounds of sugar can you
buy for $4.86?
12. At $3 a barrel, how many barrels of apples can be bought
for $77?
13. At 3 cents a dozen, how many dozen jackstones can you
buy for $5.75?
LAUNDRY BILLS.
MRS. WILSON'S LAUNDRY BILL FOR MARCH.
45
Answer all you can orally.
1. How much did the collars cost each week? The cuffs?
The handkerchiefs? The towels? The aprons?
2. What was the whole bill for each week?
3. How much did the collars cost for the whole month? The
cuffs? The handkerchiefs? The towels? The aprons?
4. How much did the collars and cuffs together cost for each
week? For the month?
5. The cuffs cost how much more than the collars for the
whole month?
6. How much more did the collars cost the first two weeks
than the last two?
7. How much more did the handkerchiefs cost, the last 2
weeks than the first 2 weeks?
8. What article of clothing cost the most for any one week?
9. What article cost the most f r the month?
10. What week was the laundry bill largest?
11. What week was it smallest?
12. Add the bills of the 4 weeks and divide the sum by 4.
13. At the price given in the list, what would it cost to have
five pieces of each kind laundered three different
times?
14. Make a laundry bill for yourself.
46
RATIONAL ELEMENTARY ARITHMETIC.
1. Draw a line 2 inches long.
2. Divide it into two equal parts.
3. Let the inches stand for feet.
4. How many feet does the line stand for?
5. Let each inch stand for 1 yard.
6. How many yards does the line stand for?
7. Draw a line 3 inches long.
8. Let each inch stand for 1 yard.
9. How many yards does the line stand for?
10. Draw a line 4 inches long. If each inch stands for one yard,
how many yards does the line stand for?
11. Draw a line 1 inch long. Let it stand for 1 yard. Hoi
many feet does it stand for?
12. Draw a line 2 inches long. Let it stand for 2 yards.
One-half of the line stands for what? One-half of tl
line means how many feet?
13. When one inch stands for 1 foot, a 4-inch line means hoi
many feet?
14. When one inch stands for 1 yard, a 4-inch line stands foi
how many 'yards?
15. When one inch stands for 1 yard, a 4-inch line meai
how many feet?
16. Let 1 inch stand for 1 yard. Draw a two yard line; a three
yard line; a four yard line. How long is each line?
How many yards does each line stand. for?
17. Draw the plan of a table in whiph 1 inch, shall stand for
1 foot. The table is 3. feet' wide* and. 8 feet long. How
long and how wide will your 'drawing be?
18. Draw a plan of .a signboard 6 feet long and 3 feet wide.
Your drawing is to be 1 inch wide and 2 inches long.
In this drawing 1 inch will stand for how many feet?
19. A road ten miles long was shown on a map by a line
2 inches long. On this map one inch meant what, length?
DRAWING TO A SCALP:
B
47
1. The above is the plan of a lot drawn to the scale, 1 inch
to 12 feet. This means that an inch in length in the
drawing stands for 12 feet in any line in the lot.
2. How many feet is it from A to B?
3. How many feet is it from A to F?
4. How many feet is it from F to E ? From D to E ? From
B to C? From C to D? From A through B to C?
From A through F to E?
5. How many feet of fence are needed to fence the lot?
6. There, are 3 feet in a yard, how many yards from A to F-?
From A to B? How many yards around the lot?
7. How many feet from A to C?
8. How many feet from F to C?
9. How many yards from A to C?
10. How many yards from F to C?
11. How many yards around the lot and from F to C over?
48 RATIONAL ELEMENTARY ARITHMETIC.
1. If the lot were square with sides the length of A to F,
how many yards around it? If square with sides the
length of A to B, how many yards around it? If square
with sides the length of B to C, how many yards
around it?
2. Taking steps 2 feet long, how many steps would one take
in walking once around the lot described on page 47?
3. Add:
427
725
687
678
246
672
608
685
982
843
294
864
573
793
981
693
921
892
268
957
892
684
798
692
684
462
391
181
4. Subtract:
246 907 872 405 690 672 492
192 265 396 272 371 395 _309
5. Multiply:
374 826 987 654 982 658 972
_2 _3 _4 _5 _4 __3 _5
6. Divide:
2)147 3)765 4)729 4)912 5)675 3)405 5)752
7. A car is 64 feet long, how long is a train of 4 such cars?
Of 5 such cars?
8. A boy lives 624 feet from the store. In going to the
store and returning, how many feet will he walk? How
many yards? If he goes to the store and returns once
a day, 4 days in the week, how many yards will he walk?
9. A rail in the street car track is 10 yards long. How many
rails in 50 yards of a single rail of track? In both rails of
track? In all the rails of 2 tracks?
USES OF SIX. 49
Answer all you can orally.
1. How many days are there in a week?
2. How many of these are working days?
3. How many working days in 2 weeks? In 3 weeks?
In 4? In 5? In 6? In 7? In 8? In 9? In 10?
In 11? In 12?
4. How many eggs in a half dozen? In one and one-half
dozen?
5. How many inches in one foot? In a half foot?
6. How many 6-inch rulers can be made from a stick 2 feet
long? From a stick 5 feet long?
7. How many candle wicks, each six inches long, can be
made from a yard of wicking?
8. Allowing six inches for each wick, how many inches of
wicking will be needed to furnish 9 lamps? For
11 lamps?
9. How many 6-inch hair ribbons will a yard of ribbon make?
10. A wheel that is 6 inches around the tire will turn how
. many times in going 36 inches? 48 inches?
11. A wheel that is 6 inches around the tire will turn how
many times in rolling 2 feet?
12. Julia found 30 eggs in the hay mow. How many half
dozens did she find?
13. Mrs. Williams bought a half dozen eggs each working day
of the week. How many did she buy in all?
14. Fifty-four lemons are how many dozen lemons? How
many half dozens?
15. The oranges in a store window were arranged in 7 groups
of a half dozen each. How many oranges were in the
window?
16. A milkman made the following sales, at 6^ a quart:
5 quarts of milk; 3 quarts; 8 quarts; 6 quarts;
11 quarts. How much did he make from each sale?
From all the sales?
50
RATIONAL ELEMENTARY ARITHMETIC.
1. How many squares in A? How many rows of six squares
each in B? In C? In D? E? F? G? H? I? J?
2. A contains 6, B contains 12. How many in C? D? E?
F? G? H? I? J? K? L?
3. A equals what part of B? What part of C? Of D? E?
4. 6 is what part of 12? What part of 18? Of 24? 30?
36? 42? 48? 54? 60? 66? 72?
5. B equals how many A's? What part of D? F? H? J?
L?
BUILDING TABLE OF SIXES.
51
1. 12 equals how many 6's? What part of 24? 36? 48?
2. C equals how many A's? What part of F? I? L?
3. 18 equals how many 6's? What part of 36? 54? 72?
4. D equals how many A's? How many B's? What part
ofH? OfL?
5. 24 equals how many 6's? How many 12's? What part
of 48? Of 72?
6. E equals how many A's? What part of J?
7. 30 equals how many 6's? What part of 60?
8. F equals how many A's? How many B's? How many
C's? What part of L?
9. 36 equals how many 6's? How many 12's? How many
18's? What part of 72?
TABLE OF SIXES
6X1= 6 6X4=24 6X7=42 6x10=60
6X2=12 6X5=30 6X8=48 6X11=66
6X3=18 6X6=36 6X9=54 6X12=72
Add the heavy center number to each number in the same
large square. Subtract it from each larger number. Multi-
ply and divide in the same way.
52 RATIONAL ELEMENTARY ARITHMETIC.
1. The height of a tree is 72 feet, which is 6 times the dis
tance around it at the ground. How many feet around
it at the ground?
2. If I buy 5 eight-cent postage stamps and give $1 in pay-
ment, how much change should I receive ?
3. Charles traveled 87 miles on his wheel in 3 days. At
the same rate how far can he go in 5 days? In 6 days?
4. In one field a farmer has 96 sheep, which are one-sixth of
his entire flock. How many sheep has he?
5. If $120 were divided equally among 6 men, how much
money would each one receive? How much would 2
receive together? 3 together?
6. A piece of cloth is 54 yards long. One-sixth of it was
sold at $2 a yard. How much was received from the
sale? How much of the piece was left? How much
was it worth at the same rate?
7. If a man earns $71 a month and spends $52 a month, how
much will he save in that time? How much will he
save in 6 months?
8. How many hours are there in 1 day ? In one-half a day ?
In one-sixth of a day? How many hours are there in
6 days?
9. A barrel holds 31 J gallons ; how many gallons will 6 bar-
rels hold?
10. A farmer owned 486 acres of pasture land. He bought
one-sixth as many acres more. How many acres did
he buy ? How many acres did he then own ?
11. A mile from north to south is 8 blocks, and from east to
west 13 blocks. How many blocks will a boy travel in
going 6 miles north and 6 miles west?
12. What is the cost of 27 yards of sewer pipe at $2 a foot?
13. How many weeks will it take a man to save $297 if he
saves $3 each week?
APPLICATION OF SIXES. 53
1. How many square inches in a rectangle that is 6 inches
long and 3 inches wide? (See page 4.) One that is
6 inches long and 6 inches wide? One that is 6 inches
long and 8 inches wide? One that is 6 inches long and 12
inches wide?
2. How many square inches in a 6 inch square? Draw
one.
3. A 2 inch square equals what part of a 6 inch square?
4. A 3 inch square equals what part of a 6 inch square?
5. 3 feet in length is called by what name? What is a figure
3 feet square called?
6. Cut from a newspaper a square foot of paper. Use it for
a pattern and cut 8 more pieces. Make a square by
placing these pieces on the floor. What are the dimen-
sions of this square in feet? In yards?
7. One square yard equals how many square feet?
8. On page 4 suppose each small square were one foot square.
How wide would the figure be? How long? How
many square feet would it contain?
9. On page 4 suppose each square in B, E, and F together
were one foot long. How long would the figure B E F
be? How wide? How many square feet would it
contain? What would be its perimeter in feet? In
yards? Find a square yard in it.
10. How many square yards in a figure 2 yards square?
How many feet long is one side of such a, figure? How
many square feet does such a figure contain?
11. Let one inch stand for a foot and draw figures containing
36 square inches. What 4 different shapes might such
figures be? Why?
12. Two blotters each contain 12 square inches. One was
2 inches wide, the other was 3 inches. What was the
length of each?
54 RATIONAL ELEMENTARY ARITHMETIC.
B
1. How long is the box A ?
inches iii one side?
How deep? How many square
BOX MAKING. 55
1. B is a piece of paper the size from which to cut such a
box without a cover.
2. How long is this paper? How wide is it?
3. The paper is then a rectangle of - - inches by
- inches.
4. What is the area of this paper?
5. A box is 2 inches long, 2 inches wide and 2 inches high.
How many square inches in the sides and bottom of
the box?
6. What are the dimensions (length and breadth) of the
piece of paper necessary to make it? What is its area?
7. What are the dimensions of the piece of paper necessary
to make a box 3 inches long, 3 inches wide, and 3 inches
deep, without a cover? t What is the area of the paper?
8. What are the dimensions of a box 4 inches deep that can
be made as in problem 7, from a piece of paper
12 inches long and 12 inches wide?
9. A box is 4 inches long, 3 inches wide and 2 inches deep.
How large must the paper be in order to make it with-
out a cover? How many square inches of paper are
necessary?
LO. What are the dimensions of the piece of leather necessary
to line a box that is 6 inches long, 2 inches wide, and
2 inches deep, without a cover? How many square
inches? What will the leather for such a box cost at
6^- a square inch?
[1. How many square feet of cloth are needed to line a box
6 feet long, 3 feet wide, and 2 feet deep, with a cover?
12. The length of a room is 6 yards, its height 4 yards. How
many square yards in one side of the room? In the
2 sides? The room is 5 yards wide, what is the area of
one end wall? Of both? Of the ceiling? Of the
floor? Of the entire inside surface of the room?
56 RATIONAL ELEMENTARY ARITHMETIC.
CURRANTS
CURRANTS
CABBAGES
BEANS
BEANS
CUCUMBERS
LETTUCE
LETTUCE
CABBAGES
ASPARA-
GUS
RADISHES
RADISHES
PEAS
PARSNIPS,
CARROTS
i
TOMATOES
POTATOES
a:
en
X
w
CORN
BEETS
TOMATOES
Q
Q
TURNIPS
I GOOSEBERRIES I I GOOSEBERRIES I
SCHOOL GARDEN. 57
1. Find the length of the plan; the width; the area. This
plan of a vegetable garden is drawn to a scale of 8 feet
to 1 inch. | of an inch equals how many feet? J of an
inch equals how many feet? \ an inch? 1 inch?
2. What is the length of the garden? The width?
3. What are the dimensions of each of the currant patches?
The areas? How many square feet in the two together?
4. Find the dimensions and the area of each space given to
gooseberries.
5. Find the length of the long middle path; the width; the
number of square feet in it.
6. How wide is each of the other paths?
7. How long is each bean bed? How wide? What is the
area of both?
8. Find the dimensions and the area of each lettuce bed.
How many square feet in the 2 lettuce beds?
9. Find the dimensions and the area of each of the smaller
spaces given to radishes; of each of the larger spaces.
How many square feet in all are given to radishes?
10. What are the dimensions of the asparagus bed? What
is the area?
11. Answer the same questions for the space given to peas.
12. Find the dimensions and area of the cucumber bed.
13. What other spaces have the same area?
14. How many square feet in all are given to cabbages? To
tomatoes?
15. The parsnip patch is how wide? How long? What is its
area? Answer the same questions for the carrot patch.
16. The parsnip space and the carrot space together are
equal in area to what space?
17. Find the dimensions and the area of the space given to
corn; to potatoes.
18. How many square feet in all are given to vegetables?
58 RATIONAL ELEMENTARY ARITHMETIC.
SALES.
Always answer all you can orally.
Arthur Hall kept a newspaper stand and this table shows
his sales for one week.
1. How many copies of each paper did he sell in the week?
2. How many copies of all papers did he sell in the week?
3. How many papers did he sell each day?
4. What sum of money did he receive each day for the Tribune ?
Free Press? News? Enquirer? Herald? Dispatch? Post?
5. What sum of money did he receive each day on all the papers?
6. What sum of money did he receive in the whole week on
each one of the papers?
7. What sum of money had he received during the week
from the sale of all the papers?
8. His pay was one-third of all he received. How much did
he earn?
9. What paper sold best during the whole week?
10. Of what paper were the sales smallest for the week?
11. What paper brought in the smallest amount of money?
12. What paper sold best on Monday? Tuesday? Wednes-
day? Thursday? Friday?
13. On Monday there were how many sales of Tribune and
Free Press?
14. On Tuesday there were how many sales of News and
Enquirer?
USES OF SEVEN, 59
1. How many days are there in a week?
2. In 14 days how many weeks?
3. How many days are there in 2 weeks? In 3? 4? 5? 6?
7? 8? 9? 10? 11? 12?
4. How many weeks are there in 21 days? In 28 days? In
35? 42? 49? 63? 84?
5. A lady bought a quart of milk each day of one week. How
many pints did she buy in all?
6. In all the common years February has 28 days. How
many weeks has February in those years?
7. Alice stayed with her grandmother 21 days. How many
weeks was she there?
8. A boy sold newspapers every day for 63 days. How
many weeks did he sell papers?
9. John is 7 years old and his brother William is 4 times as
old as John. How old is William?
10. A girl spent 70# for ribbon. How many dimes did
she spend?
11. There are six working days in one week. How many
working days are there in 7 weeks?
12. Elsie is 7 years old. Her mother is 35 years old. How
many times Elsie's age is her mother's age?
13. The Christmas holidays were two weeks long. How
many days long were they?
14. Jennie paid 7^ a pound for loaf sugar. How many
pounds could she buy for 63#?
15. The summer vacation was 6 weeks long. How many
days long was it?
16. George made a trip of 8 weeks. How many days was he
away?
17. A term of school was 12 weeks long. How many school
days were in it? How many days passed from the
beginning to the end of the term?
60
RATIONAL ELEMENTARY ARITHMETIC.
1. How many squares in A? How many rows of 7 squares
each in B? How many such rows in C? In D? E?
F? G? H? I? J?
2. A equals 7, B equals 14. To what is C equal? D? E?
F? G? H? I? J? K? L?
3. A equals what part of B? What part of C? Of D? E?
F? G? H? I? J? K? L?
4. 7 equals what part of 14? What part of 21 ? Of 28? 35?
42? 49? 56? 63? 70? 77? 84?
5. B equals how many A's? What part of D? F? H?
J? L?
6. 14 equals how many 7's? What part of 28? 42? 56?
70? 84?
BUILDING TABLE OF SEVENS.
61
1. C equals how many A's? What part of F? I? L?
2. 21 equals how many 7's? What part of 42? 63? 84?
3. D equals how many A's? How many B's? What part
of H? L?
4. 28 equals how many 7's? How many 14's? What part
of 56? 84?
5. E equals how many A's? What part of J?
6. 35 equals how many 7's? What part of 70?
7. F equals how many A's? How many B's? C's? What
part of L?
8. 42 equals how many 7's? How many 14's? How many
21's? What part of 84?
9. 49 equals how many 7's?
TABLE OF SEVENS.
7X1= 7 7X4=28 7X7=49 7x10=70
7X2=14 7X5=35 7x8=56 7X11=77
7X3=21 7X6=42 7x9=63 7X12=84
Add the heavy center number to each number in the same
large square. Subtract it from each number larger than
itself. Multiply and divide in the same way.
62
RATIONAL ELEMENTARY ARITHMETIC.
1. Add upward, downward, by lines to the right and to the
left:
7
7
6
4
5
3
2
7
7
1
2
3
4
5
6
7
7
5
6
7
3
7
5
4
7
4
7
7
7
6
7
D
7
6
6
4
7
7
7
6
7
7
7
6
6
4
3
7
1
3
3
2
2
7
4
7
2. Add these numbers; subtract them; and multiply them:
14 28 56 21 42 84 35 70 63 78 59
77777777777
83 75 94 67
7 77 7
77 89 48 99 132 570
777777
3. Divide:
7)14
7)42 7)21 7)56 7)70
7)35 7)49 7)63 7)84 7)77 6)72
4. 14 equals how many 7's? 42 equals how many 7's?
5.
28 equals how many 7's?
56 equals how many 7's?
35 equals how many 7's?
63 equals how many 7's?
7 is ^ of _^_ .
7 is I of . ..
7 is i of _ _
49 equals how many 7's ?
21 equals how many 7's?
77 equals how many 7's?
84 equals how many 7's?
7 is \ of
.7 is | of
7 is of
APPLICATION OF SKVKNS. 63
1. 7 is i- of _ -- . 7 is $ of _
7 is -jV of - --- 7 is Vo of -
7 is /, of -- is I of r
4 is of -- 7 is -\ of _
6 is J of ___ 4 is 1 of _
8 is | of -- 9 is I- of _
10 is | of _ __ 11 is J of - .
2. How many 7's are there in 15? In 29?
How many 7's are there in 37? In 45?
How many 7's are there in 50? In 25?
How many 7's are there in 57? In 48?
How many 7's are there in 86? In 78?
How many 7's are there in 73? In 82?
3. One man digs 27 feet of ditch ; another 17 feet, and a boy
digs 7 feet. How many feet do all dig?
4. On one farm there are 754 feet of fence; on another 577
feet. How much more fence is there on the first farm
than on the second?
5. A grain dealer bought 378 bushels of wheat in one place
and 747 bushels in another. He sold 707 bushels;
how many bushels had he left?
6. A man bought 7 horses at $65 apiece; how much did he
pay for all?
7. A train travels 252 miles in 7 hours; how far does it go
in 1 hour if the speed is always the same?
8. If 7 yards of silk cost $8.75, what will be the cost of
5 yards of the same?
9 In digging a well, 63 feet deep, 14 feet were dug through
clay. If ^ of the well was dug each day, how many
days were spent in digging through the clay ?
ft A farmer made a wire fence 14 yards long. He put in posts
7 feet apart, and 7 rows of wire. How many posts were
there ? How many yards of wire did he use ?
64 RATIONAL ELEMENTARY ARITHMETIC.
B
Base
Base
D
AREA OF TRIANGLES. 65
1. What is the altitude of figure A, page 64? The base?
2. Find the middle point of the altitude and the middle
point of the long side of the triangle. Suppose the
triangle cut on a straight line which passes through
these two points and the parts turned about to the
side of A, as in B.
3. What do we call the figure B? What is its length? What
is its width? What is the area of B?
4. What is the area of the triangle A?
5. Cut a 4-inch square. Draw a line between two opposite
corners, and on this line cut the square in two. What
is the altitude of one of the triangles thus made? The
base? Find the area.
The side upon which a triangle is supposed to rest, is
called its base. The shortest distance from its base to
its highest point is called its height or altitude.
6. What are the dimensions (base and altitude) of the trian-
gle C? Draw a line from the center of the base to the
point of the angle opposite. Suppose the left side of the
triangle C to be turned about and laid upon the longest
side of C, as in the figure D. What is the figure D?
7. What are the dimensions of D? What is its area?
8. What is the area of the triangle C?
9. Suppose the base of the triangle C were 8 feet and its
altitude 8 feet, what would be the area of the triangle?
10. The area of such a triangle as C may be found in another
way, as in the triangle E.
11. Find the middle points of the two sides of the triangle,
and suppose the triangle to be cut through them and
the top part equally divided and placed on the sides
of the lower part of the triangle, as in the figure F.
What figure do we then have? What are its dimen-
sions and its area?
66 RATIONAL ELEMENTARY ARITHMETIC.
1. Draw the following 9 triangles and find the area of eaeh:
The base is 6 inches and the altitude 4 inches.
The base is 8 inches and the altitude 6 inches.
The base is 9 inches and the altitude 4 inches.
The base is 5 inches and the altitude 8 inches.
The base is 12 inches and the altitude 10 inches.
The base is 11 inches and the altitude 14 inches.
The base is 18 inches and the altitude 12 inches.
The base is 16 inches and the altitude 10 inches.
The base is 15 inches and the altitude 14 inches.
2. A car contains 9 seats, each of which holds 7 persons.
How many persons can be seated in the car?
3. There are 3 cars of this size in a train. How many per-
sons can be seated in the train?
4. In front of a house there are 25 feet of sidewalk 7 feet
wide. How many square feet in the sidewalk?
5. A door is 7 feet high and 3 feet wide. How many square
feet in the door? How many square feet if the door
were 3J feet wide?
6. How many books would there be in a bookcase containing
7 shelves, if there were 12 books on each shelf? 11 on
each shelf? 9 on each shelf? 10 on each shelf?
20 on each shelf? 30 on each shelf?
7. A table is 7 feet long and 4 feet wide. What is its perim-
eter? "What is its area?
8. There are 35 pupils enrolled in one schoolroom. If 5 are
away, how many are present? What part of the whole
. number is absent? What part of the whole number is
present ?
0, A fruit dealer sells pineapples at 34^ apiece. How
much money will he receive for 7 pineapples ?
10. If I save $57 a month for 7 months, how much more
must I save to have $700?
USES OF EIGHTS. 67
Always answer all you can orally.
1. Review pages 8 and 10 as oral work.
2. How many quarts are there in a peck?
3. Two pecks equal how many quarts?
4. A grocer bought a peck of gooseberries and sold half of
them. How many quarts did he sell?
5. A woman picked a peck and a half of currants. How
many quarts did she pick?
6. At 90 a quart, what will a peck of blackberries cost?
7. At 40 a quart, what will 1J pecks of seed beans cost?
8. How many pints in a quart? How many quarts in a
gallon? How many pints in a gallon?
9. What part of a gallon is one pint?
10. At 800 a gallon, what will one pint of ice-cream cost?
11. At 180 a pint, what will a gallon of whipping-cream
cost?
12. At 96^ a gallon, wholesale, what will a pint of var-
nish cost?
13. 8 dimes equal how many pennies?
14. 8 quarts of milk cost how much at 240 a gallon?
15. A party of 40 people were seated at 5 tables. How many
were at each table?
16. Charlie earned 80 a day for 4 days, while Ben earned
the same amount each day for 7 days. What was the
difference in the whole amount each earned?
17. Mr. Brown has lived 8 times as long as his grandson, who
is 10 years old. How old is Mr. Brown?
18. At 440 a gallon, what will be the cost of a 2-quart can
of paint?
19. At 30 a pint, what will a gallon of Jersey milk cost?
20. A girl paid 560 for 8 yards of calico. What was the cost
per yard?
21. If a family uses 6 pints of milk a day, how many pints
will be used in 8 days?
68 RATIONAL ELEMENTARY ARITHMETIC.
HIM * ?!
mmmmimmm m*m
1. How many squares in A? How many rows of 8 squares
each in B? How many such rows in C? In D? E?
F? G? H? I?
2. A equals 8, B equals 16. To what is C equal? D? E?
F? G? H? I? J? K? L?
3. A equals what part of B? What part of C? Of D? E?
F? G? H? I? J? K? L?
4. 8 equals what part of 16? What part of 24? Of 32? 40?
48? 56? 64? 72? 80? 88? 96?
5. B equals how many A's? What part of D? F? H? J? L?
6. 16 equals how many 8's? What part of 32? 48? 64?
80? 96?
7. C equals how many A's? What part of F? I? L?
BUILDING TABLE OF EIGHTS.
1. 24 equals how many 8's?
2. D equals how many A's?
ofH? L?
3. 32 equals how many 8's?
of 64? Of 96?
4. E equals how many A's? What part of J
5. 40 equals how many 8's?
6. F equals how many A's?
7. 48 equals how many 8's?
24's? What part of 96?
8. 56 equals how many 8's?
9. H equals how many A's?
10. 64 equals how many 8's?
What part of 48? 72? 96?
How many B's? What part
How many 16's? What part
i
What part of 80?
B's? C's? What part of L?
How many 16's? How many
How many B's? D's?
16's? 32 's?
TABLE OF EIGHTS
8X1= 8 8X4=32 8X7 = 56 8X10=80
8X2=16 8X5=40 8X8=64 8X11=88
8X3=24 8X6=48 8x9=72 8X12=96
Add the heavy center number to each number in the same
large square. Subtract it from each number larger than
itself. Multiply and divide in the same way.
70
RATIONAL ELEMENTARY ARITHMETIC.
1. Add upward, downward, by lines to the right and to the
left:
8
8
8
8
8
8
8
8
8
7
8
6
5
8
1
7
8
6
7
4
8
6
2
7
8
5
8
2
8
5
3
6
8
4
3
7
6
7
4
6
8
3
4
5
8
3
5
4
8
2
8
8
7
8
6
4
7
1
6
8
6
8
7
3
2. Add these numbers; subtract them; and multiply them:
32 24 16 48 56 72 64 88 80 40
8888888888
13 25 37 49 79 88 67 98 386 497
888888888 8
3. Divide:
8)16 8)32 8)48 8)24 8)56 8)72
8)40 8)64 8)88 8)96 8)80 7)84
4. 16 equals how many 8's?
32 equals how many 8's?
40 equals how many 8's?
56 equals how many 8's?
88 equals how many 8's?
80 equals how many 8's ?
5. 8 is A of __.
48 equals how many 8's?
64 equals how many 8's?
24 equals how many 8's?
72 equals how many 8's?
96 equals how many 8's?
49 equals how many 7's?
8 is 1 of
APPLICATION OF EIGHTS. 71
1. 8 is \ of _. 8 is J of _ _.
8 is | of _ 8 is \ of _
8 is % of _ _. 8 is \ of
8 is ^ of _. 8is T Vof
8 is T V of _. 7 is of
6 is ^ of _. 4 is \ of
5 is -jij- of 3 is j- of
2. How many 8's are there in 17? In 34?
How many 8's are there in 47 ? In 27 ?
How many 8's are there in 56? In 03?
How many 8's are there in 71? In 81?
How many 8's are there in 20? In 42?
How many 8's are there in 59? In 67?
How many 8's are there in 76? In 30?
How many 8's are there in 85? In 98?
3 A boy picked 38 quarts of berries in one week, 42 in the
second, 28 in the third, and 18 in the fourth. How
many quarts did he pick?
4. In one school there are 858 scholars; in another there are
684. How many more are there in one than in the
other?
5. A man traveled 284 miles by rail and 8 times as far by
boat; how far did he travel by boat?
6. During the summer a family used 248 quarts of milk.
During the winter they used \ more than that. How
many quarts did they use during the winter?
7. If one boat holds 5 persons; how many boats will be
needed for a party of 40 people ?
8. In an orchard there are 56 trees in each row, and \ as
many rows as there are trees in each one; how many
rows are there? How many trees in all?
9. If 32 bushels of wheat make 8 barrels of flour; how many
bushels will be needed to make 64 barrels?
72 RATIONAL ELEMENTARY ARITHMETIC.
MEASURING SOLIDS. 73
1. Place two one-inch cubes in a row.
2. Place another row of two one-inch cubes in front of the
first row.
3. How many rows of one-inch cubes nre there?
4. How many one-inch cubes, or cubic inches, are there in
a row? How many are there in both rows?
5. Place four more one-inch cubes in a layer on top of
these cubes.
G. How many layers of cubes are there?
7. How many cubic inches are there in a layer? How many
are there in both layers?
8. Find a two-inch cube on page 72.
9. Build a two-inch cube with the one-inch cubes.
10. How many layers of one-inch cubes are there in the two-
inch cube?
11. How many rows are there in each layer ?
12. How many one-inch cubes are there in each row?
13. How many one-inch cubes are there in both rows?
14. How many one-inch cubes are there in both layers?
15. Take away one layer of cubes.
16. How many one-inch cubes are taken? What part of the
two-inch cube is taken?
17. Take away one row from the remaining layer.
18. What part of the layer is taken? What part of the two-
inch cube is taken?
19. Take away a one-inch cube from the remaining row.
20. What part of the row is taken? What part of the layer
is taken? What part of the two-inch cube?
21. A one-inch cube is what part of a two-inch cube? Two
one-inch cubes are what part? Three one-inch cubes
are what part? Four are what part? Five?
22. How many 1-inch cubes in $ of a 2-inch cube? In J of
a 2-inch cube? In of a 2-inch cube?
74 RATIONAL ELEMENTARY ARITHMETIC.
1. A cube has how many faces? What is the shape of each?
2 Draw the pattern of an inch cube, as shown in the picture.
Cut it from the paper, fold on the lines, and paste the
laps on the inside
3. How many edges has a cube? How many corners?
4. Draw a pattern and make a 2-inch cube.
5. In a 4-inch cube there are how many one-inch cubes?
6. Without thinking of the laps, how many square inches of
paper did you use in making the one-inch cube? The
2-inch cube?
BUILDING SOLIDS. 75
1. Build with cubes a solid containing two rows of 3 cubic
inches each.
2. What is its length? Its height? Its other dimension, or
width?
3. Build a solid containing two layers of two rows of 3 cubic
inches.
4. What is its width? Its height? Its other dimension, or
length?
5. Build the following solids, tell their dimensions, and the
number of cubic inches in each:
One layer of two rows of 3 cubic inches.
Two layers of two rows of 3 cubic inches.
One layer of two rows of 4 cubic inches.
Two layers of two rows of 4 cubic inches.
One layer of three rows of 5 cubic inches.
Two layers of two rows of 5 cubic inches.
Two layers of one row of 8 cubic inches.
Two layers of one row of 7 cubic inches.
Four layers of one row of 4 cubic inches.
Two layers of one row of 6 cubic inches.
Two layers of three rows of 3 cubic inches.
Four layers of one row of 5 cubic inches.
Three layers of two rows of 4 cubic inches.
Four layers of three rows of 2 cubic inches.
One layer of three rows of 8 cubic inches.
Two layers of one row of 9 cubic inches.
One layer of two rows of 12 cubic inches.
Two layers of two rows of 12 cubic inches.
Two layers of three rows of 12 cubic inches.
6. Give the dimensions of solids containing:
8 cubic inches. 12 cubic inches.
6 cubic inches. 10 cubic inches.
9 cubic inches. 16 cubic inches.
76 RATIONAL ELEMENTARY ARITHMETIC.
CUT OUT
CUT OUT
CUT OUT
CUT OUT
1. To make a box that will hold 4 cubic inches, draw a figure
like this one. Cut out the corners, fold on dotted lines,
and paste the square pieces cut from the corners over
the joinings.
2. Make a box of paper, cardboard, or wood that will hold,
when full:
5 cubic inches; 10 cubic inches;
ft cubic inches; 12 cubic inches;
8 cubic inches; 16 cubic inches;
9 cubic inches; 18 cubic inches.
CONTENTS OF HOXES. 77
1. A box is 3 inches long, 2 inches wide, and 2 inches high.
How many cubic inches will it hold when full?
2. How wide is a box that contains eight cubic inches, and
is two inches high and two inches long?
3. How long is a box that contains sixteen cubic inches, and
is two inches wide and two inches high?
4. How high is a box that contains twelve cubic inches, and
is two inches long and two inches wide?
5. A brick six inches long and four inches wide contains
forty-eight cubic inches. How thick is it?
6. A bin is four feet long, two feet wide, and four feet high.
How many cubic feet does it contain?
7. In a block of marble there are sixteen cubic feet. It is
four feet lo'ng and two feet wide. How high is it?
8. A block is six inches long, four inches wide, and one inch
thick. How many cubic inches arc there in it?
9. How many cubic feet of air will a glass case hold that is
five feet high, two feet wide, and two feet long?
0. How many cubic yards of air are there in a room that is
3 yards long, 2 yards wide, and 3 yards high?
1. A ditch is four feet wide and three feet deep. How many
cubic feet are there in a part two feet long? How
many in a part three feet long?
2. How many cubic feet will a wagon box hold that is 9 feet
long, 4 feet wide, and 2 feet high?
3. How many cubic feet are there in a pile of wood four feet
long, two feet wide, and two feet high?
4. How many cubic inches are there in a jewel-box 1 foot
long, 4 inches wide, and 2 inches deep?
5. How many cubic feet in a play-house that is 5 feet long,
5 feet wide, and 5 feet high? In one that is 3 feet by
3 feet by 5 feet? How many cubic feet in the two
houses together?
78 RATIONAL ELEMENTARY ARITHMETIC.
1. Review page 8 as oral work.
2. In a 5 -gal Ion can, how many quarts are there? How many
pints? How many gills?
3. A milk-man started in the morning with 100 quarts of
milk. How many pints did he have? How many
gallons ?
4. There are 8 people in a family and each one drinks ^ a
pint of milk. How many pints must be bought? How
many quarts?
5. From a jar containing 2 gallons of mineral water, 6 pints
were taken. How many pints were left? How many
quarts ?
6. How many bottles holding 2 quarts each can be filled
from 20 gallons?
7. A lamp burns a quart of oil every 24 hours. How many
quarts must be bought to last 32 days? How many
gallons ?
8. A milk-man had 176 quarts of milk. How many gallons
did he have?
9. How many gill cups can be filled from 2 quarts and 1 pint
of vinegar ? From 5 gallons ?
10. There are 31^ gallons in a barrel. How many gallons are
there in 4 barrels ? In 6 barrels? In 8 barrels? 3
barrels? 5 barrels?
11. A barrel holds 3LJ gallons. How many quarts in it?
12. From a barrel of gasoline how many cans may be filled if
each holds 3 quarts? How many if each holds ^ a
gallon? LJ gallon?
13. A milk-man starts in the morning with 48 gallons of milk.
How many customers can he serve if each takes 3
quarts? How many, if each takes 2 quarts? If each
takes 3 pints?
REVIEW. 79
1. Review page 10 as oral work.
2. At 9^ a peck, what will 2 bushels of oats cost?
3. What is 1 quart of beans worth if a peck is worth 72^?
4. At |2 a peck, how many bushels of clover seed can be
bought for $88?
5. A fruit dealer sold 3 pecks of nuts at 8$ a quart. What
did he receive for them ?
6. A farmer picked 2 bushels of apples from one tree and 3
bushels from another. How many pecks did he pick
from both together?
7. A grain bin holds 2 bushels. How many pecks do 7 such
bins hold?
8. During the summer a boy picked 64 quarts of berries.
How many pecks did he pick? How many bushels?
9. From a bushel of beans 2 quarts and 1 pint are taken.
How many quarts are left?
0. How many pint boxes of cherries may be filled from a
peck?
1. A man paid 60^ for 1J bushels of apples. He sold them
at 15^ a peck. How much did he receive? How much
did he gain?
2. 2 boys gathered 6 bushels of nuts. They sold 5J bushels
by the peck. How many pecks did they sell? The
remainder they sold by the quart. How many quarts
did they sell?
.3. A wheat bin holds 144 bushels. If 340 pecks are taken
out, how many pecks remain ? How many bushels ?
4. A farmer gathers from his apple orchard 5 bushels per
tree. There are 75 trees. How many bushels does he
gather? If he packs them in barrels, 3 bushels to a
barrel, how many barrels would he need? At $3 a bar-
rel, how much will he receive?
80 RATIONAL KLKMKNTARY ARITHMETIC.
1. How long will ifc take to travel 592 miles on a bicycle at
the rate of 8 miles an hour?
2. A squirrel carried into a hollow tree 8 acorns every day.
How many did he carry into the tree in 8 weeks?
3. Find the cost of 2 bushels 3 pints of cherries at 4# a pint.
4. What is the weight of 8 tubs of butter, each weighing
564 pounds?
(j. What is the cost of 12 pecks, 3 quarts of peas at 8<? a
quart ?
6. What is the cost of 8 sacks of barley, each weighing 112
pounds, at 8^ a pound?
7. How many pints in 536 gallons? In 987 gallons?
8. How many quarts in 498 pecks? In 789 pecks? In 586
pecks? In 379 pecks?
9. How many months will it take a man to save $1,000 if he
saves $8 a month?
10. How many pecks in 2768 quarts? In 7912 quarts? In
6856 quarts?
11. How many gallons in 4584 pirts? In 9728 pints? In
8136 pints?
12. How long will a barrel of oil containing 504 pints last, if
8 pints are burned each week?
13. Find the weight of 8 barrels of oat meal, each containing
192 pounds.
14. A fruit-dealer bought 8 barrels of apples at $2 a barrel,
each barrel containing 3 bushels. He sold them at $1
a bushel. How much did he get for them? How
much did he gain?
15. Allowing 30 days to a month, how many days are there
in 8 months?
16. A farmer had 420 bushels of wheat. He sold ^ of it to
one man and 304 pecks to another. How many bushels
had he left?
USES OF NINES.
81
1. Let J inch in this figure stand for
one foot. How many square
feet does the whole figure stand
for? What is tho name for
such a square?
2. How many square feet in a rect-
angle equal to two such
squares? How many square
yards?
3. How many square yards in 27 square feet?
4. How many square feet in 4 square yards? 5? 6? 7? 8?
5. How many square yards in a window 3 feet wide and 6
feet high?
6. How many square feet of plate glass are there in a store
window 6x9 feet?
7. How many square yards of plastering are there on the
walls of a room 18 feet wide, 24 feet long, and 12 feet
high? How many square yards of ceiling in this room?
How many square feet? How many square feet of tiling
would it take to tile the floor?
8. How many dresses of 9 yards each, can Alice have made
from 27 yards of cloth?
9. A hotel bought 9 gallons of milk each day in the week.
How many gallons was that in a week? In 3 weeks?
In 4 weeks?
10. At 100 a box, how many boxes of strawberries can be
bought for 900?
11. Arnold earned 100 an hour, 9 hours a day, 6 days in the
week. How much did he earn in one week? In 5 weeks?
12. A woman charged 90 an hour for sweeping offices. She
worked from 7 o'clock in the morning until 5 in the
evening, with an hour out for lunch. How much did
she earn in a day? In a week? In 6 weeks?
82
RATIONAL ELEMENTARY ARITHMETIC.
1. How many squares in A? How many rows of 9 square
spaces each in B? How many such squares in C? In
D? E? F? G? H? I?
2. A equals 9. B equals 18. To what is C equal? D? E?
F? G? H? I? J? K? L?
3. A equals what part of B? What part of C? Of D? E?
F? G? H? I? J? K? L?
4. 9 equals what part of 18? What part of 27? Of 36? 45?
54? 63? 72? 81? 90? 99? 108?
5. B equals how many A's? What part of D? F? H? J?
L?
6. 18 equals how many 9's? What part of 36? 54? 72?
90? 108?
7. C equals how many A's? What part of F? I? L?
8. 27 equals how many 9's? What part of 81? 108?
BUILDING TABLE OF NINES.
83
1. D equals how many A's? How many B's? What part
of H? L?
2. 36 equals how many 9's? How many 18's? What part
of 72? 108?
3. E equals how many A's? What part of J?
4. 45 equals how many 9's? What part of 90?
5. F equals how many A's? How many B's? How many
C's? What part of L?
6. 54 equals how many 9's? How many 18's? How many
27's? What part of 108?
7. 63 equals how many 9's?
8. H equals how many A's? How many B's?
9. 72 equals how many 9's? How many 18's?
10. 81 equals how many 9's? How many 27's?
TABLE OF NINES.
9X1= 9 9X4=36 9X7=63 9X10= 90
9X2 = 18 9X5=45 9X8=72 9X11= 99
9X3=27 9X6=54 9X9=81 9X12=108
Add the heavy center number to each number in the same
large square. Subtract it from each number larger than
itself. Multiply and divide in the same way.
84
RATIONAL ELEMENTARY ARITHMETIC.
1. Add upward, downward, by lines to the right and to the
left:
9
9
9
9
9
9
9
9
9
8
9
7
6
9
4
3
2
3
7
8
9
6
5
9
9
8
4
6
9
7
9
9
4
3
9
6
5
8
9
6
9
9
9
2
5
4
9
7
9
5
9
3
9
8
3
8
9
6
9
4
9
2
7
2
9
7
9
5
9
3
9
9
1
8
9
6
9
4
9
2
8
2. Add these numbers; subtract them; and multiply them:
47 68 45 89 93 77 90 64 99
999999999
39 88 92 46 80 209 398 768 908
999999999
3. Divide:
9)27 9)45 9)63 9)36
9)72 9)108 9)90 9)81
9)54 9)18
9)99
4. 27 equals how many 9's?
54 equals how many 9's?
63 equals how many 9's?
18 equals how many 9's?
72 equals how many 9's?
99 equals how many 9's?
45 equals how many 9's?
36 equals how many 9's?
81 equals how many 9's?
90 equals how many 9's?
108 equals how many 9's?
72 equals how many 8's?
DRILL ON NINKS
85
1 9 i 1. nf
9 is
4 of
9 is -J- of
9 is
9 is of
Q ip ^ of
9 is
9 is
fef
\ of
9 is T V of
9 is-,
9 is T V of
2. How mar
How mar
How mar
How mar
How mar
In 29?
In 56?
In 65?
In 109?
In 98?
8 is
4 of
iy 9's
iy 9's
iy 9's
iy 9's
iy 9's
in 19?
in 48?
in 39?
in 76?
in 84?
3. At
sight,
name
the sums:
5
6
7
8
9
4
8
7
7
5
4
7
8
9
3
9
6
7
9
9
5
6
9
8
7
6
5
7
4
3
3
7
5
6
8
9
4
6
9
9
2
3
4
4
6
5
6
9
8
7
10
41
22
53
84
75
36
67
98
59
6
6
6
6
6
6
6
6
6
6
4. At
sight,
name
the differences:
12
15
18
17
19
16
29
25
28
29
4
6
4
6
5
4
9
3
7
10
24
26
28
26
27
25
23
28
27
29
13
12
15
14
16
14
11
15
13
16
21
22
23
24
25
27
28
26
25
24
9
6
7
8
6
9
8
9
7
6
86 RATIONAL ELEMENTARY ARITHMETIC.
1. What is the cost of 4 dozen eggs at 9^ a dozen?
2. What is the cost of 6 feet of molding, if 9 feet cost
3. How long will it take 1 man to do the work that 9 men
can do in 11 days?
4. William earns one-ninth as much money as his father
whose wages are $63 a month ; how much does William
earn a month ?
5. In the front of a building there are 72 windows. In each
story there are 9 windows; how many stories high is
the building?
6. Jane's grandfather is 72 years of age, and Jane is one-
ninth as old; in how many years will she be 17?
7. How much more than $36 should a man have in order to
buy 9 tons of coal at $5 a ton?
8. There are 8 rows of seats in a school-room, and 9 seats in
each row; how many seats in the room?
9. Find the cost of 17 barrels of rice at $9 a barrel.
10. I had 9 dozen buttons and used 88 buttons. How many
were left? How much did I pay for all of them at 6^
a dozen ?
11. A steamer sails 298 miles a day. How far will it sail in
9 days?
12. I bought 12 barrels of flour at $9 a barrel, and sold the
flour for $95. How much did I lose?
13. At $158 an acre, what will 9 acres of land cost?
14. Alice has $11 and her father has 9 times as much and $8
more. How many dollars have both?
15. A certain line of telegraph costs $985 a mile. How much
would 9 miles cost?
16. What is a man's income in 9 years at $2385 a year?
IT. A gentleman earns $9 a day for 8 days, and spends $8 a
day for 8 days. How much has he left?
APPLICATION OF NINES. 87
1. How many square feet in a square yard?
2. A blackboard is 4 feet wide and 9 feet long. How many
square feet in it? How many square yards?
3. Each window in a building contains 9 square feet. In
6 such windows there are how many square feet ? How
many square yards?
4. There are 9 shelves in a book-case; each one contains 12
books. How many books in the case?
5. One end of a desk is 9 feet from the wall, the other end is
7 feet from the opposite wall. The desk is 3 feet and 6
inches long. How far is it from one side of the room
to the other?
6. A horse travels 6 miles an hour. How far will it go at
the same rate, in 9 hours?
7. John has 83^. How many 9^ books can he buy, and how
much money will he have left?
8. A boy pays 12^ for 3 pencils. At the same rate what will
9 pencils cost?
9. In each of 9 cars there are 57 persons. How many per-
sons in the 9 cars?
10. There are 322 rails to the mile of railroad track. How
many rails in 9 miles of track?
11. There are 9 equal lots fronting on a street 378 feet long.
How wide is each lot?
12. A man owns 5 lots. The first is worth $1,929, the second
$959, the third $1,195, the fourth $1,699, and the fifth
$989. What is the value of the 5 lots?
13. A boy takes 9 subscriptions to the Youth's Companion at
$1.75 each. How much money did he receive for
them all ?
14. A manufacturer sold 9 carriages at $195 each. How
much did he get for them ?
RATIONAL ELEMENTARY ARITHMETIC.
1. Review page 14 as oral work.
2. How many ounces are there in 1 pound? In 2 pounds?
3 pounds? 4 pounds? 6 pounds?
3. What part of 1 pound is 8 ounces ? 4 ounces ? 2 ounces ?
12 ounces?
4. Which weight shown on this page equals -| a pound?
Which one equals -^ of a pound? Which ? Which | ?
5. Which 2 weights together equal |- of a pound? Which 2
together J of a pound?
6. The 8 ounce weight equals what part of 2 pounds? Of 3
pounds?
7. The 4 ounce weight equals what part of 2 pounds? Of
3 pounds?
8. The 8 ounce and the 4 ounce weight together equal what
part of 2 pounds? Of 3 pounds?
9. How many pounds in a hundredweight?
10. How many hundredweights are there in 200 pounds? In
400 pounds?
11. How many pounds are there in |- of a hundredweight?
^ of a hundredweight? ^?
12. If a grocer has different weights, as shown in the picture,
which ones will he use in weighing Jof a pound of tea?
Which in weighing J of a pound ? T ? 6 of a pound ? y\ ?
19 59 19 19 19 119 59 15? 79 139
? f T6 r f T r T'6 r T6 f 'B f T6 f r T6 f
13. Which different weights may he use in weighing 1^- pounds
of rice? In weighing 1J pounds? 1-J- pounds? 1J
pounds?
WEIGHT. &/
1. Tliere are 60 pounds of wheat in 1 bushel. How many
pounds in 9 bushels? In 7 bushels? In 5 bushels?
2. 1 hundredweight of metal costs $6. What will 50 pounds
cost? 75 pounds? 25 pounds?
3. What is the postage at J^ an ounce on a package weigh-
ing 4 ounces? On li pounds? On 3 pounds?
4. A bushel of oats weighs 32 pounds, how many pounds in
a peck? In a quart? In 3 pecks?
5. A grocer weighs out 1| pounds of butter. What weights
does he use? How many 4 ounce weights will he use
to weigh 1-J- pounds? pound? 2 pounds?
6. Find the value of 4 pounds and 8 ounces of pepper at 20^
a pound.
7. A grocer sells 8 packages of tea, each weighing 6 ounces ;
how many ounces do all weigh together? How many
pounds ?
8. A man bought 60 bags of flour, each weighing 5 pounds.
How many hundredweights did he buy?
9. If a man buys old iron at 1$ a pound, what will he pay
for 24 pounds? For | a hundredweight?
10. How many ounces are there in 9 pounds?
11. A farmer sold 6 iubs of butter averaging in weight | a
hundredweight each. How many pounds did he sell ?
How many ounces?
12. What is the weight in pounds of 3 packages, one weighing
2 pounds, one ^ a pound and the other 3 pounds?
What is the weight in ounces?
13. A man bought 3 packages of beans weighing 8 pounds
each ; he made them into 8-ounce packages. How many
packages did he have?
14. A grocer sold J of a pound of tea, J a pound of butter, f
of a pound of coffee, and 1J pounds of sugar How
many ounces in the entire sale?
90
RATIONAL ELEMENTARY ARITHMETIC.
70?
80?
120?
1. How many squares in one row of A? How many rows of
10 squares each in A? In B? In C?
2. How many 10's in 100? In 110? In 120?
3. 10 is what part of 20? Of 30? 40? 50? 60?
80? 90? 100? 110? 120?
4. 20 equals how many 10 's? What part of 40? 60?
100? 120?
5. 30 equals how many 10 's? What part of 60? 90?
6. 40 equals how many 10's? 20 's? What part of 80? 120?
7. 50 equals how many 10's? What part of 100?
8. 60 equals how many 10's? 20's? How many 30's?
What part of 120?
9. 70 equals how many 10's?
10. 80 equals how many 10's'?
11. 90 equals how many 10's?
12. 100 equals how many 10's?
13. 110 equals how many 10's?
14. 120 equals how many 10's? 20's?
60's?
15. Name all the numbers to 100 that can be exactly divided
by 10.
16. Count by 10's to 100. Each number you name has how
many ones in the ones' column?
20's? How many 40's?
How many 30's?
20's? How many 50's?
How many 30's? 40's?
BUILDING TABLE OF TENS.
TABLE OF TENS.
91
10X1 = 10 10X4=40 10X7=70 10X10=100
10X2 = 20 10X5=50 10X8=80 10X11 = 110
10X3=30 10X6=60 10X9=90 10x12=120
1. Add these numbers, subtract them, and multiply them:
12 15 23 30 36 42 47 53 59 61 68
lOlOlOlOlOlplOlOJ-OlOlO
74 79 80 83 88 91 98 87 58 67 99
^01010^010101010101010
2. Divide
10)30 10)50 10)46 10)60 10)75 10)29 10)80
10)67 10)90 10)38 10)100 10]99 10)110 10)120
4)40 5)50 9)90 10)76 12)120 11)110 8)80
Add the heavy center number to each number in the same
large square. Subtract it from each number larger than
itself. Multiply and divide in the same way.
1)2 RATIONAL ELEMENTARY ARITHMETIC.
1. Review page 16 as oral work.
2. Write one dollar as it is written in business.
3. In the same way write 2 dollars; 3 dollars; 5 dollars.
4. Write 50 cents in all the ways you can.
5. Write $1 and 50 cents. Without using the word " cents,"
how can you tell the cents from the dollars?
6. Write 2 dollars and twenty-five cents; 7 dollars and 10
cents; ten dollars and 75 cents; twelve dollars .and
fifteen cents.
7. Write $1 and 5 cents. Where should the 5 be written?
Why? In what way should the first column to the
right of the point be filled?
8. Write $8 and 9 cents; $3 and 1 cent; $17 and 6 cents.
9. When there are no cents how should the cents' columns
be filled? What is the first cents' column to the
right of the point? Write $1, five dimes and 1 cent.
Read it.
10. Write $1 and 25 cents. Take away the dollar. What is
left?
11. Write 25 cents as in problem 13. Write 17 cents; seventy-
five cents; 4 cents; 40 cents.
12. Read:
$5.01 $9.10 $7.09 $10.20 $36.50 $30.03 $20.19
$8.02 $4.15 $9.13 $43.75 $84.62 $13.40 $12.05
13. Read, $.40, $.16, $.35, $.50, $.07, $.10, $.09.
14. Write in figures:
Nine dollars and twenty-five cents; forty dollars.
Twenty-six dollars and six cents; fourteen cents.
Ninety dollars and ninety cents; seven cents.
Thirty dollars and five cents; one hundred dollars.
Seventy-five dollars and seventy-five cents.
Eighty dollars and 9 cents.
Sixty-one dollars and 1 cent.
APPLICATION OF TENS. 93
1. If a man works 10 hours a day, how many hours does he
work in one week not including Sunday?
2. How many inches in 10 feet?
3. How many eggs in 10 dozen?
4. How many months in 10 years?
5. How many square feet in 1 square yard? In 10 square
yards ?
6. If there are 10 square feet of window glass in one win-
dow, how many in 8 windows ?
7. Mr. Reed had 70 sheep. Wolves killed three- tenths of
them. How many were left?
8. How many square inches in a 10 inch square ?
9. How many marble tiles 1 foot square will be required to
pave a hall that is 10 feet wide and 40 feet long?
10. How many square feet in the walls of a room that is 10
feet high and 10 feet square?
11. It is 6 miles to a village. A man goes and returns 5 days
each week. How far does he travel in 1 week? In 3
weeks? 6 weeks? 10 weeks?
12. There are 10 rooms in a house. In each room there are 2
large pictures and 3 small ones. How many pictures are
there in the house?
13. In one car each seat will hold 5 persons, in another 6 per-
sons and in another 2. In each car there are 10 seats.
How many persons may be seated in the 3 cars?
14. A train of 4 cars has in the first car 45 persons, in the
second 54, in the third 65, in the fourth 59. How
many persons are in the train?
15. A ten story building has 10 windows in each of the first
6 stories, and 8 windows in each of the remaining 4
stories. How many windows in the entire building?
16. A table is 10 feet long and 4J feet wide. What is its per-
imeter? Its area?
94 RATIONAL ELEMENTARY ARITHMETIC.
1. David had 3 Wyandotte hens, each of which laid an egg a
day in March and April. How many eggs did he get
from the 3 hens during those 2 months?
2. If he sold the eggs for setting at $1.50 per dozen, how much
did David receive for the eggs in March and April?
3. Adele bought 5 geraniums at 15c each. She made 2
cuttings from each and potted all the plants. How
many plants did she pot?
4. She sold all her geranium plants at 20c each. How much
did she receive for them? How much did she gain?
5. A doll was dressed for a Christmas sale. Her underclothes
cost 72c, her house dress 87c, her street dress $1.25, and
her evening dress $1.40. The doll herself cost $1.25.
What was the whole expense of making the doll ready
for the sale?
6. This doll sold for $8.00. What was the gain?
7. Clara earned enough money to buy a ping-pong set by sell-
ing roses. She sold to 6 customers a half dozen each at
the rate of $1.20 a dozen. How much did the ping-pong
set cost?
8. Isabel saved her money and bought a pony for $40. Her
father gave her a pony carriage which cost twice as much
as the pony. How much did the whole outfit cost?
9. Caleb earned $72 in 4 weeks by driving an automobile.
How much did he earn per week?
10. Richard ran his electric launch 48 miles in 6 hours. What
rate was that per hour?
11. Robert worked in an electric supply house. He sold 9
electric light bulbs for $1.62. How much was that for
each?
12. Mr. Goodwin worked in a berry-box factory. He made
966 boxes in 6 days. How many was that per day? At
that rate how many could he make in 9 days?
FUNDAMENTAL OPERATIONS IN U. S. MONEY. 05
1. Add:
$1.55
.08
4.50
5.17
8.09
$9.76
3.72
1.31
7.75
.87
$54.54
24.32
$9.30
12.10
17.68
24.33
9.77
$25.71
20.04
47.37
.75
8.10
$99.90
93.24
$85.94
57.38
19.99
6.43
.98
2. Subtract:
$56.29
15.25
$13.74
7.55
$77.55
35.95
$107.60
89.25
$446.82
128.82
$10.34
7.25
$45.32
22.50
$321.76
145.09
3. Multiply:
$2.63
2
$207.20
7
$16.24
3
$450.75
6
$37.58
4
$327.06
7
$56.17
5
$525.50
8
$10.29
5
$290.40
9
4. Divide:
2)$56.*24
4)$892.64
2)$38.56
5)$125.75
3) $27. 96
3)$45.21
4)1416.72
5) $530. 50
6) $426. 84
6)8558.72
9)$468.63
7)$637.84
8) $968
.72 8) $656. 32
5. I bought a horse for $97.00, kept him at a livery stable
for six months at $12.00 a month, and then sold him
for $175.00. Did I gain or lose, and how much?
6. Mr. A. had $756.48. Mr. B had $327.16 and Mr. C. had
$258.92. How much did they all have together?
96 RATIONAL ELEMENTARY ARITHMETIC.
1. What is the perimeter of an 11 inch square?
2. What is the area of an 11 inch square?
3. 3 loads of hay will winter one cow. How many cows will
33 loads winter?
4. How many inches in 3 feet? In 5 feet? 7 feet? 11
feet?
5. How many square inches in a rectangle that is 11 inches
long and 3 inches wide? 11 inches long and 5 inches
wide? 11 inches long and 7 inches wide? 11 inches
long and 9 inches wide? 11 inches wide and 12 inches
long?
6. How many days in 11 weeks and 4 days?
7. Find the cost of one-eleventh of 55 pounds of sugar at 6c
a pound.
8. What is the cost of three-elevenths of 99 cords of wood
at $5 a cord?
9. Find the cost of one-eleventh of 22 sheep at $7 each. Of
three-elevenths at $9 each.
10. I paid $110 house rent and one-eleventh as much for gas.
o
How much did I pay for both?
11. Isaac planted 88 seeds in 11 hills. How many seeds did
he put in one hill ?
12. How many square inches in the top of a mantel that is
11 inches wide and 48 inches long?
13. All but one-eleventh of $99 was divided among 3 people.
How much did each receive?
14. How many feet of ribbon will be required to bind a port-
folio that is 11 inches square, allowing 4 inches extra
for corners? How many yards?
15. What is the perimeter of a rectangle 7 by 11 inches'?
What is its area?
16. It is 11 miles from A to B. *How far will one travel ir
making 4 round trips?
I SKS OF KLKVKNS AND TWELVES. 97
1 . Percy was sent away to school on the first of September.
He came home for a short visit March first. How many
months had he been at school? What part of a year?
2. Ben saved a dollar a month to pay for a watch costing $20.
How many years and how many months over did it
take him to save enough money?
3. Beatrice went to school 9 months in each year. How
many months did she have vacation? What part of a
year? What part of a year did she attend school?
4. Edward, who is 9J years old, is how many months old?
His brother is 18 months younger than Edward. How
old is his brother?
5. Rudolph bought 2 settings of a dozen eggs each at the
rate of 5c for each egg. How much was that for a
dozen? For both settings?
6. Sarah made fruit salad for a luncheon. She bought 18
oranges at 20c a dozen, 19 peaches at 36c a dozen, J
pound of white grapes at 24o a pound. The other arti-
cles necessary to make the salad amounted to 72c.
What was the whole expense?
7. Sam raised 7 broods of 12 chickens each. In 4 broods all
the chickens lived, in one only J lived, in one } lived
and in one lived. How many from the 7 broods lived?
8. Amelia baked 5 dozen soda biscuits at an expense of 30c.
She sold them at lOc a dozen. Find her gain.
9. Louise went with her mother to buy a new dress. They
bought 12 yards of cloth at $1.25 a yard, 6 yards of
lining at 12c a yard, 12 yards of trimming at 7c a yard,
and 1J dozen buttons at 20c a dozen. What was the
cost of the dress?
13. Richard earned IJc a box picking berries. He picked 12
boxes a day for a week. How much money did he earn
in that way during the week?
98 RATIONAL ELEMENTARY ARITHMETIC.
1. Charles, George, and Stephen bought a fruit-stand. Charles
paid one-half of the expense, George paid one-fourth.
What part of the expense did Stephen pay?
2. The whole expense of buying the stand was $8.00. How
many dollars did each boy pay?
3. They bought 10 dozen oranges at $.20 a dozen, 4 pecks of
apples at one dollar a bushel and 15 dozen lemons at
$.20 a dozen. How much did the fruit cost? The
stand and all the fruit?
4. They sold the oranges at $.40 a dozen. How much money
did they get for them?
5. How much profit or gain did they make on the oranges?
6. They sold 8 dozen lemons at $.25 a dozen and 7 dozen at
$.30 a dozen. How much money did they get for the
lemons?
7. How much profit or gain did they make on the lemons?
8. They sold the apples at $.40 a peck. How much money
did they get for the apples?
9. How much profit or gain did they make on the apples?
10. How much profit did they make on all of the fruit?
11. They used half of their gain in making a larger stand.
How much money did they use in this way?
12. How much money did they have left to invest in more
fruit?
13. How much would they gain at the same cost and price on
10 dozen oranges? On 15 dozen lemons?
14. How much would they gain from selling:
5 dozen oranges at 5c apiece?
4 dozen lemons at 5c apiece?
6 pecks of apples at 60c a peck?
15. If the boys had divided the gain equally among them-
selves after problem 10, instead of investing in more
fruit, how much would each have received?
COST OF MEALS. W
Elizabeth and Sarah wont to cooking-school. They learned
to make this breakfast for 8 persons and to find its cost.
They used 4 melons at 7<f each, 5 pounds of fruit at 12^ a
pound, J package of puffed rice at 10^ a package, 1 quart of
potatoes at 16^ a peck, a half of a loaf of bread at 5# a loaf,
2 pints of cream at 18}# a pint, 10 tablespoonfuls of coffee
(in all i of a pound) at 40# a pound, 1 dozen Graham biscuits
at 1(V a dozen, 1 J pounds of butter at 28^ a pound, salt, pep-
per, and lard, amounting to 5#, and enough fuel to cost 10 cents.
1. What was the cost of each kind of food? Of the whole
breakfast? For each person? What would be the cost
of this breakfast omitting the melons? Omitting the
cream toast?
2. Guy's father took him to a restaurant, where they ordered
as follows:
2 orders of asparagus soup at 15^ each.
2 orders of fresh mackerel at 20^ each.
1 order of roast lamb with peas, 35^.
1 order of small steak, 45^.
2 orders new potatoes with cream sauce at 15^ each.
1 order cucumber salad with wafers, 20^.
1 order lemon ice with lady fingers, 15^.
1 order vanilla ice cream, 10^.
2 orders American cheese with hard crackers, 15^ each.
2 orders coffee at 10^ each.
What was their bill?
Dividing the bill equally, give the cost for each person.
PART SECOND.
ROSES
ASTERS
FERNS
GERANIUMS
This is the plan of a garden in which 1 inch stands for 12 feet.
1. Find in feet the length of the garden. The width. The
perimeter.
2. Find in feet the perimeter of the space given to asters;
to roses; to ferns, to geraniums.
3. How many 12-foot squares are used for asters? For
roses? For ferns? For geraniums? For the whole garden?
4. There are gravel walks on the division lines between the
parts and around the whole garden. How many feet
of gravel walk are there around the asters? The roses?
The ferns? The geraniums? How many feet of gravel
walk around the whole garden?
100
MEASURING A FLOWER GARDEN. 101
1. The space given to asters is how many feet long? How
many feet wide? How many square feet does it contain?
2. The space given to roses is how many feet long? How
many feet wide? How many square feet does it contain?
3. A 12-foot square contains how many square feet?
4. The space given to ferns contains how many 12-foot
squares?
5. The space given to ferns contains how many square feet?
6. The space given to geraniums contains how many 12-foot
squares? How many square feet?
7. Add the number of square feet given to the different kinds
of flowers. How many square feet in the whole garden?
8. A 3- wire fence 36 feet long extends along the side of the
rose garden. How many feet of wire were used? How
many yards?
9. In the geranium garden there are 7 rows of Martha Wash-
ingtons with 15 plants in each row, 12 rows of rose-
geraniums with 12 plants in each row, 9 rows of skeleton
geraniums with 18 plants in each row, and 12 rows of
scarlet geraniums with 12 plants in each row. How
many plants are in this garden?
10. A gardener is paid $36 per month. How much is that
per week?
11. The gardener hires a boy to help him 2 days in the week,
at 10 cents an hour, 6 hours a day. How much does
the boy earn?
12. The plants in the geranium garden were bought at whole-
sale and were 10 cents each. How much did they all
cost?
13. The asters were of 5 kinds: yellow, pink, white, shaggy,
and mixed. There were 9 rows of each kind with 12
plants in each row. How many plants were in the aster
garden?
102 RATIONAL ELEMENTARY ARITHMETIC.
1. 4 gallons of molasses at $.22 a quart cost how much?
2. At $.03 a foot, what will 4 yards of picture-molding cost?
3. At $.60 a bushel, what will 5 pecks of potatoes cost?
41 At $.15 an hour, how long will it take a boy to earn $3.00?
5. At $.18 a dozen, what will 6 dozen eggs cost?
6. At $.26 a pound, what will 24 ounces of butter cost?
7. How many hours from 9:30 A. M. to 6:30 P. M.?
8. A rectangle 4 feet by 9 feet contains how many square
feet? How many square yards?
9. How many yards of hall carpet will it take to carpet a
hall 15 feet long and wide enough for but one strip?
10. How many strips of carpet 1 yard wide will it take to
carpet a room 18 feet wide?
11. How many yards long must a strip be to be laid length-
wise if it is to reach from wall to wall of a room 21 feet
long?
12. If a room is 18 feet wide and 21 feet long, how many yards
of carpet a yard wide will be needed to carpet it?
13. At $.50 a yard, what will the carpeting of such a room
cost?
14. How many minutes between 11:15 A. M. and 3:45 P. M.?
15. At 4 cents a quart, how many pints of berries can you buy
for 40 cents?
16. At $.02 each morning, how much will the daily paper cost
for March of this year?
17. At 7 cents a yard, what will be the cost of three bunches
of braid, each containing 5 yards?
18. A boy bought 20 evening papers for $.15 and sold them
for 1 cent each. How much did he get for them? What
was his gain?
19. How many persons paid cash fares if a street-car conductor
collected $4.50 in 5-cent fares?
20. At three for $1, how many tennis balls can be bought for $7?
PURCHASES AND WAGES. 103
1. Thirty marbles at 6# a dozen cost how much?
2. Six tablets at 2 for 15^' cost how much?
3. At six for 5^, how many oranges can you buy for a
quarter-dollar? For 75#?
4. At 6 for 10^', how many oranges can you buy for 60^?
For $1?
5. At 40^' a yard, what is the cost of 2 yards of ribbon?
Of 6 yards? Of 6J yards?
6. At the same price, what is the cost of 6J yards? Of
f of a yard ?
7. Andrew kept an account of what he had saved and what
he earned in March and April. He earned $.15 a day
from his paper route, 5# a day for carrying a lunch-
basket 7 days in the week, 15# a week for keeping
the cellar clean, and $.40 a week for mowing the
lawn.
(a) How much did he earn each week by carrying papers?
(b) How much did he earn each week by carrying lunch 7
days?
(c) How much did he earn a week from all these things?
(d) Counting 4 weeks to a month, how much did he earn
each month?
(e) How much did he earn in the 2 months by carrying
papers? By carrying lunch? Counting 4 weeks to each
month, how much did he earn by cleaning the cellar?
By mowing the lawn?
(f) Andrew spent 3 cents a day for car-fare, and $.10 a day
for lunch. How much had he left each week?
(g) /At the end of the two months he bought a 5-dollar watch
and a rake costing $1.25. How much money did he
spend? How much had he left from the earnings of
the 2 months? Add what he had left to $5 and find
how many weeks he could pay for his lunch with it.
104 RATIONAL ELEMENTARY ARITHMETIC.
WHITE C.\
1 cup butter ($ Ib.)
>eaten separately
-t nip?* liour (2 II).)
X rpMspoonfuls baking po\
) milk (3 pt.)
I ouart hickory nuts ( 1 Ib.
1. For the hickory nut cake, find the cost of the following:
Sugar at 60 a pound ;
Butter at 24$ a pound;
Eggs at 180 a dozen;
Flour at 2J# a pound;
Baking powder as given in the rule;
Milk at 30 a pint;
Hickory nuts at 300 a pound, shelled.
2. Counting the fuel at 30, find the cost of making this cake.
3. For the white cake, find the cost of the following:
Butter at 220 a pound;
Sugar at 5^ a pound;
Milk at 4# a pint;
Flour at 4#;
Baking powder and vanilla as given in the rule;
Eggs at 24^ a dozen.
4. Counting the fuel at 2#, find the cost of making this cake.
5. If the two cakes were placed in the oven at the same time,
what would be the difference in the cost of the fuel?
6. Mrs. Moore made 2 hickory nut cakes and 3 white cakes to
sell. Besides the expense of the materials, she charged
50^ for the work of making each cake. How much did
she receive for 1 hickory nut cake? For 1 white cake?
For all the cakes she sold?
7. How much more did she receive for the 3 white cakes than
for the 2 hickory nut cakes?
PROBLEMS ON CANDY HULKS.
up granulated sugar (\ DJ
1 \ cups milk ('J pint)
1 two-inch .square of
late (3O
Flutter the si/e of a wal
(Allow \* for fue
ro%\n sugar
lled English walnu
(Allow K for fuel)
1. Find the cost of the fudges, counting the sugar at 60 a
pound, the milk at 20 for J pt., the chocolate, butter, and
fuel as in the rule. This will make 3 dozen fudges.
2. Jessie and Ethel made fudges, using this rule. They sold
the fudges at 10 each. How much did they receive?
3. Marion used double this fudge rule at Christmas time. How
many fudges did she make. How much did they cost her?
4. If fudges were made by this rule and sold at 150 a dozen,
what would be the gain?
5. If a half pound of shelled hickory nuts at 600 a pound were
added to the rule for fudges, what would be the cost of
making the fudges?
6. Find the cost of the nut candy, counting the granulated
sugar at 60 a pound, the brown sugar at 40 a pound, the
cream at 200 a pint, the shelled English walnuts at
600 a pound, and the butter and fuel as given in the rule.
7. This rule makes 5 dozen thick squares of nut candy. If
they sell at 20 a square, what is the gain on the whole?
8. Edwin made 3 times the nut candy rule. What was the
expense? He sold the squares at 100 a dozen. How
much did he receive for them? What was his gain?
9. Lena wanted to earn some Christmas money. She made
twice the nut candy rule and 3 times the fudge rule.
What did it cost her? She sold all the fudges at 20 each.
How much did she receive for them? How much did she
gain? She sold all the nut candy at 30 a square. How
much did she receive for it? How much did she gain?
106 RATIONAL .ELEMENTARY ARITHMETIC.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
How many square spaces in one row of A? How many
rows of 11 square spaces each in A? In B?
How many ITs in A? In B?
11 equals what part of 22? Of 33? 44? 55? 66?
88? 99? 110? 121? 132?
22 equals how many ll's? What part of 44? 66?
110? 132?
What part of 66? 99?
77?
88?
33 equals how many ll's?
44 equals how many ll's?
of 88? 132?
55 equals how many ll's?
132?
How many 22's? What part
What part of 110?
66 equals how many ll's? How many 22's? 33's?
What part of 132?
77 equals how many ll's?
88 equals how many ll's? How many 22's? 44's?
99 equals how many ll's?
110 equals how many ll's?
121 equals how many ll's?
132 equals how many ll's? How many 22's? 44's? 66's?
Count by ll's to 132.
Compare the number of ones with the number of tens in
each number you have just expressed.
How many 22's?
How many 33's?
How many 55's?
BUILDING TABLE OF ELEVENS.
107
TABLE OF ELEVENS.
11X1-11 11X4 = 44 11X7 = 77 11X10 = 110
11X2=22 11X5=55 11X8=88 11x11 = 121
11X3=33 11X6=66 11X9=99 11X12 = 132
1. Add these numbers; subtract them; multiply them:
39 45 50 23 47 56 73 65 89 29 99
2. Divide:
11)33 11)55 11)77 11)23 11)44 11)66 11)59
3. Measure off and mark 5J yards on the floor. How many
steps are there in 5i yards?
4. This distance, 5J yards, is a rod.
5. How many rods in 11 yards? In 22 yards? In 33 yards?
In 44 yards?
6. How many are 2 times 5$? 3 times 5\? 4 times 5J?
Add the heavy center number to each number in the same
large square. Subtract it from each number larger than
itself. Multiply and divide in the same way.
108 RATIONAL ELEMENTARY ARITHMETIC.
Draw the face of a clock, using
the Roman numerals. Cut the
hands from stiff paper or cardboard
and color them with ink. Fasten
them to the face of the clock with
a pin.
1. Show on the clock when it is
twenty minutes to one; 10 min-
utes to 3; 5 minutes after 5;
7 minutes to 12.
2. Show these times in the order given: Eight thirty; eight
forty-five; nine fifteen; ten ten; twelve fifteen.
3. Show these times: 1:45; 6:50; 3:20; 7:40; 2:37; 4:00.
4. What time is it when
(a) the minute hand is at 4, the hour hand nearest 2?
(b) the minute hand is at 12, the hour hand at 3?
(c) the minute hand is at 5, the hour hand nearest 1?
(d) the minute hand is at 9, the hour hand nearest 12?
5. Show on the clock what time you have breakfast; luncheon;
dinner.
6. Show the time when school opens; when recess comes;
when school closes.
7. Show the time when the sun rises at this time of year.
The time when the sun sets.
8. Show the time of meeting of the class you like best.
9. Show the time when your grocery opens.
10. Add:
426 842 846 627 985
389 683 726 829 286
725 782 875 846 297
Subtract:
407 572 672 862 307
296 359 343 559 196
TIME AND USES OF TWELVES.
109
1. What is the second month? Fifth month? Ninth month?
Sixth month? Eighth month? Eleventh month?
2. Learn the order of the months by number and name.
3. How many days in all of the months containing 31 days?
How many days in all the months containing 30 days?
4. How many days in January? April? March? Febru-
ary? June? August? September? July? October?
November? December?
5. How many days in the first 3 months of the year? In
the last 3 months of the year?
6. How many days in the first 6 months of the year? In the
last 6 months of the year?
7. How many days difference between the first 6 months and
the last 6 months of the year?
8. How many days in February, March, and April together?
9. In April, May and June together?
10. In July and August together?
11. In September, October and November together?
12. A man left home in the morning the first day of April and
returned home in the evening the last day of July.
How many days was he away from home?
13. How many days in the first, third, fifth, seventh, and
eighth months together?
NAMES AND ABBREVIATIONS OF THE MONTHS OF THE YEAR
IN ORDER, AND NUMBER OF DAYS IN EACH.
No.
Month.
Abbrev.
No. of
Days.
No.
Month.
Abbrev.
No.of
Days.
1
January . .
Jan.
31
7
July. .
31
2
3
4
5
February .
March . . .
April ....
Mav .
Feb.
Mar.
Apr.
28 (29)
31
30
31
8
9
10
11
August. . . .
September.
October . . .
November
Aug.
Sept.
Oct.
Nov.
31
3C
31
30
6
June.
30
12
December
Dec
31
110 RATIONAL ELEMENTARY ARITHMETIC.
1. How many square spaces in one row of A?
2. How many rows of 12 squares each in A?
3. How many squares in all of A?
4. 12 equals what part of 24? Of 36? 48? 60? 72? 84?
96? 108? 120? 132? 144?
5. 24 equals how many 12's? What part of 48? 72? 96?
120? 144?
6. 36 equals how many 12's? What part of 72? 108? 144?
7. 48 equals how many 12's? How many 24's? What part
of 96? 144?
8. 60 equals how many 12's? What part of 120?
9. 72 equals how many 12's? How many 24's? 36's?
What part of 144?
10. 84 equals how many 12's?
11. 96 equals how many 12's? How many 24's? 48 's?
12. 108 equals how many 12's? How many 36's?
13. 120 equals how many 12's? How many 24's?
14. 132 equals how many 12's?
15. 144 equals how many 12's? How many 24's? 36's?
48's? 72's?
BUILDING TABLE OF TWELVES.
Ill
TABLE OF TWELVES.
12X1 = 12 12X4=48 12x7= 84 12x10-120
12X2=24 12X5=60 12X8= 96 12x11 = 132
12X3=36 12X6 = 72 12X9=108 12X12 = 144
1. Add these numbers; subtract them; and multiply them:
28 53 45 33 48 57 74 66 90 38 99
12 12 12 12 12 12 12 12 12 12 12
67 89 78 49 96 50 87 29 82 59 88
1212121212121212121212
2. Divide:
12)36 12)60 12)72 12)28 12)49 12)56 12)66
12)71 12)108 12)99 12)120 12)84 12)144 12)132
3. 4 X 9 = ?
8X7 = ?
5 X 9 = ?
3 X 12 = ?
30 X 6 = ?
49 X 7 = ?
72 X 12 = ?
88 X 8 = ?
Add the heavy center number to each number in the same
large square. Subtract it from each number larger than
itself. Multiply and divide in the same way.
112 RATIONAL ELEMENTARY ARITHMETIC.
1 hour 1 day 1 week 1 year
60 minutes 24 hours 7 days 365 days
52 weeks
12 months
1. How many minutes in 1 hour? In 2 hours? 3 hours?
5 hours? 8 hours? One half an hour? One-fourth
of an hour? Three-fourths of an hour?
2. What part of an hour are 10 minutes? 30 minutes? 45
minutes? 15 minutes?
3. How many hours in a week?
4. How many weeks in 147 days?
5. A boy is 8 years and 4 months old. How many months
old is he?
6. The train leaves the station at 8.05. It is a 12 minutes'
walk to the station. At what time must one start in
order to catch the train?
7. A boy leaves home at 7.30 e^ch morning and returns from
work at 6.15 in the evening. How long is he away
from home? How long is he away in 6 days?
8. A train leaves the station at 7.15 and arrives in the city
at 7.42 in the morning. Returning, it leaves the city
in the evening at 5.40 and arrives at 6.11. How long
does a man spend on the train who goes back and forth
each day for 10 days?
9. A boy leaves home for school at 8.35 and reaches the
school room at 2 minutes before 9. He returns home
for lunch at noon, taking the same time on the way each
trip. How long is he on the way in 1 day? In 5 days?
10. School begins at 9 o'clock and dismisses at 15 minutes
before 12; opens at 1.30 and closes at 3.45. How long
is the forenoon session? How long is the afternoon
session? How long are both together?
11. If 15 minutes were allowed for recess both morning and
afternoon, how long would the sessions be together?
APPLICATION OF TWELVES. 113
1. Review pages 18 and 19 as oral work.
2. How many months old is a boy who is 7 years old ? How
'many weeks old is one who is 11 months old?
3. How many months old is a boy who is 11 years old? 12
years old?
4. How many weeks in 6 months?
5. How many minutes in one-half a day?
6. How many minutes from 7.15 a. m. to 8 o'clock a. m. ?
7. How many minutes from 8 o'clock p. m. to 9.15 p. m. ?
8. How many hours from 5 in the morning until 9 at night?
9. A boy goes to bed at 9 o'clock and gets up at 6. How
long is he in bed?
10. A boy plays ball in the morning from 7 until 9, and in
the afternoon from 4 until 6. How many hours does
he play?
11 A train leaves Chicago at 9 o'clock in the morning and
arrives in Cincinnati at 6 in the evening. How many
hours is it on the way?
12. A train leaves Chicago at 10.30 in the morning and
reaches Buffalo at 12.20 at night. How many hours is
it on the way?
13. A train leaves Washington at 9 o'clock in the morning,
and reaches New York at 2.15 in the afternoon. How
many hours is it on the way?
14. A train leaves Toledo at 4.30 p. m., reaches Cleveland at
9.10 p. m., and Buffalo at 2.40 a. m. How long is
it on the way from Toledo to Cleveland? How long
from Toledo to Buffalo?
15. A boat leaves Chicago at 8.30 in the morning, reaches
Milwaukee at 11.30, and leaving Milwaukee at 6.15 in
the evening, reaches Chicago at 9.15. How many
hours does it take to make the round trip? How many
hours from the time the boat leaves Chicago until if
returns ?
114 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 21, 51, 61, and 111 as oral work.
2. Albert is 5J years old. Edwin is 18 months older than
Albert. How old is Edwin? What is the difference
in years and parts of a year?
3. Mr. Walker gave his grandson, Willard, $5 to put in the
bank each year of his life. How much had Willard
put in the bank when he was 5 years old? 7? 12?
4. Lyman ran a mile in 10 minutes. John walked the same
distance in a quarter hour. It took John how many
minutes longer than Lyman? How many seconds?
5. A golf-player hired a caddy who worked for him 3 hours
and 20 minutes, at the rate of 15 cents an hour. How
much did the caddy receive?
6. Gerald earned $5 picking strawberries at the rate of 10
cents an hour. How many hours did he work?
7. Arthur, Harold, and Burton rented a boat for 6 hours for
$1.20. How much was that per hour? The boys
divided the expense equally. How much did each pay?
8. Paul and Herbert ran an automobile at the rate of 96
miles in 12 hours. How much was that per hour?
9. A carrier pigeon flew a distance of 560 miles in 7 hours.
How far was that per hour? At this rate, how far
could the pigeon fly in 5 hours? In 12 hours?
10. Wallace drove to his grandfather's, a distance of 90 miles,
in 12 hours. How far was that per hour?
11. Willie took a 5-hour steamboat ride, and in that time
traveled 90 miles. How far was that per mile?
12. Frank and Willis ran a race. Frank ran a mile in 7
minutes. Willis ran the same distance' in 12 minutes.
The difference is what part of an hour?
13. Paul's hat fell into the river and 6 hours later was found
42 miles farther down the river. How fast was the
river flowing?
FIVES, SIXES, SEVENS AND TWELVES. 115
1. Frank and David had an animal show one month. They
had 12 guinea pigs, 12 white mice, 7 rabbits, 6 pigeons,
5 dogs, and a pony. How many animals had they?
2. It cost them 55 cents a day for feed for the animals.
How much was that for a week? For 6 weeks?
3. They had the show in a lot, a part of which they fenced
off. This enclosed space was 20 feet long and 12 feet
wide. What was its area?
4. The pony was taught to walk a flat board which ran
around the top of the fence. How far did he walk in
going around it once?
5. The pony walked around the lot on the board 5 times
in 3 minutes. How many feet was that per minute?
6. There were three performances each day. The morning
one lasted from 8:45 to 9:30. How long was it?
7. The admission to the morning performance was 3 cents,
to the afternoon performance 5 cents, and to the even-
ing performance 7 cents. The first day of the show
8 persons attended in the morning, 7 in the afternoon,
and 12 in the evening. What did the boys receive
during that day? How much had they left after
subtracting the price of the feed for the animals?
8. The boys hired a phonograph for evening performances,
at 2 cents a night. How much did it cost in
a week of 6 days? Counting the phonograph and
the food, what were their expenses for 4 weeks?
9. One of the dogs was taught to jump from the top of a
ladder 28 feet high. At equal distances on this ladder
were platforms. The first was J of the way up. How
many feet from the ground was it? How many feet
from the ground was the second platform? The third?
How many feet between the first and third! plat-
forms?
110 RATIONAL ELEMENTARY ARITHMETIC.
WRITING AND READING NUMBERS.
1. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
2. How many different characters are given above?
All numbers, no matter how large, may be represented by
these figures.
3. 243
Reading the 3 alone we say 3 ones. Reading the 4 alone
we say 40 or 4 tens. Reading the 2 alone we say 200
or 2 hundreds.
4. If we were to write above each figure a separate name it
would appear:
5 8 a
WHO
243
if we were to call these all ones, we would read it as
243 ones or units.
5. How would you read 3,243?
6. This new figure, 3, placed before the other number, we
call thousands. How then would you read 10,243?
7. Large numbers are divided into periods of 3 places each,
beginning with ones. Thus 243 is one period. 3,243
has 2 periods. These periods are separated by commas,
for convenience, as follows:
Ones
9, 4 5 6
How many periods in the following numbers? Separate
the periods by commas:
346 4684 26 3781 1032
WRITING AM) UKAlHXc; NUMBERS. 117
1. Head the following numbers, pointing off periods:
5784 8752 9872 6375 7365
3586 7678 6498 8988 8989
2987 5425 5674 7988 6543
2. Write the following numbers, with ones in the right hand
column, with tens, hundreds and thousands in their
columns as shown on the opposite page:
Seventeen. Two hundred twenty-seven. One hundred
seven.
Thirty-one. Three hundred twelve. One hundred.
Sixty-eight Sixty hundred eighty. Nine hundred.
One thousand. Eleven thousand. Eight hundred.
One thousand two hundred. Six hundred twenty- ^ive.
One thousand sixty. Two hundred seventy-five.
One thousand six hundred fifty. One hundred seven.
One thousand ten. One thousand one hundred.
Five thousand six hundred fifty-five. Nine hundred.
Three thousand three hundred. Seventy -five.
Three thousand thirty. Four hundred twenty -five.
Six thousand six. Eight hundred seventy-nine.
3. Write in words or read from the oage:
125 683 1200 4816 5090
307 469 3049 1010 9847
590 303 5060 5064 3005
483 791 2009 3100 4200
4. In writing numbers for addition and subtraction, it is
more convenient to place ones underneath ones, tens
under tens, hundreds under hundreds, etc.
5. Write for addition the following numbers:
640, 35, 1282, 6, 821, 64, 8, 2305
6. Write the following for subtraction:
From 872 take 6. From 6475 take 242. From 3684
take 27.
118 RATIONAL ELEMENTARY ARITHMETIC.
MEASURE OF LENGTH.
1. Review page 3 as oral work.
2. Measure off distances of 1 in., 1 ft., 1 yd., 1 rd.
3. Robert repaired two rods of fence for his father.
How many yards was that? How many feet?
4. Susan had a hat which measured 1J yards around
the rim. At the back of rim was a knot of
ribbon. The hat blew off and rolled on its rim
down the street. Susan counted the number
of times it turned by the marks of the knot of
ribbon in the dust. There were nine marks.
How many yards did her hat roll?
TABLE.
1 rd. = 161 ft. = 5J yds.
1 yd. =3 ft.
1 ft. = 12 in.
SURFACE MEASURE.
5. Review pages 5, 53, and 81 as oral work.
6. On page 81, what does the drawing represent?
To what scale is it drawn? Using paper and
ruler, measure off and cut out a square yard.
Divide into square feet and cut again.
7. Divide each side of your square foot of paper
into inches by placing points. How many
inches are there on each side? Connect ex-
actly opposite points by drawing straight lines,
dividing the square foot with square spaces.
Each space has what area? How many square
inches in 1 row? In all the rows? How many
square inches in one square foot?
TABLE.
1 sq. yd. =9 sq. ft.
1 sq. ft. = 144 sq. i]
THREES, SIXES, NINES, ELEVENS, TWELVES. 119
1. Review pages 51, 83, 107, and 111 as oral work.
2. Ben and Richard were given a box of tools for Christmas.
Among the tools were a foot ruler, a yard-stick, and a
long tape-measure. Their father allowed them to have
a vacant lot for a play-yard. They fenced the lot
with wire, using 80 feet of wire to go around it once.
The lot was 20 feet wide. How long was it?
3. How many yards long was the lot? How many yards
wide?
4. The boys made a 3-wire fence. How many feet of wire
did they use?
5. In making the fence they first placed posts at the corners
and every 5 feet between. How many posts were used?
6. A line 1 rod long was drawn from the middle of one side
through the middle of the field to divide it into 2 equal
spaces. How many yards long was the line? How
many feet?
7. In one corner of the lot the boys built a workshop. If was
built against the corner of the fence and extended 9
feet along one side of the lot and 6 feet along the adjoin-
ing side. What was the area of the floor? How
many square yards in it?
8. The workshop was 7 feet high. How many square feet
in each side wall? Each end wall? All the walls?
How many square yards in all the walls?
9. There were 2 windows in the shop. One had 2 panes,
each 12 by 15 inches, and the other 4 panes 10 by 12
inches. How many square inches of glass were used?
10. The door was 6 feet high and 3 feet wide. How many
square yards of space did it fill?
11. Under a tree in one end of the lot the boys built a bench
6 feet long and 18 inches wide. What was the area of
the top of the bench?
120 RATIONAL ELEMENTARY ARITHMETIC.
SCALE DRAWING OF TILING. 121
1. Page 120 shows a scale drawing of one inch to 2 ft. It is
the picture of the tiling in a small hall. How long is
the hall? How wide is it?
2. The expense of tiling the 4 corners, A, was $1.80. How
much was that per square foot?
3. The cost of tiling the outside border on the north, B
(without the corners), was $2.40. How much was that
per square foot? At that rate, what was the cost of
tiling the whole outside border, B?
4. The expense of tiling the corners, C, was $1.30 for each.
How much was that per square foot? How much was
it for the 4 corners?
5. How many square feet in D? In the 2 D's?
6. At 55 cents a square foot, how much did it cost to tile
D? The 2 D's?
7. The cost of tiling one inside border, E, was $2.88. How
much was that per square foot?
8. At the same rate, what did the 2 E's cost?
9. What is the area of F? Of G?
10. The cost of tiling F was $2.70. How much was that per
square foot? At that rate, what was the cost of tiling
the 2 F's?
11. The cost of tiling G was $3.12. How much was that per
square foot? At that rate, what did it cost to tile the
2G's?
12. What was the expense of tiling the 2 Fs and the 2 G's
together?
13. What was the expense of tiling the 2 E's, the 2 D's, and
the 4 C's?
14. What was the cost of tiling the entire outside border,
counting the corners?
15. What was the cost of tiling this whole hall?
16. How many square feet in the hall?
122 RATIONAL ELEMENTARY ARITHMETIC.
LIQUID MEASURE.
1. Review pages 8, 9, and 67 as oral work.
2. Dorothy bought for the Christmas baking, 3 quarts of
molasses, at 120 a quart; 2 quarts of maple* syrup, at 220
a quart; 2 quarts of cream, at 200 a quart; $ gallon
of cherry vinegar, at 220 a gallon; and 3 pints of milk,
at 6 cents a quart. What was her bill?
3. Amelia made 4 gallons of lemonade for a picnic. She
sold it in pint glasses, at 5 cents a glass. How much
did she receive for it?
4. Willis sold 9 gallons of milk at 6 cents a quart. How
much did he receive for it?
5. Walter bought a gallon pail. He carried it full 31^ times
to fill a barrel. How many gallons did it take?
TABLE.
1 barrel (bbl.) - 31J gal.
1 gal. 4 qt.
1 qt. =2 pt.
DRY MEASURE.
6. Review pages 10 and 11 and 67 as oral work.
7. Anderson shelled 50 bushels of corn a day for 6 days.
How many bushels did he shell in the week? How
many pecks?
8. James picked 7 pecks of tomatoes for his grandmother to
can. How many quarts was that?
9. Archie gathered 5 bushels of apples from the ground in
his father's orchard. How many pecks was that?
10. If they sold at 50 cents a peck, how much money did he
receive for them?
TABLE.
Ibu. == 4pk.
1 pk. =8 qt.
1 qt. =2 pt.
TWOS, FOURS, AND EIGHTS.
123
1. There were 3 crews of 8 oars each in a boat race. How
many men rowed in the race?
2. An ocean liner crossed the Atlantic in 8 days. How
many trips of that length could it make from August
first to September second?
3. In an art gallery were 32 oil paintings and i as many
etchings. How many etchings and paintings were in
the gallery?
4. Amanda hired a pony carriage in the park at 8 cents an
hour. She kept it 2J hours. What did she pay for it?
5. Amelia sold 4 dozen paper roses at 2 cents each. How
much did she receive?
6. Add:
279
372
782
372
687
684
698
698
987
249
726
496
726
684
872
842
891
982
928
698
7. Subtract:
407 598
316 499
326
197
682
721
129
8.
9.
Multiply :
4872
4
8649
8
38765
3
7642
4
8347
8
17563
4
12643
3
6498
4
8)2046
Divide :
4)7205
8)6723
4)1062
2)13716
4)26718
8)19464
2)11356
124 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 14 and 15 as oral work.
2. How many 2-oz. packages of cinnamon can be made
from 1 Ib. of cinnamon?
3. How many 4-oz. packages of ginger can be made from
5 Ibs. of ginger?
4. What is the cost of a 2-oz. package of pepper at 40 cents
a pound?
5. How many ounces in J pound? In \ Ib.? In \ Ib.? In
fib.? In |lb.?
6. What will 4 oz. salted almonds cost at 60 cents a pound?
7. What will 12 oz. caramels cost at 32 cents a pound? .
8. What will 9 oz. spices cost at 48 cents a pound?
9. What will 12 oz. cheese cost at 16 cents a pound?
10. A grocer bought 25 Ib. tomatoes at 3 cents a pound, sold
15 Ib. at 5 cents a Ib., 7 Ib. at 3 cents a pound, and the
rest spoiled. How much did he make on the tomatoes?
11. A dealer bought 50 Ibs. coffee at 26 cents a pound. He
divided it into 1-lb. sacks and sold it all at 35 cents a
sack. If the sacks cost \ of a cent apiece, how much
did he make on the coffee?
12. Find the total cost of 8 Ib. candy at 35 cents a pound, and
of 12 Ib. of nuts at 12 cents a pound?
13. Find the total cost of this bill:
3 Ib. butter at 27 cents a pound.
5 Ib. honey at 18 cents a pound.
7 Ib. beefsteak at 14 cents a pound.
25 Ib. flour at 4 cents a pound.
4 Ib. cheese at 11^ cents a pound.
14. Find the total cost of this bill :
4 oz. cloves at 60 cents a pound.
2 oz. pepper at 48 cents a pound.
12 oz. cheese at 12 cents a pound.
4 Ib. crackers at 6 cents a pound.
MEASURES OF WEIGHT. 125
1. How many 5-lb. sacks of salt are there in a 300-lb. barrel
of salt?
2. A grocer paid $2.40 for a 300-lb. barrel of salt and sold it
out in 5-lb. sacks at 5$ each. How
much did he make?
3. If a grocer pays 2J cents a pound for
flour and sells it at 4 cents a pound,
how much does he make on a 50-lb.
sack? A 100-lb. sack? A 25-lb.
sack?
4. How many sacks of 50 Ib. each can be
made from 525 Ibs. of flour?
5. How many sacks of 5 Ibs. each can be
made from 280 Ib. of salt?
6. A bushel of potatoes weighs
60 pounds. What is the
weight of 6 bushels? 8
bushels? 12 bushels? 25
bushels? 36 bushels?
7. A bushel of shelled corn weighs 56 pounds. How much do
4 bushels weigh? 9 bushels? 12 bushels? 16 bushels?
28 bushels?
8. The persons in a picnic party of 6 people weighed 178 Ib.,
136 Ibs., 125 Ibs., 82 Ibs., and 64 Ibs. How much did
the whole party weigh? ' What is the difference be-
tween the weights of the heaviest and the lightest
persons?
9. If the total weight of a party of 12 persons was 1200 Ibs.
and all persons were of the same weight, what was the
weight of a single person (average weight of a
person) ?
10. Find the average weight of a person of the party of
problem 8?
126
RATIONAL ELEMENTARY ARITHMETIC.
12
10
10
Figure A Figure B
1. Multiply each number in the outside spaces of Fig. A
by the center number.
2. Change the center number in Fig. A to:
5; 3; 7; 6; 4; 8; 9; 12; 11; 10.
3. Each time the center number is changed, multiply all the
other numbers by it.
4. Divide the center number in Fig. B by each of the
other numbers. When there is any remainder, name
it, also.
5. Change the center number to:
21; 24; 28; 36; 42; 44; 45; 48; 60; 54; 56; 64; 65; 66;
72; 81; 88; 90; 96; 100; 121; 132; 108; 144.
6. Each time the center number is changed, divide each of
the other numbers by it.
7. How many 2's in 6? 8? 10? 12? 24? 50? 56? 90?
124? 132? 144?
8. How many 3's in 9? 15? 21? 33? 39?
9. How many 4's in 8? 12? 24? 16? 32? 20?
10. How many 5's in 25? 20? 60? 45? 35?
11. How many 6's in 18? 12? 24? 42? 48? 66? 72?
54?
12. How many 7's in 35? 49? 21? 14? 63? 42? 70?
13. How many 8's in 16? 32? 48? 64? 24? 40? 56?
THE DOZEN. 127
Find the cost of:
1. 3 dozen eggs at 18 cents a dozen.
2. 5 dozen oranges at 25 cents a dozen.
3. 4 dozen lemons at 20 cents a dozen.
4. 6 dozen bananas at 22 cents a dozen.
5. 2 dozen tablets at 9 cents a tablet.
6. 7 dozen pencils at 35 cents a dozen.
7. 8 dozen buttons at 27 cents a dozen.
8. 12 dozen candles at 10 cents a dozen.
9. 10 dozen spools of cotton at 50 cents a dozen.
10. 11 dozen spools of silk at 90 cents a dozen.
11. 15 dozen erasers at 25 cents a dozen.
12. 14 dozen pairs of scissors at $1.80 a dozen.
13. 13 dozen pairs of stockings at $1.50 a dozen.
14. 16 dozen pairs of suspenders at $1.25 a dozen.
15. 19 dozen pens at 5 cents for each pen.
16. 17 dozen bottles of ink at 3 cents a bottle.
17. 18 dozen bags of salt at 5 cents a bag.
18. 12 dozen tooth-brushes at $1.60 a dozen.
19. 10 dozen bottles tooth-powder at $1.00 a dozen.
20. 15 dozen pears at 30 cents a dozen.
21. 8 dozen pretzels at 8 cents a dozen.
22. 16 dozen loaves of bread at $.05 a loaf.
23. 19 dozen foot-rules at 1 cent apiece.
24. 14 dozen blotters at 5 cents a dozen.
25. 15 dozen pieces of dustless crayon at 10 cents a dozen.
26. 18 dozen tubes of paste at 50 cents a dozen.
27. 13 dozen bottles of glue at $1.00 a dozen.
28. 9 dozen boxes baking powder at 15 cents a box.
29. 8 dozen jars preserved ginger at 25 cents a jar.
30. 4 dozen photo frames at 10 cents each.
31. 15 dozen papers of pins at 5 cents a paper.
32. 11 dozen papers hooks and eyes at 5 cents a paper.
128 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 28 and 29 as oral work.
2. Of the school children in a certain city 3,495 are boys and
2,837 are girls. What is the total school attendance?
3,495 girls 7 and 5 are 12, 1 ten and 2 units.
2,837 boys Write the 2 units. Then, 1 ten and 3 tens
6,332 total an( j 9 tens are 13 tens, = 1 hundred and
3 tens. Write the 3 tens.
Continue in this way till all numbers are added.
Show how the last two figures, the 3 and the 6, are
found in the total.
Read the total.
3. In a town there are 1676 grown persons and 2475 children.
How many people are there in this town?
4. In one library there are 3528 books, and in another, 4695
books. How many in both libraries?
5. There are 5374 miles of railroad in one state and 2868
miles in another. How many miles of railroad in both
states?
6. In one year a fruit grower sold 3448 boxes of berries and
3976 boxes the next year. How many boxes of berries
did he sell during those two years?
7. A man bought a lot for $2,350 and built a house on it
which cost him $7,898. What did both cost him?
8. Add:
2037 8226 4587 1284 7431 3368 3643
4256 975 3624 7536 1869 4852 5892
4768
3579
1928
4536
5948
6384
7463
1359
2468
3746
2879
3726
1597
1859
5762
3478
6712
4726
8721
6975
6721
3498
7842
6721
3497
6829
8982
9762
EXERCISES IN ADDITION. 129
1. Four loads of coal were delivered at a residence. The
first weighed 2564 pounds, the second 3148' pounds, the
third 2866 pounds and the fourth 2645 pounds. What
was the total weight of coal delivered?
THE WAY WE ADD.
2564 Ib. 5 (and 6), 11, (and 8), 19, (and 4), 23, = 2
3148 Ib. tens and 3 units. Write 3, as shown. Then,
9*u* IK' 2 (and 4) ' 6 ' (and 6) ' 12 ' (and 4) ' 16 ' (and 6)> 22;
^!5 l 22 tens are 2 hundreds and 2 tens. Write the
b ' 2 tens. Then 2 (and 6), 8, (and 8), 16, and so on.
In adding we speak only the numbers outside
the (). Check, or test, the correctness of your addition
by adding the columns from the top downward.
2. How can you prove your result in problem 1? Why
should you always prove your results in addition?
3. A man had 5 farms. In the first there were 160 acres, in
the second 88 acres, in the third 275 acres, in the fourth
96 acres and in the fifth 324 acres. How many acres
are there in the five farms?
4. There are 375 pupils in one school building, 640 in another
and 583 in another. How many children are there in
the three buildings?
5. Add and test your results:
1729 3546 1892 1563 2623 1089 2703
2354 1273 4203 2427 1206 721 3145
4162 2098 461 5314 4257 5147 605
1431 1754 2574 256 1714 2425 2804
947 6126 1245 4678 6924 3987 3004
2753 825 3256 963 728 4058 289
1388 1268 1367 2837 1256 874 1452
5234 1834 2765 1234 473 1498 3257
130 RATIONAL ELEMENTARY ARITHMETIC.
1. A man paid $2684 for a house, $398 'for furniture and
$265 for a horse and carriage. How much did he pay
for all?
2. A lot cost $1540, the sidewalk $116, the house $6535, the
barn $975. How much did they all cost?
3. A ship sailed 234 miles the first day, 275 miles the second
day, and the third day as far as in the first two. How
far did it sail in the three days?
4. Three vessels are loaded with copper. The first carries
34T tons, the second 1256 tons, the third 4384 tons.
How many tons do they all carry?
5. From Detroit to Buffalo it is 251 miles; from Buffalo to
New York City 410 miles; from New York to Washington,
D. C., 228 miles. How far is it from Detroit to New
York City? From Detroit to Washington by way of
New York City?
6. From Burlington to Omaha it is 296 miles; from Omaha
to Lincoln 39 miles; from Lincoln to Denver, 484 miles.
How far is it from Burlington to Lincoln? From
Burlington to Denver?
7. From Milwaukee to La Crosse it is 281 miles; from La
Crosse to St. Paul, 131 miles; from St. Paul to Minne-
apolis, 10 miles. How far is it from Milwaukee to
Minneapolis?
8. From Omaha to Cheyenne is 516 miles; from Cheyenne to
Ogden, 484 miles; from Ogden to Sacramento, 743
miles. How far is it from Omaha to Sacramento?
9. How far is it from the town where you live to the capital
of your state? From the town where you live to
Washington, I?. C.? From your home town to San
Francisco?
10. Using the distances found in railway time tables, make
and solve problems like those above.
11. Using the scale of miles given on a map, make and solve
problems like those above.
PROBLEMS IN ADDITION. 131
1. A man has 156 books in one case, 275 in another and in a
third 145 more than in both of the others. How many
books has he in the 3 cases?
2. A factory made 540 bicycles in January; 375 in Febru-
ary; 643 in March, and 856 in April. How many did
it make in the 4 months?
3. A man delivered 4 loads of coal. In the first were 2150
pounds; in the second, 1975 pounds; in the third, 2260
pounds, and in the fourth, 2315 pounds. How many
pounds were delivered in the 4 loads?
4. A carpenter was paid $1375.50 for building one house;
$3240.75 for another; $1658.50 for a third. How
much did he receive for building the 3 houses?
5. The cash sales of a certain merchant were on Monday,
$253.25; Tuesday, $167.54; Wednesday, $365.80;
Thursday, $453.65; Friday, $385.42, and on Saturday,
$563.85. What were the cash sales for the week?
6. A man bought a lot for $2154. He paid $453 for grading
and digging a cellar, and $165.40 for a sidewalk. He
built a house to cost the same amount that he had spent
for the lot and all improvements. How much did he
invest in the lot and house?
7. A man's salary was $2300 a year. He also received $135
interest, $426 rents, and from all other sources a sum
equal to these three amounts. What was his annual
income ?
8. The yield from one field of wheat was 275 bushels; from
a second, 562^ bushels; from a third, 458 bushels, and
from a fourth, 346J bushels. What was the entire
yield from the 4 fields?
9. From A to B is 416 feet and 6 inches; from B to C, 375
feet; from C to D, 456 feet and 6 inches. How far is
it from A to D?
132 RATIONAL ELEMENTARY ARITHMETIC.
SCHOOL SUPPLIES.
Box paper, per box . . .
Pen tablet, each
Envelopes, package. . .
Pencil tablet, small, eac
Pencil tablet, large, eacl
Penholder, each
Pens, per doz
Pencils, soft, each ....
Pencils", medium, each.
Pencils, hard, each .
. 15 | Colored pencils, each
05 ! Ink, small bottle
.03 Erasers,
05 Brass ed;
05 i Note-books, thick, each . . '. .
. 10 j Paper fasteners, p<
,01 j Note-book covers, t,..,...*,.^^..
03 | Note-book covers, large, each
,05 j Pencil sharpeners, each
ALICE SMALL,
Pleasantville, Ohio.
Box of Paper $0.35
.05
.05
.03
.05
.15
Alice bought a box of paper, a
pencil tablet, a hard pencil, an
eraser, a brass edged ruler,
and a small note-book cover.
How much did she spend?
Pencil Tablet.
Hard Pencil
Eraser
Brass Edged Ruler .
Small Book Cover..
2. Charles bought three colored pencils, a bottle of ink, a
thick note-book, a penholder, two dozen pens, two soft
pencils, and a pencil tablet. How much did he spend?
3. Harry bought two packages of envelopes, three five-cent
pencil tablets, 2 pen tablets, 2 pencils of each kind, a
5-cent eraser, and a brass-edged ruler. He gave the
clerk a dollar. How much change was due him?
4. William bought a large note-book cover, a pencil sharpener,
2 dozen paper fasteners, 4 medium pencils, a 5-cent
eraser, 2 pen tablets. He gave the clerk one dollar.
What was the correct change?
5. At prices given in the above list, how much would it cost
to supply a school of 45 children each with the following :
a pen tablet; two 3-cent pencil tablets; a penholder; a
dozen pens; 2 soft pencils, and a brass-edged ruler?
6. Make problems supplying a number of pupils in your
school with some of the articles in the list.
FURNISHING A HOME.
PRICES OP FURNITURE.
133
Metal \
Dressei
Wash-s
Davenport :...... 55.00
Bookcase 15.00
Small desk 12.50
Combination desk and
bookcase 33 . 00
Morris chair 15.00
(Quarter-sawed oak dining-
table 29.75
Dining-room chair 3.95
Kitchen table . 3.00
Bedroom stand
Dressing-table
Shaving-stand
Hall chair ;
Stiff-backed chair. . . .
Armchair
Foot r,est
Large desk
Wicker rocker
Polished topped stand
Sideboard
1. At the prices given in this list, what is the cost of furnish-
ing a kitchen with a small range, a kitchen table, a
refrigerator, and a spice chest?
2. Find the cost of a quarter-sawed oak dining-table, a side-
board and 6 dining-room chairs.
3. Find the cost of furnishing a room with a metal bedstead,
a dresser, a washstand, a polished topped stand, a
stiff-backed chair, and 2 common rockers.
4. Find the cost of furnishing a room with a metal bedstead,
a shaving-stand, a dresser, a bedroom stand, a rocker,
a stiff-backed chair, and a foot rest.
5. Find the cost of furnishing a room with a metal bedstead,
a dressing-table, a small desk, a rocker, and a stiff-
backed chair.
6. Find the cost of furnishing for a living-room a daven-
port, a Morris chair, 2 wicker rockers, 2 common rock-
ers, 2 stiff-backed chairs, a foot rest, a bookcase, a large
desk, and a polished topped stand.
7. Find the cost of buying for a house 2 metal bedsteads,
2 dressers, a shaving-stand, a dressing-table, 4 rockers,
a Morris chair, and a davenport.
8. Furnish rooms as you wish and find the cost of furnishing.
134 RATIONAL ELEMENTARY ARITHMETIC.
1. A horse traveled 7 miles an hour the first hour of a journey,
6 miles an hour the next 2 hours, and 5 miles an hour
the next 5 hours. How many hours did he travel?
How far did he travel in that time?
2. A man walked 4 miles an hour for 3 hours, 5 miles the
next hour, and 3 miles an hour the next two hours.
How many hours did he travel? How far did he travel
in that time?
3. In an automobile race one of the racers ran his car 90
miles an hour for 6 hours and 95 miles an hour for 6
hours. What distance did he travel in the 12 hours?
4. A grizzly bear traveled 11 miles 1 day, twice as far the
next day, one-half as far the third day as the second.
How far did he travel in the 3 days?
5. A boy rode on his bicycle 10 miles the first hour, the same
distance and 5 miles more the second hour, which was
three-fourths of what he rode the third hour. How far
did he ride the second hour? The third? In the three
hours?
6. A special train made the following runs: The first hour
28 miles; the second hour 8 miles farther than the
first; the third hour two-thirds as far as the second,
and the fourth hour 40 miles. How far did it run the
second hour? The third? In the 4 hours?
7. In a large city factory there are 28 persons working on
the first floor, one-half that number on the second floor,
4 times as many on the third as on the first floor, one-
half as many on the fourth as on the third, and 30 on
the fifth. Make a list of the number of persons on
each floor. How many persons on the 5 floors?
8. In a small library there were 78 science books, one-half as
many histories and 3 times as many story books as
science books. How many books were in the library?
PROBLEMS IN ADDITION. 135
1. Joseph paid $18 for a spring suit, two-thirds as much for
an overcoat, one-ninth as much for a hat as for the suit,
and one-sixth as much for 2 shirts as for the suit. How
much did the overcoat cost? The hat? The 2 shirts?
How much money did he spend in all?
2. Alice paid $12 for a new coat, one-half as much for a
skirt, one-third as much for a hat as for the coat, one-
fourth as much for a pair of shoes as for the coat, and
one-third as much as the shoes cost for a new pair of
gloves. How much did the skirt cost? The hat? The
shoes? The gloves? How much did Alice spend in all?
3. Julian spent 20 cents for shoe-polish, one-fourth of a dol-
lar for a tooth-brush, three-fourths as much for soap as
for polish, and twice as much for a hair-brush as for
a tooth-brush. How much did the tooth-brush cost?
The soap? The shoe-polish? The hair-brush? How
much did Julian spend in all?
4. Andrew bought a leather cap for 50 cents, a fishing-rod
for one-half as much, a pair of rubber boots for 4 times
as much as for the cap, a fish-basket for 3 times as
much as the cap cost, and a can of bait for 15 cents.
How much did the fishing-rod cost? The rubber boots?
The fish-basket? How much money did he spend alto-
gether?
5. Herman bought the following:
5 packages of petunia seed at 5 cents a package.
2 packages giant pansy seed at 20 cents a package.
J pound of nasturtium seed at 10 cents an ounce.
1J ounces of canary bird vine seed at 14 cents an ounce.
4 packages of aster seed at 10 cents a package.
3 packages' of sweet-william seed at 8 cents a package.
6 packages of columbine seed at 10 cents a package.
What was his bill?
136 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 33 and 34.
2. A man paid $425 for one horse and $246 for another.
How much more did one horse cost than the other?
From $425 6 from 15 leaves what?
take 246 4 from 11 leaves what?
$ ? ? ? 2 from 3 leaves what?
3. The walls and ceilings of one room contain 444 square
feet; those of a second room contain 159 square feet
less. How many square feet in the second room?
From 444 square feet Explain how each figure of the
take 159 difference is found.
J '> (I K
4. A gentleman's salary is $2650 a year; if his expenses for
the same time are $2075, how much does he save in one
year? Test.
5. If one ship sails 645 miles in 3 days, and another sails
712 miles in the same time, how much farther does the
second sail than the first? At the same rate, how much
farther would it sail in one day? In 9 days?
6. 223 - 144 = ? 10. 362 - 279 = ? 14. 902 - 873 = ?
7. 201 178 = ? 11. 666 177 = ? 15. 777 188 = ?
8. 542 - 263 = ? 12. 975 - 887 = ? 16. 864 - 579 = ?
9. 831 - 548 = ? 13. 274 - 187 = ? 17. 743 - 654 = ?
18. On Tuesday a merchant placed in the bank $465. On
Saturday he drew out $278. How much did he still
have in the bank? Test.
19. At an election the successful candidate received 913 votes,
and the unsuccessful candidate 658 votes. Find the
majority of the former. Test.
20. Find the difference between one year and 287 days.
21. A cistern holds 235 barrels of water when full. It now
contains 178 barrels. How many more barrels will it
hold?
EXERCISES IN SUBTRACTION. 137
1. Subtract 4586 from 6352.
F 5 6352 ^ e sma ^ numbers written above the
S bt t 4586 figures of 6352 show how to think
6352 into parts to subtract 4586 from
it. The numbers mean that 52 is 40 + 12, then 34 = 20
and 14, and 62 = 50 and 12.
-^ 6i !?^!, 4 Tell where the 14 above the 4 comes
2. From 7374
Subtract 4687 fr m; the 16 ab Ve the 7; the 12;
2687 the 6>
3. Solve in the way you like the better:
Subtract :
4352 6234 8132 9457 5321 3324 7563
2676 1395 5786 3869 1867 1657 2786
8967 8241 7241 7294 7182 9256 6842
3429 3819 398 5076 3647 7498 3715
7586 6493 4250 8593 5721 5345 5765
3248 4729 1575 7279 3809 2675 3629
4792 6820 8901 7002 6840 7080 8200
3489 5761 6820 6111 3471 4121 6712
4802 3768 8421 6704 8782 6818 2176
4000 3200 300 6110 4010 3720 617
3007 4800 3000 3710 6704 6070 4000
2060 2170 2210 2000 3078 307 2099
138 RATIONAL ELEMENTARY ARITHMETIC.
1. A tank that holds 3324 gallons lacks 1576 gallons of being
full. How many gallons does it contain?
From 3324, minuend,
take 1576, subtrahend.
1748, difference or remainder.
Explain how each figure of the difference is found.
2. One year a grocer sold 17,206 dozen eggs and the next
year 21,119 dozen. How many more dozens did he sell
the second year than the first?
3. Find the unknown number and test the result in each case:
Difference or Remainder.
869
76,928
4. During the year 1897, 2321 immigrants went to live in
Louisiana and 1872 went to live in Texas. How many
more went to Louisiana than to Texas?
5. The battleship New York takes the place of 8200 tons of
water when it is afloat; the battleship Texas, of 6315
tons. How much more water does one ship displace
than the other?
6. The coast line of North America is 24,040 miles; that of
South America, 13,600 miles; and that of Europe, 17,200
miles. How many more miles of coast line has North
America than South America? North America than
Europe? Europe than South America?
7. In 1896, 6511 horses were brought into this country from
British North America; in 1897, 4777. How many
more were brought in in 1896 than in 1897?
Minuend.
Subtrahend
(a) 3211
2933
(b) 7235
6856
(c) ?
5945
(d) 85,004
25,687
(e) 62,130
38,685
(f) ?
91,617
PROBLEMS IN SUBTRACTION. 139
1. From a farm containing 1100 acres, the owner sold 894
acres. How many acres had he left?
2. The area of Virginia is 42,450 square miles; of Pennsyl-
vania 45,315 square miles. Which is the larger? How
much?
3. A farm cost $3215. The buildings cost $627 less than
the farm. How much did the buildings cost?
4. Subtract and test each result:
(1) (2) (3) (4) (5) (6)
4*352 8132 9457 5321 6234 9257
2672 5786 3869 1867 1395 6389
(7)
(8)
(9)
(10)
(11)
(12)
3324
7563
7241
9256
8200
2354
1657
2786
2398
7498
6712
1876
(13)
(14)
(15)
(16)
(17)
(18)
4250
4060
3006
4523
3132
7345
1575
2099
2217
2657
1854
5868
(19)
(20)
(21)
(22)
(23)
(24)
* 6352
9374
7374
5432
8513
5345
4576
4687
4687
1845
6729
2678
5. One railroad has 5214 miles of track; another has 2767
miles of track. How much more track has the first
than the second?
6. A gentleman's income one year was $1985 and the next
year it was $2140. How much greater was his income
the second year?
7. Two vessels start from the same point at the same time
and in the same direction. The one travels 829 miles
while the second is traveling 1014 miles. How far are
they apart?
140 RATIONAL ELEMENTARY ARITHMETIC.
1. A slow river flows 15,840 feet an hour. A rapid river flows
36,960 feet in an hour. What is the difference in the
distances covered by the two in one hour?
2. A carriage was bought for $325, a horse for $175, and a
sleigh for $150. A payment of $125 was made on the
carriage, a payment of $112 on the horse, and a payment
of $56 on the sleigh. How much was there left to pay
on the carriage? The horse? The sleigh? On all?
3. Subtract:
4,726 8,092 8,294 6,826 4,072
3,987 7,963 7,982 5,982 3,987
67,829
39,879
67,000
59,811
68,750
58,792
83,607
59,879
96,702
69,892
89,020
84,948
82,020
72,919
80,980
25,751
71,000
36,987
10,101
9,899
47,020
39,891
36,072
32,697
78,987
58,999
60,507
57,251
98,572
95,989
4. From the beginning of the Mississippi River to the Gulf of
Mexico the water travels 4,200 miles. The Amazon River
is 3,600 miles long. How much longer is the Mississippi
than the Amazon?
5. One car contains 35,352 pounds of coal, another contains
26,475 pounds. How much more does the first contain
than the second?
6. How many persons are there in the capital city of your
state? How many persons in the capital city of some
adjoining state? Find the difference in the population
(number of persons) of these two states.
7. Make problems similar to 6, using the population of other
states and of cities.
DRILL IN FUNDAMENTAL OPERATIONS. 141
1. Ellen earned 90 cents and spent 35 cents and a dime.
How much had she left?
2. Edward bought a $1.35 football and gave the clerk a
2-dollar bill. How much change did he receive?
3. Mary's mother gave her 85 cents. She bought a 10-cent
tablet and a 25-cent book-cover. How much money
had she left?
4. Fred received $1.27 selling papers. He had to expend
$.92 for new papers. How much did he gain?
5. A picture was bought for $92.00 and sold for $125.00.
How much did the owner gain?
6. A horse that was bought for $118 was sold for $138.
What was the gain?
7. Butter was selling at 42 cents, but was reduced or cut in
price 7 cents a pound. What was then the selling price?
8. A cow was bought for $47 and sold for $34. What was
the loss?
9. A man's wages were raised from $1.25 to $1.85 a day.
What was the gain in 1 day? In 1 week of 6 days?
10. What was the gain of this man in 4 weeks? What was
the gain in 2 months?
11. His expenses were $1.00 per day. How much did he
save a day after his advance?
12. How much did he save in a week? In 4 weeks?
13. From a field containing 78 sheep, 14 were taken at one
time, 10 at another, and twice 9 were taken. How
many sheep were left in the field?
14. A boy was given $5 for car-fare for 3 months. The first
month his car-fare amounted to 99 cents; the second
month to $1.05, and the third month to $2.07. How
much had he left of the $5?
15. Out of 107 rose bushes set out, 18 died and 29 were pulled
up. How many werejeft to grow?
142 RATIONAL ELEMENTARY ARITHMETIC.
1. Review page 37.
2. If a man earns 27 cents an hour, how much will he earn
in a ten-hour day?
3. How many fingers and thumbs are there on four dozen
pairs of gloves?
4. Multiply each of the following numbers by 10; by 100:
4, 6, 8, 10, 3, 9, 7, 5, 11, 14, 25, 73, 243, 649.
How may we multiply a whole number by 10? By 100?
5. If one spool of darning cotton contains 45 yards, how
many yards will 30 spools contain? 45 yards
30 times 45 yards equals how many 30
times 10 times 45 yards? 1350 yards
How may we multiply any number by another number
ending in zero?
6. What is the cost of 900 bushels of oats at 36 cents a bushel?
7. Multiply:
84 96 75 68 237 485 379 946
20 30 40 50 60 70 80 90
49 54 124 272 234 563 847
300 400 500 600 700 800 900
8. What will 40 tons of hay cost at $18 a ton?
9. A bushel of wheat weighs 60 pounds. What is the weight
of 231 bushels?
10. If a train goes at the rate of 40 miles an hour, how far
will it go in 24 hours?
11. How many times will a clock strike in 30 days if it strikes
156 times each day?
12. How many ounces are there in 17 pounds?
13. How many cubic feet of sand are there in 13 one-horse
loads, each containing one cubic yard?
MULTIPLICATION. 143
1. A garden is 53 feet long and 24 -feet wide. How many
square feet does it contain?
Why do we call the mul-
Multiplicand 53 square feet, tiplicand square feet?
Multiplier, 24 What does the multiplier
212 tell?
1060 4 times 53 square feet = ?
Product, 1272 square feet. 20 times 53 square feet = ?
24 times 53 square feet = ?
2. What is the cost of 72 bushels of corn at 47 cents a bushel?
3. A ship can sail 225^1111168 a clay in fair weather, and 160
miles a day in stormy weather. How many miles can
it sail in 27 days if 13 of these days are stormy?
4. School is in session 6 hours a day. How many hours is it
in session during 26 weeks of 5 days each?
5. There are 38 rows of trees in an orchard, each containing
95 trees. How many trees are there in the orchard?
6. There are 37 kegs of nails, each weighing 137 pounds.
Each keg, when empty, weighs 8 pounds. Find the
weight of the nails without the kegs.
7. Compare the product of 27 times 54 with that of 54 times
27.
How can you test the correctness of your work in multi-
plication?
8. Solve:
(a)
(b)
(c)
(d)
(e)
(0
Multiplicand,
47
89
68
85
78
92
Multiplier,
14
15
16
17
18
19
Product,
9. Multiply and test the correctness of each result:
67 35 56 76 145 476 398 714 974
23 32 43 53 37 27 57 83 75
144 RATIONAL ELEMENTARY ARITMETIC.
1. A merchant buys 4 dozen pairs of shoes at $2.25 per pair.
How much did they cost?
2. A boy reads one book of 316 pages every 2 weeks during
the year. How many pages does he read in the year?
3. There are 189 teachers in the schools of a city. Each one
has 49 scholars enrolled. How many scholars are
there in the city ?
4. A lot is 195 feet long and 53 feet wide. How many
square feet does it contain?
5. A train runs 37 miles in an hour. How far will it run in
two days at the same rate?
6. A man bought 37 horses at $69 each. How much did
they cost him?
7. A merchant bought 149 rolls of carpet. Each roll con-
tained 68 yards. How many yards of carpet did he buy ?
8. There are 8 cars an hour on a street car line, and each
carries 36 persons. How many persons ride on the
road from 6 o'clock in the morning until 6 in the
evening ?
9. A conductor collects 27 5^ fares, and 6 3^ fares on each
trip for 9 trips. How much money does he collect?
10. A boy gets $3.75 a week and spends 29^ each week. How
much money will he have at the end of 18 weeks at the
same rate?
11. A boy sells 29 papers each day 6 days in a week. How
many papers does he sell in a year?
12. If there are 17 apples in half a peck, how many apples
are there of the same size in 13 bushels ?
13. A miller bought 118 bushels of wheat at 78^ a bushel.
How much did it cost him?
14. A boy makes up a club of 17 subscribers for Harper's
Young People at $1.65 each. How much money should
he collect?
PROBLEMS IN MULTIPLICATION 145
What is the cost of the following articles?
1. 138 pounds of creamery butter at 18# a pound?
2. 215 pounds of dairy butter at 17^ a pound?
3. 348 dozen strictly fresh eggs at 9^ a dozen?
4. 48 bushels of new potatoes at 85^ a bushel ?
5. 464 pounds of turkeys at 8J^ a pound?
6. 378 pounds of chickens at 9^ a pound?
7. 17 barrels of choice apples at $3.25 a barrel?
8. 29 barrels of common apples at $2.35 a barrel?
9. 67 bunches of bananas at 78^ a bunch ?
10. 29 boxes of lemons at $2.75 a box?
11. 19 boxes of California oranges at $1.95 a box?
12. 13 crates of pineapples at $3.75 a crate?
13. 23 crates of tomatoes at $2.35 a crate?
14. 17 barrels of sweet potatoes at $3.75 a barrel?
15. 378 pounds of white sugar at 4-J^ a pound?
16. 456 pounds of yellow sugar at 4^ a pound?
17. 17 bags of coffee at $5.83 per bag?
18. 14 tons of timothy hay at $9.50 a ton?
19. 275 bushels of barley at 43^5 a bushel?
20. 58 bushels of No. 1 wheat at $1.05 a bushel?
21. 65 bushels of No. 2 wheat at 98^ a bushel?
22. 165 bushels of No. 1 corn at 42^ a bushel?
23. 235 bushels of No. 2 corn at 39^ a bushel?
24. 256 bushels of white oats at 34^ a bushel.
25. 27 bales of cotton at $6.34 a bale?
26. 47 barrels of flour at $6.50 a barrel?
27. 39 bags of bran at $1.35 a bag?
28. 464 pounds of corn meal at \\$ a pound?
29. 19 barrels of buckwheat flour at $3.25 a barrel?
NOTE. These problems may be varied each week, or each month, bf
taking the market quotations in the newspapers and substituting the prices
quoted for those given in the problems.
146 RATIONAL ELEMENTARY ARITHMETIC.
A LIST OF PRICES IN A CANDY STORE.
2. Cream-dipp
3. Caramels . .
4. Peppermint
35 8 .60
10. Chocolate-dipped aim
11. Chocolate-dipped pec
30 . 60
60 1 . 20
50 1.00
50 1 . 00
1. Which is the cheaper, to buy 2 1-pound boxes of pepper-
mint pats or 1 2-pound box? How much?
2. Which is the cheaper, and how much, to buy 2 1-pound
boxes of cream-dipped Brazils, or one 2-pound box?
3. Which is the cheaper, and how much, to buy a 2-pound
box of chocolate creams, or 2 1-pound boxes?
4. What is the difference in cost between 5 pounds of choco-
late creams, bought at different times, and a 5-pound
lot?
5. What is the difference in cost between 5 pounds of cream-
dipped Brazils bought at different times and a 5-pound
lot?
6. Which costs the more, and how much more, to buy 5
pounds of chocolate pats, or to buy two 2-pound boxes
and a separate pound?
7. Which costs the more, and how much more, 3 pounds of
fudge or 3 pounds of peppermint pats?
8. How could you buy the following for the least money:
7 pounds of chocolate creams? 4 pounds of paste?
6 pounds of caramels? 7 pounds of cream-dipped Brazils?
PROBLEMS IN MULTIPLICATION. 147
Solve orally whenever possible.
1. At 11 cents a pound, what will a 3-pound chicken cost?
2. At 18 cents a dozen, what will 2 dozen eggs cost?
3. At 15 cents a jar, what will 5 jars of Imperial Cheese cost?
4. At 41 cents each, what will 3 woodcocks cost?
5. At 98 cents per bushel, what will 2 bushels of hickory
.nuts cost?
6. At $1.10 per bushel, what will 5 bushels of onions cost?
7. At $8.00 a box, what will 5 boxes of string beans cost?
8. At $1.75 a bunch, 2 bunches of jumbo bananas, cost how
much?
9. At 29 cents a pound, what will 3 pounds of dairy butter
cost?
10. At 35 cents a pound, what will 3 pounds of creamery but-
ter cost?
11. At $6.50 a barrel, what will 2 barrels of Cape Cod cran-
berries cost?
12. At $9 a keg, what will 9 kegs of Malaga grapes cost?
13. At $3 per case, what will 15 cases Red Spanish pineapples
cost?
14. At 35 cents a dozen, what will 3 dozen lemons cost?
15. At 25 cents a jar, what will 9 jars of preserved ginger
cost?
16. At a Saturday market sale a lady bought the following:
2 roast chickens at $1.00 each.
4 half-pint glasses of cooked cranberries at 5 cents a
glass.
2 dozen tea-biscuit at 10 cents per doz.
2 pounds of macaroons at 40 cents per pound.
What was her bill?
17. Traveling 78 miles a day, how long will it take a man to
make a trip of 25,350 miles? How many weeks, and
how many days over, will that be?
148 RATIONAL ELEMENTARY ARITHMETIC.
1. A boy who had 370 pennies in his bank, exchanged them
for dimes. How many dimes did he receive?
How many tens are there in the divi-
10c)_370c dend? In the divisor? What is the
<P
quotient?
2. How many weeks will it take a man to earn $860 at $20
a week?
How many tens are there in the dividend?
How many tens are there in the divisor?
* What is the quotient?
3. If a grain merchant sells 300 bu. of grain a day, how long
will it take him to sell 74700 bu.?
The number of hundreds of bu. in the
300 )74700 dividend divided by the number of
? hundreds of bu. in the divisor equals
what?
4. Divide 20, 30, 40, 60, 90, 70, 80, each by 10. What is
a short way to divide by 10 when the dividend ends
in zero?
Divide 250, 520, 750, 640, 980, 370, each by 10.
5. Divide 400, 900, 800, 500, 300, each by 100. In such
cases what is a short way to divide by 100?
Divide 7500, 8900, 2400, 6400, 3700, each by 100.
6. Divide 7000, 9000, 2000, 8000, each by 1000. In such
cases what is a short way to divide by 1000?
Divide 75000, 26000, 367000, 845000, each by 1000.
7. Solve:
480 - 30 3600 -s- 1200 16000 * 2000
720 - 40 2700 * 900 21000 - 7000
540 - 60 6300 -s- 700 60000 * 12900
270 - 90 13200 4- 1100 25000 + 5000
650 - 50 8400 * 400 24000 - 3000
490 - 70 5000 * 1000 54000 -s- 9000
LONG DIVISION. 149
1. Review pages 43 and 44.
2. If a steamboat goes at the rate of 21 miles an hour, how
long will it take it to go 252 miles?
12 How many times is 21 contained in 25 tens?
21)252 If 21 tens is subtracted from 252, how
210 [ = 21 X 10 many times will 21 be contained in
the remainder?
42 = 21 X 2 252 - 21 == 12 Prove it by multiplying
Wf/Ky- 21 by 12.
3. Solve: 021)462 21)672 21)294 22)264 22)484
4. An orchard contains 768 trees. If there are 3^ rows of
trees, how many trees are there in each row?
How many times is 32 contained in 76
24 tens?
32)768 If 32 times 2 tens is subtracted from
768, how many times will 32 be con-
tained in the remainder?
768 - 32 = 24 Prove it.
5. Solve and prove:
21)420 32)960 43)8600 53)10600 64)1280
82)1640 63)1890 72)2160 91)18200 83)2490
83)1743 42)4620 71)4260 91)4732
Solve and prove:
756 - 42 = 1118 - 43 = 1368 - 72 = 1606 - 73 =
992 - 62 = 1196 - 92 = 1951 -?- 93 = 1909 + 83 =
884-52= 1512-5-63= 1325-53= 1148-82 =
768 - 24 = 4884 - 44 = 2954 - 14 = 1360 - 34 =
150
RATIONAL ELEMENTARY ARITHMETIC.
1. 1955 pounds of coal were put into 23 bags holding equal
weights. How many pounds were in each bag?
LONG DIVISION.
85 quotient.
Divisor. 23)1955 dividend.
184
115
115
remainder.
Answer, 85 pounds.
First find how many times
23 goes in 195 thus:
2 in 19, 9 times. But
9X23 = 207. 207 is larger
than 195. We now decide
23 goes only 8 times
in 195.
Sub tract 8X23 ( = 184) from
195, getting 11. Annex the next figure (5) of the
divfdend. Then 2 in 11, 5 times. 5 X 23 = 115. Sub-
tracting, find the remainder 0. This means 23 goes
exactly 85 times in 1955.
2. The area of Maryland is nearly 12216 square miles. About
how large would one of its 24 counties be, if all were of
the same size?
3. If each box holds 29 pencils, how many boxes are needed
_42
29)1218
116 = 29 X ?
~58
58 = 29 X ?
4. Divide:
to hold 1218 pencils?
29 being nearly 30, use 30 as a
trial divisor.
24)912 27)1161 34)1564 38)1824 46)1702
38)1634 48)1728 59)~1534 49)1715 67)2278
53)1378 57)1881 59)2714 62)1736 66)3168
68)3672 74)4144 79)4819 83)5312 87)4872
5. There are 1248 pupils in a certain school and there are
48 pupils in each recitation room,
rooms are there in the school?
How many recitation
PROBLEMS IN DIVISION. 151
1. A boy sells 98 penny papers a day that cost one-half cent
apiece. How many days will it take him to clear
$12.74?
2. A ton of coal occupies a space of 35 cu. ft. How many
tons will a car hold whose capacity is 840 cu. ft.?
3. The cost of a cement sidewalk, 7 ft. wide and 50 ft. long,
was $49. How much did it cost per sq. ft.?
4. A pane of glass 19 in. wide contains 665 sq. in. How
long is it?
5. It cost $31.20 to lay an oak floor at 16 cents a sq. ft.
How many sq. ft. did the floor contain?
6. A vineyard contained 306 grapevines, planted in rows.
Each row contained 18 vines. How many rows were
there?
7. A farmer sold a number of cattle at an average of $59 a
head, receiving $4248. How many head of cattle did
he sell?
8. How many spaces of 330 ft. are there in a mile?
9. At 75 cents per 1000 cu. ft. of gas, how many thousand
cu. ft. must a man have burned whose gas bill was
$35.25?
10. A man received $26.22 for a load of corn at $.46 a bu.
How many bu. did the load contain?
11. 2808 pencils were distributed equally among 9 schools.
Each school distributed its share equally among 13 of
its rooms. How many pencils did each rpom receive?
Solve in two ways.
12. Write problems based on the* following facts:
Dividend. Divisor. Quotient.
(a) 1843 men. 97 men. ?
(b) 3717 sq. in. ? 63 inches.
(c) ? $34 160 men.
(d) 2376 books. 88 books. ?
152 RATIONAL ELEMENTARY ARITHMETIC. '
1. To send a money order of $60 costs 20 cents. How many
such orders could be sent for $4.00 or 400 cents?
2. 40 rods = 1 furlong. How many furlongs in 9240 rods?
3. A Mark (German money) equals about 24 cents in United
States money. How many marks in $5.52? In $6.96?
In $11.38?
4. It costs $23 to make a trip from New York to Chicago.
At that rate, how many persons could go from New
York to Chicago for $575?
5. A man spent $900 in buying equal amounts of coal for
45 families. How many dollars were spent for each
family?
6. 1536 acres of land were divided equally among 32 farmers.
How many acres were given to each?
7. 2400 selected apples were packed in 32 baskets. How
many apples were packed in each basket?
8. A library of 1092 volumes was arranged on 42 shelves.
How many volumes were on each shelf?
9. At 60 cents each, how many footballs will $7.20 buy?
10. In a block containing 21 houses, a girl counted 315 win-
dows. How many windows was that to each house?
11. A hall containing 768 square feet was 24 feet wide. How
long was it?
12. At 15 cents each, how many shirt waists can be laundered
for $3.00?
13. At 22 cents an hour, in how many hours will a man earn
$5.28?
14. A granite block containing 60 cubic feet is 4 feet long and
3 feet wide. How high is it?
15. How many dozen pineapples, at 84 cents a dozen, can
be bought for $12.60?
16. How many dozen eggs, at 23 cents a dozen, can be bought
for $5.98?
PROBLEMS IN DIVISION. 153
1. At 80^' a gallon, what is the value of one quart?
2. How many years do 1728 months equal?
3. If 8 gallons of syrup cost $12.80, what does 1 gallon costV
One pint?
4. A boy in school for 7 years and 4 months studies history
during one-eighth of the time. How many months
does he study history?
5. A man pays $50 a month for rent, and ^ as much for gas.
How much does he pay for both?
6. A grocer sold 6 pounds of tea for $4.80. How much did
he get a pound for it? How much an ounce?
7. A person bought land for $4572, he sold it for T ! T more
than it cost; for how much did he sell it?
8. How many cans holding 5 pounds each can be filled from
2 hundredweights of coffee?
9. A girl divided one-third of 195 nuts equally among 5
friends. How many did each receive?
10. How many feet long is a platform 720 inches long?
11. In a fire a man lost one-twelfth of his goods, all of which
were valued at $9,876. How many dollars worth of
goods did he lose?
12. A farmer owning 1,272 acres of land divided it into 2
equal parts; one of these parts he again divided into 3
equal parts, giving one of these parts to each of his
3 sons, and keeping the rest himself. How many acres
had he left? How many acres had each son?
13. A book case contained 203 books, each of the 7 shelves
containing the same number of books. How many
books were there on a shelf?
14. A man sold 11 bicycles for $495. They were all sold for
the same price. For how much did he sell each one?
15. A man sold 9 horses ir f or $783, receiving the same price
for each one. For how much did he sell each horse ?
154
RATIONAL ELEMENTARY ARITHMETIC.
PERSONAL ACCOUNTS OF Two BOYS.
MoivtKLy Account
Weekly Accourvt
McxrcK
4
5
6
.7
6
asu
/5
lo
10
10
06
10
15
/^
^OMXA_<IAAX
4-curiAVAO vovJk
>5o
3o
Yeeurly Expense
6 *
/^
4o
1. Find the daily expense for each day in the weekly account.
In a year, how much was spent for car fare? Lunches?
2. At the salary given in the monthly account (the yearly
expenses as given), how much would be saved in a year?
In 5 years?
3. At the salary given in the weekly account, how much
would a boy earn in a year? How much would he save,
counting the yearly expenses as given?
4. Make and solve other problems from these accounts.
PROBLEMS OF SALES. 155
A merchant offered the following lots of goods for sale:
2 suits boys' clothes $ 8 . 50
15 dozen handkerchiefs 27 . 00
12 dozen pairs suspenders 36 . 00
50 boxes (each containing J dozen pairs) of
stockings 60 . 00
3 dozen shirt waists 16 . 20
1 dozen pairs trousers 15 . 00
J dozen waistcoats 3 . 00
3 dozen caps 5 . 40
4 dozen hats 12.00
10 boxes of collars, each holding dozen 6 . 00
1. As sold in this way, what was the cost of:
Each suit?
Each dozen handkerchiefs?
Each handkerchief?
Each dozen pair of suspenders?
Each pair of suspenders?
Each box of stockings?
Each half-dozen pairs of stockings?
Each pair of stockings?
Each dozen shirt waists?
Each shirt waist?
Each pair trousers?
Each dozen caps?
Each dozen hats?
Each box of collars?
Each half-dozen collars?
Each collar?
2. A second merchant bought the whole lot of goods at $187.
Did the first merchant sell for more or less than the
price offered? How much difference between the IV;D
prices?
156 RATIONAL ELEMENTARY ARITHMETIC.
1. An acre of tobacco is valued at about $52, an acre of
sweet potatoes at $37, an acre of sugar beets at $30,
and an acre of peanuts at $14. At this rate, what is
the entire value of 2 acres of each?
2. To send a telegram from Chicago to San Francisco costs
$.75 for the first 10 words, and 5 cents for each added
word. What would a message of 19 words cost?
3. At 40 cents for the first 10 words, and 3 cents for each
added word, what will it cost to send the following
telegram from Chicago to New York City: ''Express
two hundred Mother Goose, fifty Jo's Boys, one hundred
twenty Little Women"?
4. Mrs. Brown had 3 sons. John earned $5 a week, Harry
earned $7, and William as much as the other two to-
gether. How much did William earn? How much did
they all earn?
5. John saved \ of his money each week. How many dollars
did he save? How many did he spend?
6. Harry saved J of his money. How many dollars did he
save? How many did he spend?
7. William saved J' of his money. How many dollars did he
save? How many did he spend?
8. How much did the 3 boys together save in a week? How
much did they spend in a week? In a month?
9. A room is 12 x 15 feet. How many strips of carpet a
yard wide will be needed to carpet it? How long must
each strip be? How many yards will it take for the
whole room? What will it cost at 40 cents a yard?
10. A mounting block of granite contained 24 cubic feet and
was 2 feet high and 3 feet wide. How long was it?
11. A lamp post 12 feet high was 2 feet in the ground. What
part of it was in the ground? What part was in the
air? How many feet were in the air?
MISCELLANEOUS PROBLEMS. 157
1. An Angora kitten was bought for $6 and sold for more
than that price. What was the selling price?
2. If peanuts are bought at $5 a bushel and sold at 5 cents a
half-pint glass, what is the gain on a bushel?
3. The railroad fare from Chicago to Madison, Wis., is $3.92.
What will it cost for 5 persons to make the trip and
return?
4. What is the difference between the buying price and the
selling price of a bicycle that was bought for $35 and
sold for T more than it cost?
5. A boy bought 3 oranges for 10 cents, and traded them for
5 apples. What were the apples worth apiece in money?
6. A boy bought a pony for $35. He had it shod for $2,
and kept it a month at an expense of $4. He then sold
it for $40. Did he gain or lose, and how much?
7. One spring the robins arrived in the country bordering
the southern part of the Great Lakes March 2. The
bluebirds came 25 days later. On what date did
the bluebirds arrive?
8. In 1900 the government gave $25,000 to the reindeer sta-
tions in Alaska. Only $19,330 was used. How much
was left?
9. During the week ending March 4, 1905, there were received
in the stockyards, Omaha, 69,296 cattle, 6,124 calves,
178,077 hogs, and 73,400 sheep. The shipments for the
same week were 32,191 cattle, 327 calves, 62,953 hogs,
and 19,896 sheep. How many cattle, calves, hogs, and
sheep were received during that week?
10. How many cattle were not shipped? How many calves?
How many hogs?' How many sheep?
11. How many animals remained?
12. At 18 cents a pound, how many pounds of sirloin steak
can be bought for 90 cents?
158 RATIONAL ELEMENTARY ARITHMETIC.
ooo
o m
1. What part of the square, 0, = A?
2. What part of A = B? What part of B = C?
3. B = what part ofO?
4. C = what part of 0?
5. How many A's = 0? How many B's? C's?
6. In 1 how many J's? J's? J's?
7. What part of J = J?
8. What part of J = J?
9. What part of J - J?
10. J = how many J's? How many J's?
11. What is the sum of J and J?
12. What is the sum of J and J?
13. J + I - ?
14. i + I = ?
15. J + J - ?
16. One half a dollar and J of a dollar are equal to what part
of a dollar?
17. One-fourth of a pie and J of a pie are what part of a pie?
18. Marie cut a pie into 8 pieces and gave each one in the
family one piece. There were 4 in the family. What
part of the pie was used?
19. Harry bought a piece of wire.' He divided half of it
into fourths, and half into eighths. How many of each
did he have? He used J of the wire. How many
eighths did he use?
FRACTIONS. 159
1. On page 158, E is what part of the square, 0? How
many E's = 0? How many E's = D?
2. How many F's in 0? How many G's in F? How many
G's in 0? G = what part of F? What part of 0?
3. How many H's in G? In F? In D?
4. How many J's in 0? In 1?
5. How many \s in 1? How many T Vs in 1?
6. How many J's = J?
7 TTrnxr inonir 1'cs = 2?
= ?
8.
How many T Vs = J?
!? 5?
J? 3?
9.
What is
the sum of J
and J?
10.
What is
the sum of J
and ?? J
: and J?
11.
W T hat is
the sum of \
and T V?
i and A?
12.
What is
i ofj?
13.
What is
}ofA? Of
? Of A
? Of H?
14.
*+.-
?
J + i
?
i + i ~
?
4 ~H i ~
?
i -I- i
1 i t -
5
l + * =
J
[JU
1
|J* =
?
?
1+1 =
?
* + t =
I
S + i
?
4 + iV =
?
i + i f
t + A = ?
J + 5 =T
15. Amanda cut a cake into 12 pieces. She put J the cake
into a box, J on a plate, and the rest on a paper. How
many pieces were in the box? On the plate? On the
paper?
16. Willard bought a round chocolate loaf. He divided half
of it into sixths and the rest into twelfths. He gave
away 4 of the sixths and 3 of the twelfths. What part
of the cake did he give away?
160
RATIONAL ELEMENTARY ARITHMETIC.
=
1. Draw a square and show the answers to these problems:
1 = ? 4 = ?
42 36
1 What is J of i? What
1 What is 4 of 4? What
What is 4 of 1? What
What is 4 of 12? What
What is f of 6? What
What is f of 9? What
What is | of 8? What
3 times = ?
3 times J = ?
3 times f = ?
3 times f = ?
3 times J = ?
i-i =
i-i=? i
3. What is 4 of i?
What is 4 of 4?
What is 4 of J?
4. What is 4 of 6?
What is 4 of 6?
What is 4 of 9?
What is i of 8?
5. 2 times 4 = ?
2 times J = ?
2 times f = ?
3 times 4 = ?
3 times I = ?
tt-i =
1-1 =
is i of i?
is i of i?
is i- of f ?
is i of 4?
is i of 12?
is J of 12?
is 4 of 18?
4 times J =
4 times J =
4 times J =
4 times f =
4 times | =
6. f i of 6 = ?
2 times <! * of 6 = ?
i of 8 = ?
i of 8 = ?
1 of 8 - ?
4 of 10 = ?
4 of 12 = ?
f of 12 = ?
7.
3 times
S.
4 times <
r i of 6 = ? | of 8 = ?
f of 6 = ? t of 10 = ?
of 6 = ? I of 10 = ?
I J of 8 = ? I of 10 = ?
[ } of 12 = ? | of 12 - ?
i of 16 = ?
J of 15 = ?
i of 16 = ?
} of 8 = ? \ of 25 = ?
J of 12 = ? i of 15 = ?
t } of 8 - ?
i of 6 = ?
i of 6 - ?
i of 8 = ?
i of 9 = ?
1 of 9 = ?
J of 16 = ^
i of 18 - ?
i of 12 - ?
J of 12 = ?
f of 12 = ?
J of 9 = ?
f of 9 - ?
} of 20 = ?
} of 20 = ?
| of 20 =
i of 18 = ?
I of 18 - ?
MIXED NUMBERS.
161
1. Into how many parts is A divided?
2. Find \ of A. How many 4ths of A in J of A?
3. How many 8ths in \ of A?
4. Find \ of A. How many 8ths of A in { of A?
5. Into how many parts is B divided?
6. Find i of B. How many 6ths in J of B?
7.
6. n o . ow many
How many 6ths in J of B?
T I '(ti M0 M9 *-* \A.l T 1
How many 6ths
_-is in Jof B?
8. Into how many parts is C divided?
9. Find i of C. How many lOths in of C?
10. How many lOths in i of C?
11. How many i's in 1J A? In 1J? In 2?
12. How many J's in 1J A? In 1}? In If? In 2}?
13. How many t's in 1J A? In It? In 31? In 5|?
12. How many 4 o m
13. How many J's in
14. How many J's in 1J B? o. 3i A3i ^ 3
15. How many t's in H B? It? H? t I
16. How many t's in It C? It? If? 2|?
17. How many T V's in 1A C? In 1A?
2 T \? 3i? 3|?
18. 1J + 2J = ? 19.
In
1}?
1J?
In 31?
If? 2f?
If? ^ B?
+ H = ?
+ 2J = ?
1J + 2J
li + H -
2i + 5| -
If + li =
11 + H
2J-H=T
20.
3| 4. it = ?
=
H+ ..
H + 1A - ?
31 -If =T
~li =?
162 RATIONAL ELEMENTARY ARITHMETIC.
1. What i the weight of 4 packages together, the first
weighing ^ of a pound; the second, ^ of a pound; the
third, f of a pound; and the fourth, 1^ pounds?
2. A tailor uses 4^ yards of cloth for a coat; 1^ yards for a
vest; and 3 T 5 F yards for a pair of trousers. How many
yards does he use for the suit?
3. A man sold 3^ pounds of butter to one customer, 2^ pounds
to another, and 4| to a third. How many pounds did
he sell to all three?
4. A lady spends |- of the year in the city, |- of the year at
the seashore, and the rest of the year in traveling?
What part of the year does she spend in traveling?
5. From a piece of cloth 15 yards long, 8J- yards were sold
at one time and 2 \ yards at another time. How many
yards were sold in all? How many yards were left?
6. A baker having 5 dozen biscuits, sold 1J dozen to one
man, and 3J dozen to another. How many dozen did
he sell in all? How many had he left?
7. of John's kite string is whip-cord, the rest is cotton
string in 2 pieces, the first piece is -J as long as the
whip-cord. What part of the entire string is the first
piece of cotton string? The second piece?
8. A grocer having f of a dozen of pineapples, sold ^ of
them. What part of a dozen did he sell?
9. One boy stays in the country ^ of each year, a second boy
stays ^ as long as the first boy? What part of the
year does the second boy stay ?
10. How many boxes holding ^ of a pound of candy each, can
be filled from ^ a pound ? From J of a pound ? From
1-J- pounds?
11. A man bought 1^ pounds of nuts and divided them equally
among his 5 children. What part of a pound did each
receive?
PROBLEMS IN FRACTIONS. 168
1. A boy bought at the grocery 1 pound of sugar, 1 pounds
of butter and ^ pound of tea. How many ounces did
the three weigh together?
2. A man bought 3} pounds of sugar and returned 12 ounces
of it. How many ounces did he keep?
3. A grocer put 5 pounds of sugar into 2 equal packages.
How many ounces in each package?
4. A woman bought at the grocery 1| pounds of butter at
24^ a pound; a quarter of a pound of tea at 60^ a
pound and 4 pounds of sugar at o^f a pound. How
much was her bill?
5. A clerk sold one customer 7 yards of cloth at 80^ a yard;
9 yards of ribbon at 16^ a yard and \ a yard of velvet
at $1.50 a yard. What was the amount of his sale?
b'. A man bought a hatchet for 75^. a saw for $1.25, 6
pounds of nails at 4^ a pound, and 2 dozen screws at 9^
a dozen. What was his bill ?
7. A grocer bought 3 barrels of sugar containing 198 pounds
each, at 4^ a pound; a box of tea containing 23
pounds at 45^ a pound, and 2 sacks of coffee containing
7o pounds each at 20^ a pound. What was his bill?
8. A merchant bought 3 dozen pairs of shoes at $2.25 per
pair, one dozen at $2.50 a pair, and one-half dozen at
. . ...$2.75 a pair. How much was his bill?
9. A bookseller bought 50 books at 36^ each, 2 dozen boxes
of paper at 13^ each, 9 dozen pencils at 11^ a dozen.
What was his bill?
10. Railroad fare is Bf per mile. From Chicago to Aurora it
is 37 miles; from Aurora to Galesburg, 126 miles; from
Galesburg to Burlington, 43 miles. What is the fare
from Chicago to Aurora ? From Aurora to Galesburg ?
From Galesburg to Burlington? What is the fare
from Chicago to Burlington?
164 RATIONAL ELEMENTARY ARITHMETIC.
1. A man owns a lot on which he builds 2 houses. The first
is 24J feet wide and 63 feet long; the second is 25
feet wide and 62J feet long. What is the area of the
ground covered by the two houses?
2. The lot is 125 feet long and 60 feet wide. What is the
area of the ground not covered by the houses?
3. On each side of 360 feet of the length of a street which is
60 feet wide, there is a sidewalk 7 feet wide. What is
the area of the remainder of the street?
4. A railroad runs a train of 3 cars every 30 minutes from 6
o'clock in the morning until 6 in the evening. How
many cars run over the track in' the 12 hours?
5. A man mails 40 letters requiring 2^ postage each, 375
circulars requiring 10 postage each, and 36 packages
which require 40 each. What is the cost of the postage
on the whole?
6. A man subscribed for the Youth's Companion for one
year at $1.75, for St. Nicholas for 6 months at $2.50 a
year, for the Century for 3 months at $4 a year and
for McClure's for 18 months at $1 a year. How much
must he pay for all the subscriptions?
7. A boy bought 24 1-cent papers at f ^ each, 16 2-cent papers
at 1J^ each and 5 10-cent magazines at 7^ each. He
sold his entire stock at regular prices. How much
money did he make?
8. A boy gets $3.75 for a week's work; he pays 10^ each
day for lunches, buys a ball for 15^ and a stamp album
for 75^. How much money does he have left at the
end of the week?
9. A man gets $17.50 a week for four weeks. In that time
he pays $11 for rent, buys half a ton of coal at $7.50 a
ton, pays $12.75 for groceries and $6.93 for dry goods.
How much money has he left from his salary?
MISCELLANEOUS PROBLEMS 165
1. 48 men dig a cellar in 18 days. In how many days could
12 men dig it?
2. How many -J- pound packages can be made from 18 chests
of tea, each containing 60 pounds?
3. How many pounds of sugar at 6^ a pound will equal in
value 258 gallons of syrup at 40^ a gallon?
4. A merchant exchanged 70 barrels of sugar at $22.50 per
barrel for flour at $5 per barrel. How many barrels of
flour did he receive ?
5. If 250 desks which cost $9 each are sold for $12 each,
what will be the gain?
6. What will 144 quarts of strawberries cost at 50^ a peck ?
7. What is the difference between 829 tons and ^ of 9648
tons?
8. Mr. Monroe spends $139.65 in January, $15.25 more in
February than in January, and $15.25 more in March
than in February. How much does he spend in all?
9. A gentleman paid for a purchase -with a $5 bill, and
received back in change one half-dollar, 3 quarters, 2
dimes and 2 nickels. What was the amount of his
change? What was the amount of his purchase?
10. Find the distance in inches around a room that is 18 feet
long and 14 feet wide.
11. A woman received $10,000 for a farm. She gave $1000
to a church, $500 to a school, and $2980 to a hospital.
How much of the money had she left?
12. A carpenter bought 464 feet of lumber at one time and -J
as much at another time. How many feet did he buy
in all?
18. There are 387 squares of marble in the floor of the dining-
room and seven-ninths as many in the parlor floor.
How many squares in the parlor floor? How many in
both floors?
166 RATIONAL ELEMENTARY ARITHMETIC.
1. A man paid $24 for a suit of clothes, J as much for a pair
of shoes, -J- as much for a hat. What was the cost of
the entire outfit?
2. A man paid for his house $4860; the lot cost him ^ as
much as the house; the grading, fencing and street
cost J as much as the lot. What did the three cost him ?
3. A bookseller sold $128 worth of books in one day. They
cost him J less than he sold them for. How much was
his profit and what did the books cost him ?
4. A bookseller sold 64 books at 12J^ each, 48 books at 15^
each, and 60 books at 25^ each. How much money
did he receive?
5. There are 60 pupils in the school room. 24 of them have
4 books each, 26 of them have 3 books each, and the
remainder have 5 books to each group of 2 pupils.
How many books are there in the room ?
6. A man is 48 years old; his wife is 44; the oldest son is
J as old as the father and mother together; the second
son is J as old as the father. What is the sum of the
ages of the father, mother and two boys ?
7. A boy left home for college on the morning of Septem-
ber 5th. He returned home on the morning of Decem-
ber 23rd. How many days was he away from home ?
8. A family bought 1 quart of milk every day in January,
February and March of a Leap Year. How many gal-
lons did they buy in the 3 months?
0. For $20 in gold a man received a five-dollar bill. 7 silver
dollars, and the rest equally in half dollars and quar-
ters. How many half dollars did he get? How many
quarters ?
10. How many yards of wire are needed to build a fence six.
wires high around a garden 48 feet wide and 72 feet
long?
TIME.
A SCHOOL PROGRAM.
Latigiiage, A.
Language, H.
Arithmetic, A.
Heading, B.
Morning | Exorcises.
Written Work, B.
Written Work. A.
Written ;'
Writing, '
Music,
Geography, A.
Geography, B.
Kec <
Oral Spell i
Calisthenics.
Study Heading *
Study Arithnu
A and'B.
, A and B.
A and B.
A and B.
Study Geography. B.
Study Geography. A.
1 Find the time given to each recitation.
2. Find the time given to morning exercises; to morning
recess; to music; to afternoon recess; to calisthenics
in the morning; to drawing.
3. How much time does the A class spend in reciting and
studying arithmetic? Reading? Geography?
4. Answer the same questions for the B class.
5. How much time, during one whole da} , is given to calis-
thenics and recesses? To writing, music and drawing?
6. How long is the morning session? The afternoon session?
7. How long are the two sessions together?
8. How long are the two sessions, not counting recess times?
9. If a boy from another grade came in and recited in Lan-
guage, A, Arithmetic, B, and Geography, A, how many
minutes would he spend in this room? How many hours?
10. If a girl from another grade recited in this room in Read-
ing, B, Arithmetic, B, Geography, B, and Drawing, how
many hours and parts of an hour would she spend in
this room?
168 RATIONAL ELEMENTARY ARITHMETIC.
GROCERY PRICE LIST.
Mocha coffee, per pound. . . .
er pound
i vguu powder), per pound
Crackers, per pound
Cinnamon, per pound
Black pepper, per pound
Ivory soap, per 100 bar box
Fete-naphtha " " "
Corn meal, per 100 pounds .
Salt (100 sacks per bbl.), per
Graham flour (196 Ibs. to a b
Winter wheat flour (196 Ibs. i
Spring wheat flour " "
Straight grade flour '' "
Baking powder, per do/,, l-lli
Canned corn, ' "
Canned tomatoes '
('aimed peaches. ' " "
Canned peas ' ' " "
('aimed salmon ' '' "
.33
.50
.06*
.30"
.17
4.00 per ba
4.10 " '
1.50 peril).
1.90 2 sack:
3.90 peril).
5. 15 per bb
6.20
4., SO
2.40 per c:
.96 " '
NOTE: Prices of groceries change from time to time and are dif-
ferent in different places. Make problems using the prices in your local
papers. The following problems use the price list here given.
One Saturday a grocer put up the following orders:
1. 3 pounds Mocha coffee; 2 pounds gunpowder tea; i
pound cinnamon; J pound black pepper; J dozen bars
Ivory soap; 10 pounds corn meal; 4 sacks of salt. What
was the amount of this bill?
2. One barrel straight grade flour; 2 cans baking powder;
\ doz. cans each of corn, tomatoes, peaches, peas, and
salmon. What was the amount of this bill?
3. For Mr. M. E. Potter:
One barrel spring wheat flour; 100 pounds corn meal; 20
sacks of salt; 40 pounds of Graham flour; and 100 bars
of Fels-naphtha soap. What sum will pay Mr. Potter's
bill if the grocer reduces it 5# on each dollar?
BUYING GROCERIES. 169
1. For Mr. E. G. Smith:
One barrel spring wheat flour; 30 pounds Graham flour;
J dozen cans baking powder; 2 pounds cinnamon; 3
pounds crackers; 50 sacks salt. What was the amount
of Mr. Smith's bill? How much did the grocer gain?
2. For G. A. Tanby:
2 pounds gunpowder tea; 50 pounds corn meal; 50 pounds
Graham flour; 4 cans tomatoes; 3 cans peaches; 5 cans
salmon. What was the amount of Mr. Tanby 's bill?
What did the grocer gain?
3. For G. W. Williams:
5 pounds Java coffee; 3 pounds tea; 4 pounds crackers;
1 dozen bars Fels-naphtha soap ; one barrel winter wheat
flour; J dozen cans baking powder; J dozen cans peas;
\ dozen cans salmon. What was the amount of Mr.
Williams' bill? How much did the grocer gain?
4. The following list of goods would cost the grocer how
much?
50 pounds cinnamon; 25 pounds black pepper; 3 boxes
Ivory soap; 2 barrels salt; 6 barrels spring wheat flour;
1 dozen cans baking powder.
5. How much money would the grocer receive for the list
in problem 4?
6. How much would the grocer gain from selling the list in
problem 4?
7. The following list of goods would cost the grocer how
much?
One barrel Graham flour; one barrel spring wheat flour;
one barrel winter wheat flour; one barrel straight grade
flour; 3 dozen cans baking powder; 2 dozen cans each
of corn, tomatoes, peaches, peas, and salmon.
8. How much money would the grocer gain from selling the
list in problem 7?
170
RATIONAL ELEMENTARY ARITHMETIC.
For Suinme
Tennis slipper
"erwear . .
stockings. . . .
Neckties. .
For Winter
Suit
Overcoat
Slices
Hat
Cap
Rubbers (a pair)
Sweater .
TIC, 6 yd. (ft-
v. 7 vd. (a.
Gloves (a pair;
Serge, ."> yd. (a 12}
Cloak. . .'. $9..i
Shoes 2.C
Hat 2.(
mimon, .5 vu. (it i;
Muslin. 10 'vd. (ft . . 12
1. School supplies for one year cost $4.75 for each of a family
of six children. What was the cost for all six children?
2. There was bought one month for a boy each item in the
above list of Boys' Clothing for summer. What was
the whole cost? What would have been the cost for
4 boys?
3. In October each item in the list of Boy's Clothing for
winter was bought for a boy. What was the whole
cost? What would it have been for 3 boys?
4. Each item in the list of Girls' Clothing for summer was
bought for a girl. What was the whole cost? What
would it have been for 3 girls?
5. Make other problems from these lists, such as the cost for
a family of 2 boys and 3 girls for clothing for winter,
for summer; the cost of 2 pair of shoes, 2 hats, 2 pairs
rubbers, etc., for cash.
EXERCISES FOR PRACTICE. 171
1. How many yards of carpet will be needed to cover a floor
27 feet long and 24 feet wide?
2. A dog-kennel that is 4J feet high, 2 feet wide, and 4 feet
long, contains how many cubic feet?
3. How many feet of fence will be needed to fence a garden
' 36 yards long and 27 yards wide?
4. How many books, each filling a space of 96 cubic inches,
can be packed in a box containing 4608 cubic inches?
5. Add:
7026 6726 6728 6724
7968 9872 9739 3072
9872 6879 8725 5192
9763 8979 9734 6789
8429 7269 2459 1978
6. Subtract:
4072 6720 6729 3072
3987 5987 5989 1998
7. Multiply:
4276 6725 7268 8796
36 98 49 57
8. Divide:
27)24516 98)9702 47)3055
65)2015 90)2250 85)9726
9. Anson earned $4.25 each week for 14J weeks. How much
did he earn in that time?
10. Louise bought 14 yards of cloth at 92^ a yard, 9 yards of
ribbon at 45^ a yard and a piece of lace at 70^. She
gave in payment a 20-dollar bill. How much change
should she receive?
172
RATIONAL ELEMENTARY ARITHMETIC.
SHIPPING SALT ON LAKE MICHIGAN.
The Kelton is a steamboat engaged in carrying salt between Manistee,
Michigan, and Chicago, Milwaukee, and South Chicago. Look up all these
places on a map.
1. The Kelton left Chicago at 3:30 Monday afternoon for
Manistee, 176 miles from Chicago. The boat reached
Manistee at 7:30 Tuesday morning. How many hours
did it take? How many miles an hour did the boat
go?
2. At Manistee, the boat was loaded with 6,500 barrels of salt.
The cost of loading was $1.00 per hundred barrels, and
it took 7 hours to load. At what hour was the loading
completed and what was the cost of loading per hour, if
loading began as soon as the boat reached Manistee?
3. The boat left for Milwaukee, 88 miles from Manistee, at
2:30 Tuesday afternoon, and reached Milwaukee at
12:30 Wednesday morning. How long did it take and
how many miles an hour did the loaded boat run?
4. The unloading at Milwaukee began at 7 o'clock Wednesday
a. m. and it took 10 hrs. An hour was taken for dinner.
How long since the boat left Chicago?
MEASURES OF LONG DISTANCES. 173
1. Measure these two lines. Suppose them to be
drawn to the scale of 1 inch to 3 feet.
2. What does the short one represent?
3. How many times the short line is the long one?
4. If the short line represents 1 yard, how many
yards does the long one represent?
5. If the short line represents 3 feet, how many feet
does the long one represent?
6. Name the distance which the long line represents.
7. How many feet in a rod?
8. How many yards in a rod?
9. How many feet in a yard?
10. How many inches in a foot?
11. 320 times what the long line represents is a mile.
12. How many yards in a mile?
13. How many feet in a mile?
14. How many rods in a mile?
15. A boy walks 60 rods. How many yards does he
walk? How many feet?
16. A lot 6 rods wide is divided into 2 equal lots.
How many feet wide is each lot?
17. A lot is 3 rods wide and 6 rods long. How many
yards around it?
18. A bridge is 8 rods long and 2 rods wide. How
many feet long and wide is it?
19. A rope 12 rods long is wound into coils, each coil
using 6 feet of rope. How many coils are
there?
20. How many rods around a farm 2 miles square?
21. How many rods around a farm 3 miles square?
22. A lot 3 rods long is how many feet long?
23. A horse trotted a mile in 3 minutes. How many
feet was that per second?
174 RATIONAL ELEMENTARY ARITHMETIC.
1 foot 1 yard 1 rod 1 mile
12 inches 3 feet, 5^ yards 320 rods
Winches 16^ feet 1760 yards
5280 feet
1. A block is 18 rods wide and 22 rods long. How many
yards is it around the block? How many feet?
2. A boy lives 64 rods from school. If he goes home at
noon how many yaids does he travel in a school week?
3. A man lives 2J miles from his office. He goes to his
office each day. How many rods does he travel from
Monday morning until Saturday night?
4. A lot is 82^ feet wide and 165 feet long. What is the
cost of fencing it at 18# a yard? At 750 a rod?
5. The rails on a railroad are 2 rods long. How many rails
are there in a mile of railroad track?
6. It costs 850 a linear foot for making a street. What will
be the cost of a quarter of a mile of such a street?
7. A boy rode 7j- miles on his wheel. How many rods did
he ride?
8. It is 38 yards west from the door of John's house to the
school. If he went to the store 45 yards east and then
to school, how many yards did he walk? How many
feet?
9. How many yards of border will be required for a room 21
feet long and 18 feet wide?
10. The tire of a wheel measures 6 feet. How many revolu-
tions will it make in going 24 rods ?
11. A boy steps 2 feet. How many yards will he step in 30
steps? How many steps will he take in walking a
mile? In walking J a mile? ,In walking J of a mile?
12. If there are 8 blocks in a mile, how many feet are there
in a block?
13. A field is ^ a mile square. How many miles will a man
travel in going around the field?
MEASURES OF DISTANCE. 175
A B C
1. This line is drawn to a scale of 1 inch to the mile. A
man goes from C to A and returns lo B. How many
miles has he traveled?
2. From B he goes to C and retuius to B. How many miles
has he traveled?
3. From B he goes to A and back io B. How many rods
has he traveled?
4. Suppose the line to be drawn to a scale of 8 rods to 1
inch. How many yards from A to B? From B to C?
From A to C?
5. John lives at B, Ned at A anl Hi-' s< hool-house is at C.
John goes to Ned's house in the morning, then to
school, and home in the evening. How many rods has
he traveled?
6. The next day Ned goes to school and John is not there.
He goes back to John's home and they go back to
school together and each returns home in the evening.
How many rods has Ned traveled? How many yards?
7. Let each boy count the number of steps to his home from
school, write it down and the next day find how many
feet the distance is if his steps have been 2 feet long.
If he steps 1J feet. Tell whether it is nearer a mile,
^ a mile, J of a mile or J of a mile.
8. How many feet in ^ a mile? J of a mile? ^ of a mile?
9. 2 boys start out from home and walk in opposite direc-
tions. They take 8 steps to the rod. How many rods
apart are they when they have each taken 80 steps?
10. Is the distance they are .apart nearest to J, ^ or to a mile?
11. A boy takes 80 steps of 2 feet each in a minute. How
far will he walk in 15 minutes? Is the distance nearer
to or a mile?
176 RATIONAL ELEMENTARY ARITHMETIC.
I
B
D
The above is a map of a country road starting from the street A X,
and drawn to a scale of one inch to four miles.
1. How many miles is it from the street to B? ToD? ToG?
2. How many miles is it from B to G? From D to G?
3. How far is the road B C from the street ? How far is D E ?
4. How far is the road F G from the road D E?
5. How far is the road F G from the street?
6. How far, in a straight line, is the road A B from the road
F E?
7. How far is the end of the road at G from the nearest point
of the street ?
8. How far is G from the nearest point in the road A B?
9. The distance from B to C is what part of the distance
from F to G? What part of D to E? What part of
C to D ? What part of A to B ? What part of D to F ?
10. The distance from F to G is what part of the distance from
A to B? What part of the distance from D to E?
11. The distance from C to D is what part of the distance
from A to B? What part of the distance from F to G?
MEASURES OF DISTANCE. 177
(Call one inch on the map on the opposite page one-half a mile.)
1. How far is it from A to B? From A to C? From A to
D? From B to C? From E to F? From E to G?
/Oall one inch on the map on the opposite page one-third of a mile.)
2. How far is it from A to B? From A to C?
3. If a man can walk from A to B in 15 minutes, how long
will it take him at the same rate to walk from D to E ?
4. If the wheels of a bicycle turn twice around in going one
rod, how many times will they turn in going six miles ?
5. John rides on his new King bicycle 1 J miles in 8 minutes ;
Harry rides at the same speed for 5 minutes. How
many more rods does John ride than Harry?
6. There are in a room 5 windows 9 feet high. How many
yards of material of single width will be required to
make curtains for the windows, making 2 curtains for
each window? What will be the cost at 6^ a yard?
7. The windows in a school room are 7 feet high and there
are 4 of them. How many yards of material will be
required for one curtain at each window if 1 foot is
allowed extra for each curtain ? What will be the cost
of the material at 25^ a yard?
8. Each step in the staircase is 6 inches high and 1 foot
wide. How many feet of stair carpet will be required
if there c?e 12 steps ? What will be the cost of the
carpet at 75^ a yard?
9. fn a library 35^ feet long and 23J feet wide, there are
book shelves on one side and one end of the room. How
many feet of boards, in length, will be required to
make 5 of these shelves?
10. A pile of 10 blocks is placed 6 yards from a basket. If a
child starts at the blocks and carries 1 at a time to the
basket until he has carried all the blocks, and returns,
how far will lie have walked ?
178
RATIONAL ELEMENTARY ARITHMETIC.
1. Add:
12J
25
37^
5O
62^2
75
87^2
100
12} 12}
124
12}
12} 12}
12*
12} 12}
12}
12}
124 12}
12*
12}
12}
12}
"191 "1 O 1
12*
12}
12}
12} 12}
121
12}
124 12}
12*
12 1 12}
121
12}
12J
121
9
12 1 X 2
12} X 6 -
12} x 3 -
12} x 7 -
12} X 4 -
12i v 8 -
12} X 5 = .
3.
25 X 2 =
25 - 12} =
25 x 3 -
50 - 12 -
25 x 4 -
7K - 1% =
50 x 2 -
100 12] -
4.
25 is what pa
,rto50?
Of 75?
Of 100?
50 is what part of 75? Of 100?
75 is what part of 100?
5. 12} is what part of 25? Of 50? Of 75?
12} is what part of 100?
6. How many times 12} is 37}? 62}? 87}?
7. What part of 100 is 37}? 62}? 87}?
TWELVE AND A HALF. 179
1. A woman sold 4 dozen eggs at 12^ a dozen. How much
did she get for them ?
2. What is the cost of 5 pounds of butter at 124^' a pound?
3. How many 12Jr/ in a dollar? In J of a dollar? In a
half dollar? In 75#?
4. A boy bought a dozen little chickens at 12J$ each. The
feed cost him 75$ and he sold the chickens when they
were grown at 25$ each. How much did' he make in
the chicken business?
5. A farmer hired a boy to watch his corn-field and prom-
ised him 12-J^ for every 3 squirrels and 12-J# for every
5 crows that he killed. At the end of a week the boy
turned in 6 squirrels and 10 crows. How much money
should the farmer pay him ?
6. A woman bought 10 yards of ribbon at 12# a yard and 8
yards of silk at 87-J0 a yard. What was the cost of the
ribbon? Of the silk? Of both together?
7. A boy bought a ball for 12J#, a bat for 25^ and a glove
for 37J0. How much did he pay for his base-ball
outfit?
8. A girl bought a doll for 25^, a tablet and pencil for 12J^
and a book for 37J^. How much change should she
receive if she gave the storekeeper $1 ?
9. A book-seller bought 5 books at 12^ each, 8 boxes of
paper at 12-|^ each and 7 dozen pencils at 12J^ a
dozen. What was the cost of the whole?
10. A hall is 12J feet wide and 6 times as long. How long
is it?
11. A board is 12 J inches wide and 7 times as long. How
many inches long is it?
12. A boy bought 3 dozen eggs for f of a dollar, and sold
them for f of a dollar. What part of a dollar did he
gain ? How many cents a dozen 1 did he gain ?
180 RATIONAL ELEMENTARY ARITHMETIC.
1. A clerk sold 1 piece of silk cord 4J feet long, another 7-J
feet long. How many yards did he sell in all ?
2. A man wishes to put 2 rows of wire above a fence 12 rods
long. How many feet of wire does he need ?
3. How many yards of carpet are needed to lay one width
in a hall 22 J feet ]ong and on a flight of 16 stairs, each
step requiring 1-J feet of carpet?
4. John rides 12 miles, his brother f as far. How many
rods does his brother ride ?
5. A field is 160 rods long and 80 rods wide; how many
feet of wire will enclose it twice ?
6. A man left home and drove 5 miles east; turned and drove
1,000 rods back. How far was he from home?
7. The hall of a hotel is 14 yards long and 16^ feet wide.
How many feet of border will be required to go around
the walls?
8. How many boards 12 feet long will make a fence 1 mile
long, if there are 3 rows of boards?
9. One walk is 150 feet long, a second 80 feet long, and a
third 240 feet. What is the length in yards of all
together ?
10. How many miles long is a track having on 1 side 352
rails, each 30 feet long?
11. A street-car company lays 7 miles of track, J of it running
east and west, the rest north and south. How many
rods of track are there in all? How many running
each direction?
12. A boy walked 2 miles, taking steps 2 feet long. How
many steps did he take?
13. In building a fence around a field of a mile long and ^
of a mile wide, a farmer used old material for 2,250
yards, and purchased the rest. How many yards of
fencing did he buy?
TIME AND DISTANCE. 181
1. A horse can go 1 mile in 6 minutes. How many rods
can lie go in an hour?
2. A carriage wheel measures 12 feet around the outside.
How many times will it turn around in going 3 miles?
In going 5 miles?
3. A wheel is 10 feet around the outside. How many yards
will it move in going around 120 times on the ground?
4. A lot is 23 yards wide. How many rods will a man walk
in crossing the lot 8 times?
5. A boy's top-string is 2 yards long, he cuts from it a piece
18 inches long. What is the length in feet of the
remaining part?
6. A mile of gas pipe is laid at $5 a rod. What is the cost
of laying?
7. A block is 18 rods wide and 24 rods long. How many
steps of 2 feet in length will a boy take in going around
it once?
8. A street car goes 10 miles in an hour. At the same rate,
how many rods will it go in 15 minutes?
9. At 25^ a foot, what will be the cost of 4 rods and 1 foot
of hose?
10. A boy starts from his home and takes 80 steps of 2 feet
each in a minute. He walks at that rate as far as he
can go and return in 10 minutes. How far was he
from home when he turned to go back?
11. A man walked 4 miles an hour and a boy walked 2 miles
an hour. Ihey started in the same direction at the
same time. How many rods apart were they in 15
minutes ?
12. What will be the cost of a ditch half a mile long at $1.25
a rod?
13. What is the distance around a lot which is 50 yards and
2 feet long and 8 yards and 1 foot wide?
182
RATIONAL ELEMENTARY ARITHMETIC.
1. Give the number of
12's in
3'sin
ll's in
2.
7.
of 320 =
T V of 320 =
2 X 320 = .
5 x 320 = .
8. What part of 320 is 40?
! of 320
T ! g of 320
sV of 320
3 x 320
4 X 320
What part is 80?
20?
REVIEW PROBLEMS. 183
1. If 1 cord of wood cost $5-J, how much will 4 cords cost?
2. How many 12 pound packages of sugar can be made from
72 pounds?
3. How many bins holding 5 A bushels qan be filled from 16|
bushels of grain ?
4. x A man walked 16J miles 1 day and 5 J miles the next.
How many miles did he walk in all ? How many miles
farther the first day than the second?
5. At $5-| a ton, how many tons of coal can be bought for
$22?
6. 11 men received $132 for digging a ditch. They shared
the money equally. What did each one receive?
7. A farmer bought 16 sheep at $3 each and sold them at
the rate of 3 for $12. What was the entire cost? How
much did he receive? What was his gain?
8. A flag staff 48 feet high was broken into 2 pieces, 1 piece
being 3 times as long as the other. What was the
length of each piece?
9. What is the cost of a bale of cotton containing 400 pounds,
at 5J# a pound? At 7# a pound?
10. From a bin holding 77 bushels, 55 bushels were taken
out. How many bins holding 5-J bushels each can be
filled from the remainder?
11. $40 a month is paid by a man for his rent; his other
monthly expenses are 7 times as much. What is the
amount of his other expenses ? Of total expenses ?
12. What is the average rate of speed made by a train travel-
ing 320 miles in 8 hours?
13. A grain dealer sold 320 bushels of corn in 40 bushel
loads. How many loads did he sell?
14. A bushel of wheat weighs 4 pounds more than a bushel
of corn. What is the difference in weight between 80
bushels of each?
184 RATIONAL ELEMENTARY ARITHMETIC.
1. Draw diagrams on a scale of 3 feet to 1 inch for rooms
of the following dimensions:
12 feet long and 9 feet wide.
24 feet long and 18 feet wide.
30 feet long and 27 feet wide.
33 feet long and 21 feet wide.
15 feet long and 12 feet wide.
21 feet long and 12 feet wide.
27 feet long and 15 feet wide.
24 feet long and 15 feet wide.
Give perimeters in feet. In yards.
2. Draw diagrams on a scale of 3 yards to 1 inch, for lots of
the following dimensions:
15 yards long and 12 yards wide.
18 yards long and 15 yards wide.
12 yards long and 6 yards wide.
15 yards long and 9 yards wide.
24 yards long and 12 yards wide.
33 yards long and 15 yards wide.
21 yards long and 12 yards wide.
27 yards long and 12 yards wide.
Give perimeters in yards. In feet.
3. Draw diagrams on a scale of | mile to 4- inch, for fields
of the following dimensions:
^ mile long and -J- mile wide.
1 mile long and -J- mile wide.
2 miles long and 1|- miles wide.
1 miles long and ^ mile wide.
1 miles long and 1 mile wide.
-J mile long and ^ mile wide.
1 miles long and |- mile wide.
1^ miles long and f mile wide.
Give perimeters in miles. In rods.
PART THIED.
This is the plan of a square garden drawn to a scale of an inch to 1 yard.
1. Measure the figure. What is its length? Its width?
2. How many feet long would the lot be? How many feet
wide?
3. Count the number of square yards. By what name have
we known 16J feet? By what name have we known 5i
square yards?
4. If the figure were 320 times as long and wide as repre-
sented, how long would it be? How wide?
5. What would you call such a square figure?
6. Referring to figure A on page 110, if each square repre-
sents 1 square inch, how long would the side of this
figure be? How many rows of 12 square inches are in
it? How many square inches would it contain?
185
186 RATIONAL ELEMENTARY ARITHMETIC.
1. How many square inches in a square foot? (See p. 185.)
2. How many square feet in one row on one side of a square
yard? How many rows of the same number of square
feet? How many square feet in a square yard?
3. How many square yards in a square rod? (See p. 185.)
4. How many yards in 2 square rods?
5. How many yards in one-half of a square rod?
6. How many yards in 2-| square rods?
7. A garden contained 2J square rods and was 1 rod wide.
How long was it?
8. A lot contained 20 square rods. How many square yards
in it?
9. A lot containing 80 square rods was sold for $240. How
much was that a square rod?
10. A lot containing 160 square rods was sold at the rate of
$3 a square rod. How much was received for it?
11. A street in a village was 6 rods wide and 40 rods long.
How many square rods did it contain? How many
square yards?
12. A street 250 rods long contained 10 blocks. Not counting
crossings, how many rods was that for each block? How
many yards for each block? How many feet?
13. At $5 a front foot, how much will it cost to pave a street
in front of a lot that is 33 feet wide?
14. If the paving in problem 14 extends to the middle of a
street 3 rods wide from curb to curb, how many square
feet are provided for in front of this lot?
15. A street is 28 blocks long. Each block, including cross-
ing, is 15 rods long and 5 rods. wide. How many
square rods does the street contain?
16. A field 16 rods long and 10 rods wide contains how many
square rods? What is its perimeter in rods? In yards?
In feet?
MEASURING SURFACES.
187
B
The above is a plan of a garden drawn to a scale of 12 feet to 1 inch.
1. To find the area of the entire garden, first divide as indi-
cated by the dotted lines.
2. The area of B is equal to how many square feet? How
many square yards?
3. Find the area of D in square feet. In square yards.
The area of C.
4. Find the area of A in square feet. In square yards.
5. Find the area of the entire garden in square yards.
6. C is what part of A?
D is what part of C? Of A?
B is what part of D ? Of C ? Of A ?
7. If 1 inch on the plan represents 4 yards, what is the area
of each section in square yards? In square feet?
8. If 1 inch on the plan represents 8 rods, what is the area
of each section in square rods?
188 RATIONAL ELEMENTARY ARITHMETIC.
TABLE OF SQUARE MEASURE.
144 sq. in. (square inches) = 1 sq. ft. (square foot).
9 sq. ft. = 1 sq. yd. (square yard).
30 sq. yd. = 1 sq. rd. (square rod).
160sq. rd. = 1 A.
640 A. =1 sq. mi. (square mile).
1. In 60 A. how many sq. rd. ?
2. In 32 sq. rd. how many sq. yd. ?
3. In 63 sq. yd. how many sq. ft. ?
4. In 37 sq. ft. how many sq. in.?
5. In 56 A. and 13 sq. rd. how many sq. rd. ?
6. In 47 sq. rd. and 9 sq. yd. how many sq. yd. ?
7. In 37 sq. yd. and 7 sq. ft. how many sq. ft. ?
8. In 134 sq. ft. and 47 sq. in. how many sq. in. ?
9. Add:
60 A. 15 sq. rd. 16 sq. rd. 4 sq. yd.
137 A. 40 sq. rd. 47 sq. rd. 8 sq. yd.
256 A. 56 sq. rd. 64 sq. rd. 15 sq. yd.
186 A. 49 sq. rd. 32 sq. rd. 3^ sq. yd.
10. Add:
14 sq. yd. 2 sq. ft. 4 sq. ft. 43 sq. in.
11 sq. yd. 4 sq. ft. 6 sq. ft. 84 sq. in.
4J sq. yd. 3 sq. ft. 7 sq. ft. 17 sq. in.
11. Subtract:
18 sq. ft. 56 sq. in. 16 sq. yd. 7 sq. ft. 18 A. 86 sq. rd.
5 sq. ft. 13 sq. in. 11 sq. yd. 3 sq. ft. 5 A. 17 sq. rd.
12. Multiply:
6 sq. ft. 24 sq. in. 6 sq. yd. 3 sq. ft. 3 A. 80 sq. rd.
6 3 2
APPLICATION OF SQUARE MEASURE. 189
1. A board is 13 feet and 4 inches long and 12 inches wide.
What is the area of 1 side in square feet?
2. A house 24 feet wide covers 72 square yards of ground.
How long is it and what is the distance around it?
8. The blackboards in a schoolroom are equal to 1 black-
board 54 feet long and 4 feet wide. How many
square feet of surface in all of the blackboards, and
what will it cost to slate them at 360 a square yard?
4. How many acres of ground in 4000 square rods ?
5. What will a farm 240 rods long and 60 rods wide cost at
$35 an acre?
6. A man has 10 acres and 90 square rods. He buys 8 acres
and 70 square rods. How much land does he then
have?
7. How many square feet in the floor of a room that is 24
feet long and 12-| feet wide? What will it cost to
paint the floor at 25^ a square yard?
8. How many square yards of cloth will it take to cover a
table that is 48 inches long and 36 inches wide?
9. The floor of a hall 36 feet long and 6 feet wide is paved
with marble blocks 1 foot square. How many blocks
did it take to pave the hall ?
10. A hall 24 feet long and 6 feet wide is paved with tile 6
inches square. How many tiles were required?
11. A room is 18 feet long, 15 feet wide and 9 feet high.
How many square yards in the floor and ceiling. How
many square yards in the walls?
12. How many square feet of flooring in a 9 story building
which is 55 feet wide and 123 feet long?
13. How many square feet of sidewalk in 9 blocks of 275
feet each, if the sidewalk is 8 feet wide?
14. A building is 150 feet long and 40-J feet wide. How
many square yards does it cover?
190 RATIONAL ELEMENTARY ARITHMETIC.
1. Divide:
264 by 11, by 21, 31, 41, 51.
528 by 12, by 22, 32, 42, 52.
377 by 13, by 23, 33, 43, 53.
434 by 14, by 24, 34, 44, 54.
675 by 15, by 25, 35, 45, 55.
352 by 16, by 26, 36, 46, 56.
2. Divide each of the following numbers by 13, 14, 16, 29,
38, 46, 57, 74, 88, and 97.
118 154 172 120 156 188
213 237 248 253 269 293
3123 3234 3345 3456 3567 3785
4678 5788 6879 7890 8901 8493
9012 8123 7243 6542 5987 9648
3. A man paid $31.46 for eggs at 13^ a dozen. How many
dozen did he buy ?
4. A tank holds 300 barrels of water. When it is -fa full,
how many barrels does it hold?
5. In a flock of 1,736 sheep, ^ of the number were lambs.
How many lambs were there?
6. A man bought 20 feet of piping for $6.40. How_ much
per foot did it cost?
7. A man bought 18 yards of cloth for $36.72. How much
did it cost a yard?
8. A man bought 25 pictures, paying for them $925. If
each one cost the same, what was the cost of one picture?
9. A grocer sold 19 pounds of butter for which he received
$4.37. How much per pound did he get?
10. A boy can ride 15 miles an hour on his bicycle. At the
same rate how many hours would it take him to ride
5,136 miles?
11. The schoolroom floor contains 1,100 square feet and is 25
feet wide. How long is it?
PROBLEMS OF DIVISION. 191
1. A grain dealer sold 665 bushels of oats in loads of 35
bushels each. How many loads did he sell?
2. A man paid $79.58 for butter at 23^ a pound. How many
pounds did he buy?
3. A lot contains 4,232 square feet and is 23 feet wide. How
long is it?
4. If 24 horses cost $1,080, what is the average cost of one?
5. 3,300 bushels of grain were put into 22 bins of equal
size. How many bushels in each bin?
6. In laying a railroad 1,200 miles long, one-sixth of it was
built over hilly ground, and one twenty-fourth of it
over water, the rest ran over level ground. How many
miles of railroad in each part?
7. If there are 40 single seats in each room in a schoolhouse,
how many rooms will be needed to seat 1,680 pupils?
To seat 8,640 pupils?
8. A merchant bought 2 dozen pairs of shoes for $52.80.
How much did he pay a pair?
9. How many ponies at $50 each can be bought for $1,000?
10. A bookseller bought 1,485 books. They were packed in
15 boxes with an equal number in each box. How
many books were there in each box?
11. A coal dealer shipped 2,916 tons of coal in cars of 18 tons
each. How many such cars did he ship?
12. A grocer bought a quantity of butter at 22 cents a pound,
and paid for it all $10.56. How many pounds did he
buy?
13. How many packages containing 24 ounces each can be
made from 15 pounds of tea?
14. A man sells horses at $85 apiece. How many horses
must he sell to receive $1,020?
15. How many loads of corn, each 22 bushels, will be needed
to fill a crib that holds 264 bushels?
192 RATIONAL ELEMENTARY ARITHMETIC.
13
1
13
2
26
3
39
4
52
6
65
6
.
78
7
91
1. 13 X 2
1
3 v
- 5
13 X 3
1,
} X
' 6
13 X 4
_
1
3 v
' 7
_
2. 13 is wl
Of 91
3. 39 -f i:
lat
If
} -
pai
rt c
2
6?
C
)f
19 f
C
>fj
78
8?
_u
13
>f 6
5? Of 52?
26 4- li
* -
65
4-
13
_
52 -f 1;
] -
91
18
_
4. 8
13
9
13
1
1
1
3
r
l
f
*
6
13
1
1
2
3
10 5
13 13
5. How many stripes in our flag?
6. How many red stripes?
7. How many white ones?
8. How many states were there when the number of stars
was three times the number of stripes?
9. When will the number of stars be 4 times the number of
stripes ?
10. 5 times the number of stripes in our flag is the year of
the nineteenth century in which the Civil War closed.
In what year did the war close?
11. From the Declaration of Independence to the World's
Fair in Chicago was 9 times as many years as there are
stripes in the flag. How long was it?
PUOBLKMS IN VALUES- RATIO. 10.3
In the following problems, the phrase "at- the same rate" is understood.
1. -8 pounds of butter cost 750. What is the cost of 4
pbuutls ?
2. If 9 barrels of flour cost $45, what is the cost of 7 bar-
rels?
8. 5 acres of land cost $250. What is the cost of 7 acres of
land?
4. I received $63 for 9 weeks' work. What should I receive
for 12 weeks' work?
5. What is the cost of a dozen chairs if J of a dozen cost
$12?
6. If I pay 40 for 10 marbles, what should I pay for 25
marbles?
7. When eggs sell at 300 for 2 dozen, what is the cost of J
of a dozen?
8. A dozen pairs of boots cost $30. What is the cost of 8
such pairs?
9. When 2 gallons of syrup cost $1.50, what is the cost of 3
quarts ?
10. A man receives $1200 a year and spends $45 a month.
How much does ho save the first months? How
much does he spend?
11. A piece of string is G lengths of an 18-inch rule. How
many feet long is it?
12. A man had on his wagon 30 bushels of wheat, of which
he sold at 950 a bushel. The remainder he sold at 980
a bushel. What did he receive for the entire load?
13. The curtains for a room with 3 windows cost $5. What
will they cost for a room with 12 windows?
14. 3 dozen neckties cost $1.80. What is the cost of 4 neck-
ties?
15. A car runs 4 miles in 20 minutes. How far will it run
in 3 hours?
194 RATIONAL ELEMENTARY ARITHMETIC.
NOTE lu plastering, many contractors make no deductions for win-
dows or doors on account of the extra time necessary to do the work care-
fully around the frames. In all the problems, therefore, on plastering,
unless otherwise stated, the walls are counted as solid.
1. A room is 9 feet by 21 feet and 9 feet high. How many
square yards in the walls ? In the ceiling ? What will
it cost to plaster the walls and ceiling at 21 # a sq. yd. ?
2. A room is 12 feet square and 10 feet high. What will
it cost to plaster the walls and ceiling at 23^ per
sq. yd. ?
3. What will be the cost of plastering the walls of a room 9
by 12 feet and 9 feet high at 45^ a square yard?
4. What will be the cost of plastering the ceiling of a room
24 feet square at 28^ a square yard?
5. Mr. Jones wishes to plaster the walls and ceilings of 3
rooms. The first room is 9 by 12 feet, the second 12
by 15 feet and the third 15 by 18 feet. The height of
each room is 9 feet. What will be the cost of plaster-
ing the three rooms at 28^ a square yard?
6. What would be the cost of carpet a yard wide for the
three rooms at 75^ a yard?
7. The floor of a room contains 324 square feet. One side
of it is 4 yards long. How many yards long is the
other side?
8. '.The 4 walls of a square room 8 feet high contain 384
square feet. What is the length and the width of the
room?
9. The top of a desk is 2 feet and 6 inches wide and 4 feet
long. How many square feet does it contain?
10. What is the length of a wall 12 feet high the area of
whose side is 3 times 264 square feet?
11. A room is 10 feet wide and 11J feet long. A rug on the
floor is 2J yards wide and 3 yards long. How much of
the floor is not covered by the rug ?
PRODUCTS BY FOURTEEN.
I!).',
U
1
14
2
28
3
42
4
56
6
70
6
84
7
98
1. Add:
14
14
14
14
14
14
14
28
56
28
28
28
14
56
2. 14 x 3 =
14. v
6 -
14 x 2 --
14- v
7 -
14 v n -
14. v
4 -
3. 14 is what part of 28? Of 56? 42? 70? 84?
4. How many 28's in 42? 70?
84?
56?
98?
5. 42 is how many 14's? 28'
8?
What part
of 56?
6. 56 is how many 14'
s? 28's?
42's? What par
98?
7. 70 is how many 14's? 28's?
42'
s? 56
's? W
28
28
42
14)_98
14)70
98?
Of 70?
of 70?
What part
of 98?
8. 84 is how many 14's?
9. A man fed his horse
28's? 42's? 56's? 70's?
1^ pecks of oats each day for 4
weeks. How many bushels of oats did he feed him ?
10. Mr. Jones traveled 195 mi. each day for 2 weeks. How
far did he travel in the two weeks?
11. A train ran 14 miles in 30 minutes. How far would it
run at the same rate in 2^ hours?
12. A piece of ground 1008 ft. wide is divided into 14 equal
lots. What is the width of each lot?
196 RATIONAL ELEMENTARY ARITHMETIC.
TRIANGLES. 197
1. Review page 121.
2. How long is the base of the triangle A on the opposite
page?
3. What is the altitude of the triangle?
4. Into what rectangle can you change the triangle A?
5. What is the area of this rectangle?
6. What, then, is the area of the triangle A?
7. What rule would you give for finding the area of such a
triangle ?
8. Measure the triangles B, C, D and E, and give the dimen-
sions in each case of the rectangle into which you can
change the triangle.
9. What is the area of each of these rectangles?
10. What, then, is the area of the triangle B? Of the tri-
angle C? OfE?
11. If you were to make a rectangle whose width was the base
of A, and whose length was the altitude of A, would
you change the largest angle of the triangle ?
12. Such an angle we call a right angle and every triangle
which has such an angle is called a right-angled tri-
angle.
13. What triangles on the opposite page are right-angled
triangles ?
14. If an inch of the plan represented a yard, what would be
the area of each triangle in feet?
15. Find the area of the following right-angled triangles:
Base three feet, altitude six feet.
Base four feet, altitude three feet.
Base six feet, altitude eight feet.
Base eight feet, altitude ten feet.
Base twelve feet, altitude eight feet.
Base fifteen feet, altitude twelve feet.
Base ten inches, altitude five inches.
198 RATIONAL ELEMENTARY ARITHMETIC.
AREAS. I'M)
NOTE. The plan on the opposite page represents a garden, which has
been cut into various parts by the walks running through it. The plan is
drawn to the scale of 10 feet to an inch.
1. Measure the line around the entire plan and find the
length of the path around the garden.
2. From these measurements, what is the area of A?
8. What is the area of B?
4. What is the area of C?
5. What is the area of D?
6. What is the area of E?
7. What is the area of F?
8. How many square feet are there in the entire garden ?
9. A is what part of B? C? D? E? F?
10. F is what part of the entire garden ?
11. How did you find the area of C?
12. How did you find the area of D?
13. In what other ways beside finding the areas of the tri-
angles could you find the area of the entire garden ?
NOTE. Suppose the plan on the opposite page, representing a piece of
land, is drawn to a scale of one inch to 8 rods.
14. What will be the value of A at 250 a sq. rd. ?
15. What will be the value of B at 300 a sq. rd. ?
16. What will be the value of C at 280 a sq. rd. ?
17. What will be the value of D at 270 a sq. rd. ?
18. What will be the value of E at 260 a sq. rd. ?
19. What will be the value of F at 290 a sq. rd.?
20. How many sq. rds. in the entire field?
21. How many acres?
22. How many sq. yds. in A.?
23. How many sq. ft. in B ?
24. How many sq. yds. in C?
25. How many sq. ft. in D ?
26. How many sq. yds. in E ?
27. How many sq. ft. in F?
200 RATIONAL ELEMENTARY ARITHMETIC.
1. A woman who raises chickens put 13 eggs under each of
6 hens. The first hatched out all but 1, the second all
but 2, the third all but 3, the fourth all but 4, and the
others all but 5 each. How many chickens were
hatched?
2. How many pigeons will it take to pick up a bushel of corn
(56 Ibs.) if each one picks up 4 oz. ?
3. A man buys 12 tons of hay for $80 and sells it for 60#
per cwt. How much does he make?
4. An expressman receives $3.25 per day for 30 days. It
costs him 30^ per day to feed his horse. He pays $4.20
for repairs to his wagon. How much has he left?
5. An express company carries 400 packages at 15^/ each,
28 trunks at 50^ each, and 12 bicycles at 40^ each.
What does it get for them all ?
6. There are 40 street cars on one line and each can carry
60 people. How many people will they all carry in 12
round trips if | carry their full number each way and
the remainder carry 30 persons each way?
7. A baker has 400 loaves of bread. He sells at 5^ per
loaf, 60 loaves at 4#, and gives the rest away. How
much does he get for the bread ?
8. How many sheep must there be to produce a ton of wool
if the wool from each sheep weighs 4 Ibs. ? If each
sheep produces 5 Ibs. ?
9. How many balls of kite string will it take to reach 8^
miles if each ball contains 80 yards? 110 yds.?
10. A farmer raised 840 bu. of potatoes on 5 acres of land.
What was the value of the average produce of 1 acre at
400 per bushel?
11. A man set out 12,000 cabbage plants, but j of them died
and -jig- of the remainder were blighted. What did he re-
ceive for the rest at $3 per hundred?
MISCELLANEOUS PROBLEMS. 201
1. An orchard of 600 trees produced 3 bbls. of apples to the
1 tree. The owner sold them at $1.40 per bbl., but the
barrels cost him 25^ each. What did he get for the
apples after paying for the barrels?
2. A peach orchard produced 210 bu. of peaches. If 1 bu.
fills 5 baskets, what is the value of the crop at 20^ a
basket?
3. A farmer pays some boys 1^ per box for picking berries,
and the boxes cost him -J-0 each. If lie sells 1000 boxes
of berries for $60.00, what is his share of the money?
4. A boy's pay for a week's work at berry-picking at !</ per
box was $5.40. How many boxes did he pick daily, on
mi average, 'during the six days?
5. A farmer sells 1000 boxes of berries to a city grocer at
6# per box. It costs the grocer $5.00 to get them to
the city and he sells them at 8# per box. . What is his
gain ?
6. A woman who kept chickens bought 12 bu. of feed for
them at 35^ per bu. She sold 120 doz. eggs at 12^
a doz. and 40 chickens at 25# each. How much more
did she receive than she paid out?
7. How many chickens averaging 5 Ibs. each and worth 6^
per Ib. can be bought for $75?
8. If 15 chickens are worth as much as 1 sheep, and 6 sheep
are worth as much as 1 cow costing $28.80, what is 1
chicken worth?
9. A carpenter builds a fence for $56. Thft lumber costs
him $15 and he pays each of three men $2.75 per day
for four days. What is his share of the $56?
10. A man earns $1.50 every day he works and pays 50^ a day
for his board. If he only works 16 days during the
month of May, how much has he left after paying his
board?
202 RATIONAL ELEMENTARY ARITHMETIC.
BEET-SUGAR PRODUCTION OF THE UNITED STATES.
*Ton= the long ton of 2240 pounds.
1. If the two beet-sugar factories of New York in 1903 pro-
duced equal amounts, how many tons did each factory
produce during that year? How many pounds did
each produce during that year?
2. If the seven beet-sugar factories of California in 1902 pro-
duced equal amounts, how many tons did each factory
produce during that year? How many pounds?
3. If an equal number of acres was sown to produce beets
for each factory, how many acres were producing for
each facfory of Colorado in 1903? In 1902?
4. If an equal number of acres was sown to produce beets for
each factory, how many acres were producing for each
factory of Michigan in 1903? In 1902?
5. Make other problems on this table comparing the pro-
duction of different states and their values at current
newspaper prices.
PROBLEMS IN TIME. 203
A LIST OF DATES OF BIRTHS AND DEATHS OF NOTED PERSONS.
Paul Revere .
Benj. Franklin
Wm. McKinlev
Jan. 1, 1735 1818 Andrew Jackson.. Mar 15, 17f>7 1845
Jan. 17, 1706 1790 Kosa Bonheur . Mar. 22, 1822 1899
Jan. 29, 1843 lOOHHuns ('. Andersen. April 2, 1805 1875
T imes G. Blaine .Jan. 31, 1X30 1803 Washington Irving April 3, 1
Abraham Lincoln Feb. 12, 1809 1865 John Bui-rough
Charles Dickens . Feb. 7, 1X12 1870 U. S. Grant
Geo. Washington. Feb. 22, 1732 1799 Audubon
James R. Lowell. Feb. 22, 1819 1X91 Queen Victoria
Henry W. Long-
fellow . . Feb. 27. 1807 18X2 Patrick Henrv
April 3, 1S37 ....
April 27, 1822 1885
May 4, 1780 1851
May 24, 1819 1901
Mav 29, 1730 1799
1. What is the month and day of your birth?
2. In what year were you born?
3. How old are you to-day?
4. Find how many years each person in the above table
lived.
5. Which was the older, and how much older, William Mc-
Kinley or James G. Blaine? James Russell Lowell or
Henry W. Longfellow? Abraham Lincoln or U. S.
Grant?
6. How many years ago (now) was each person born?
7. The birthday of William McKinley occurs how many days
after that of Benjamin Franklin?
8. The birthday of Henry W. Longfellow occurs how many
days before that of Andrew Jackson?
9. How many days between U. S. Grant's birthday and that
of Patrick Henry?
10. How many years, months, and days have passed since
Queen Victoria was born?
11. Answer the same question for Benjamin Franklin; James
Russell Lowell; Rosa Bonheur.
12. Make problems using the dates of births of pupils in your
class.
204
RATIONAL ELEMENTARY ARITHMETIC.
1. In the first layer of blocks in this solid, how many rows of
4 blocks each? How many blocks in the layer? How
did you find this? In all 3 layers, or the entire solid,
how many blocks are there? How did you find this?
How then do you find the number of cubic feet in any
square-cornered solid?
2. How many inch cubes are there in a block 2 inches long,
2 inches wide and 1 inch high? See page ..2 How
many inch cubes are there in a block 4 inches long, 2
inches wide and 1 inch high?
3. How many inch cubes are there in a block 6 inches long,
4 inches wide and 1 inch high? How many inch cubes
are there in one row? How many of these rows are
there in the block?
4. How many cubic inches are there in a box that is 4 inches
long. 3 inches wide and 1 inch high ? 2 inches high ?
3 inches high?
5. How many cubic inches are there in a box 4 inches long,
2 inches wide and 2 inches high?
f>. A block is 5 inches long, 2 inches wide and 3 inches high.
How many cubic inches are there in it?
SOLIDS AND CAPACITY. 205
1. A pencil box containing 24 cubic inches is 3 inches wide
and 1 inch high; how long is it?
2. A block is 3 feet long, 3 feet wide and 3 feet high ; how
many cubic feet does it contain? What is the area of
one side of such a block in square feet? In square
yards? How many cubic yards in a block 1 yard long,
1 yard wide and 1 yard high? How many cubic feet
in such a block ?
3. A room is 5 yards wide, 7 yards long and 4 yards high.
How many cubic yards are there in the room ?
4. A cellar is 7 yards long, yards wide and 3 yards deep.
How many cubic yards of earth were taken out in
digging the cellar?
5. The foundation wall of one side of a building is (55 feet
long, 4 feet high and II feet wide. Ho\v many cubic
feet does it contain ?
6. A box is 7 feet long, 3 feet wide and contains 03 cubic
feet. How high is it?'
7. A bin is 3 feet wide, 4 feet high and contains 72 cubic
feet. How long is it?
8. A coal-bin is 12 feet long, 6 feet wide and 7 feet high.
How many cubic feet of coal will it hold ?
9. A car is 61 feet long, 10 feet wide, and 10J feet high. How
many cubic yards does it contain?
10. A man has 4 bins, each 5 feet long, 4 feet wide and 3 feet
high. How many cubic feet of coal will they hold to-
gether ?
11. A bin is 12 feet long, 9 feet wide and 6 feet high. How
many cubic yards does it contain ?
12. 1 box is 4 feet long, 3 feet wide and 2 feet high. A sec-
ond is 5 feet long, 3 feet wide and 2 feet high. A third
is b* feet long, 5 feet wide and 4 feet high. How many
cubic feet in the 3 boxes?
206
RATIONAL ELEMENTARY ARITHMETIC.
1. Keview pages 69 and 128.
2. How many edges do you see
on this block? How
many edges has this
block?
3. Measure its edges. How
long are they? Are all
the edges of the block of
equal length ? What do
you call such a block?
4. If you should place 12 of these cubes in a row, how long
would the row be?
5. If you should place 12 of these rows side by side, how
wide would the whole be?
6. How many cubes would you use?
7. What figure would the upper surface of the cubes form ?
8. How many square inches would there be in this surface?
How many inch cubes would you use in forming this
layer ?
If you should place another layer of cubes on those
already used, how many cubic inches would you have?
How many if you used 3 layers ? 4 layers ? 5 layers ?
6 layers? 7 layers? 8? 9? 10? 11? 12?
10. Suppose the picture represents 12 layers of inch cubes,
each layer containing 12 rows of 12 cubes each. What
would the edges measure ? What would you call such
a cube? How many cubic inches would it contain?
11. If you should take one-half of this cube and divide into 4
equal cubes, what would each cube measure?
12. What part of the whole cube would each be?
13. How many cubic inches in each part?
14. How many cubic inches in three-eighths of a cubic foot?
In seven -eighths? In one-fourth? In three-fourths?
9.
MEASURING; SOLIDS AND CAPACITY. LMIT
1. A strawberry box is 6 inches long, 4 inches wide and 4
inches deep. How many such boxes can be packed in
a case 2 feet long, 1 foot wide and of a foot high ?
2. There are 231 cubic inches in 1 gallon. How many
gallons can be put into a pail holding 693 cubic inches ?
3. How many boxes 12 inches long, 6 inches wide and 3
inches high can be packed in a case 6 feet long, 4 feet
wide and 4 feet high ?
4. How many cubic feet of air will a glass jar 24 inches long,
18 inches wide and 12 inches high hold?
5. From a vessel holding 2 cubic feet of water 864 cubic
inches were taken. How many cubic inches remain?
How many cubic feet?
6. In 1 jar there are 864 cubic inches of liquid ; in another
2592 cubic inches. How many cubic feet in a third
jar, holding as much as the first and second together?
7. A man put 12 inches of sand into a box 9 feet long and
5 feet wide. How many cubic feet of sand in the
box?
8. A wagon box 3 feet wide and 9 feet long is 1^ feet deep.
How many cubic feet will it hold?
9. A ditch 45 feet long and 2 feet wide contains 630 cubic
feet. How deep is the ditch?
10. A freight car is 32 feet long and 6 feet wide inside and is
filled with sand 3 feet deep. How many cubic feet of
sand are in the car?
11. A wall is 44 feet long 5| feet high and 18 inches thick.
How many cubic feet in the wall?
12. A sidewalk is 6 inches thick and 6 feet wide. How many
cubic feet in 124 feet of the sidewalk?
13. In a building there are 18 pillars 2 feet by 18 inches
and 14 feet high. How many cubic feet in these
pillars?
208 RATIONAL ELEMENTARY ARITHMETIC.
TABLE OF CUBIC MEASURE.
1728 cu. in. (cubic inches) = 1 cu. ft. (cubic foot).
27 cu. ft. = 1 cu. yd. (cubic yard).
128 cu. ft. = 1 cord.
231 cu. in. =1 gal.
2150$ cu. in. (nearly) == 1 bu.
1. Add:
cu. yd.
7
cu. ft.
6
cu. in.
27
cu. yd.
6
cu. ft.
14
cu. in.
55
2
10
250
2
2
17
4
2
41
3
3
40
8
3
3
1
2
160
3
4
120
8
4
50
cu. yd.
20
cu. ft.
10
cu. in.
75
cu. yd.
4
cu. ft.
7
cu. in.
800
7
5
50
7
6
600
5
1
64
3
4
20
3
8
125
2
2
8
2
3
800
9
7
300
2. Subtract:
cu. yd.
10
cu. ft.
25
cu. in.
1200
cu. yd.
9
cu. ft.
18
cu. in.
350
6
16
900
5
9
275
cu. yd.
14
cu. ft.
20
cu. in.
800
cu. yd.
11
cu. ft.
15
cu. in.
920
7
13
246
6
7
256
3. Multiply:
cu. yd.
6
cu. ft.
7
cu. in.
576
cu. yd.
12
cu. ft
6
cu. in.
432
3
4
TAHLK OF (TKK' MKASI'KK. 200
1. A boy carried enough wood to make a pile 4 ft. long, 2 ft.
wide and 2 ft. high. What part of a cord did he carry?
2. "What must be the cubic contents of a jar to hold | of a
gallon? 2.ygals.? 4} gals.?
3. How many cubic inches are there in a bin holding 2 bu. V
Jbu.? 5Jbu.? 4Jbu.? OJ bu.?
4. A cord of wood is usually piled 8 ft. long and 4 ft. wide.
How high is it?
5. A bin holds 16 bu. How many cubic inches does it con-
tain ?
G. A water trough contains 12 gals, of- water. It is 14 in.
wide and 9 in. deep. How long is it?
7. How many cu. yds. of earth will be excavated for a cellar
that is 24 ft. long, 21 ft. wide and 12 ft. high?
8. From a cellar 36 ft. long and 18 ft. wide 6804 cu. ft. of
earth was taken. How deep was the cellar?
9. How many cu. yds. of rock was blasted from a tunnel that
is 9i ft. high, 80 ft. long and 12 J ft. wide?
10. A cubic foot of water weighs 1000 ounces. What will
water enough to fill a trough 6 ft. long, 2 ft. wide, and
lij- ft. deep weigh in pounds?
11. If oil weighs as much as water, what is the weight of a
cubic foot of oil in pounds?
12. A street sprinkler holds 168 cu. ft. of water. How much
does it hold in pounds ?
13. If such a street sprinkler is emptied every 24 minutes
during 9 hours, how many buckets of water are used if
a bucket holds -J of a cu. ft. ?
14. A rectangular tank 6 ft. wide, 10 ft. long, and 3 ft. deep
is full of water. What is the weight of the water?
15. 35 cu. ft. of coal will weigh about 2000 pounds. How
many tons will a wagon box 7 ft. long, 3 ft. wide, and
2 ft. high weigh if loaded full ?
2-10
RATIONAL ELEMENTARY ARITHMETIC.
1
2
3
4
6
6
1. Add:
15
15
*
5
15
30
45
60
76
90
15 15 15 15
30 45 60 30
15
15
2. 15 x 2 =
15 X 4 =i
15 X 5 =
15
15 x 3 =
15 X 6 =
15)45
45
30
30
30
15)60
15)90
How many 30's? 45's? What
How many 30's? 45's? 60's?
3. 15 is what part of 30? 60? 45? 90? 75?
30 is how many 15's? What part of 45 ? 60? 75? 90?
45 is how many 15's? How many 30's? What part of
60? Of 75? 90?
60 is how many 15's?
part of 75? Of 90?
75 is how many 15's?
What part of 90?
90 is how many 15's? How many 30's? 45's? 60's?
75's?
4. A boy bought 3 dozen oranges at the rate of 150 a dozen.
What did they cost him?
5. A girl bought 12 handkerchiefs at the rate of 2 for 15#,
What did they cost her?
6. Railroad fare for a picnic excursion was 15^ for the round
trip. How much was collected on a train of 9 cars
with 65 persons in each car?
PRODUCTS OF FIFTKKN. 211
1. At a school entertainment there were 186 grown people
who paid 150 each and 324 children at 100 each. The
expenses were $15.25. How much was left for the
school?
2. A class of 25 pupils have a spelling lesson of 15 words.
15 of them write the lesson once, 6 of them write it
twice, and 4 write it three times. How many words
were written by each pupil? By all the pupils together?
3. The pupils of a school put $14.06 into the Penny Savings
Bank on Monday and take out $2.40; they put in $7.24
on Wednesday and take out $1.56, and they put in
$9.28 and take out $4.10 on Friday. How much more
do they put in than they take out for the week?
4. A peddler buys 15 bu. of apples at 900 per bushel and
sells them at 150 per half peck. How much does he
make if he sells them all ?
5. A banana peddler buys 100 dozen bananas for $7.50. He
sells J of them at 150 per dozen, ^ of them at 10^ per
dozen, 20 dozen at 50 per dozen, and the rest spoiled.
How much does he make?
6. A junk dealer buys 1000 pounds of old iron for $1.20 and
400 pounds of lead for $6. He sells the iron for 40 per
pound and the lead for 3^0 per pound. How much does
he make?
7. A milk dealer sells every day 6 cans of milk each holding
8 gallons. How many customers has he if each one
takes 2 qts. ? If each takes 3 pts. ?
8. If he pays 900 per can for the milk, and sells it for 50
per quart, how much does he gain ?
9. A sugar plantation in Cuba produces 480 hhds. of sugar,
averaging 540 Ibs. in weight. What is the value of
the sugar at 2|0 a pound? At 20 a pound, what is the
value of the sugar from 15 such plantations?
212
RATIONAL ELEMENTARY ARITHMETIC.
TABLE OF LIQUID MKASTKK
4 si. (gills) = 1 pi, (pint).
2 pi,
4 r,|,
1. Review pages 9 and 78 as oral work
2. Add:
= 1 qt. (quart).
= 1 gal. (gallon).
= 1 bbl. (barrel).
gal.
qt.
P t.
gal.
qt.
P t.
bbl.
gal.
qt.
4
2
1
7
3
2
14
1
3
1
1
2
2
3
,6
3
bbl.
gal.
qt.
gal. qt
. P t.
lihd. bbl.
gal.
qt.
1
20
1
15
1
1
16
1
11
1
2 3
1
15
1
3.
Subtract :
gal.
qt.
pt.
gal.
qt,
pt.
gal.
qt.
pt,
7
4
2
4
2
2
14
6
3
3
3
1
2
1
1
4
4
2
bbl.
gal.
qt.
bbl.
gal.
qt.
bbl.
gal.
qt.
3
30
2
4
15
3
1
31
2
1
21
2
1
8
1
4.
Multiply:
gal.
qt.
pt.
gal. qt. pt.
bbl.
gal.
qt.
2
3
1
7
1
2
2
10
2
2
4
3
5. A milkman starts with 42 gal.; sells of the milk to pri-
vate customers, the rest to a hotel. How many quarts
does he sell to the hotel?
6. A druggist put 1 qt. of liquid into bottles holding -J- gi.
each. How many bottles did he use?
7. How many jelly glasses holding f of a pt. each can be
filled from 1 gal. of jelly?
APPLICATIONS <*F M^l'Il) .MKASrilK.
1. Jlo\v many pint bottles will hold 2 gals. 1 pi. <>f
What is it worth at 13</ a quart?
2. If a gallon of wine cost $4, what will 5 pts. cost?
3. From a milk can holding 8 gals., j 3 ,. of the milk was spilled.
How many quarts were left? How many gallons?
4. How much ice cream will a man make if he uses a gallon
and a half freezer and has it full twice, and half full
the third time?
5. How many gals, in 412 gills?
0. What part of 12 gals, is 4 gals. ?
7. A man sold 12 cans of mineral water, each holding gals.
at 15^ per gal. How much did he receive?
8. How many oil barrels, each holding 45 gals., can be filled
from a tank holding 10.800 gals, of oil?
9. A hotel uses 25 gals. 3 pts. of milk each day. How much
does it use in 3 weeks ?
10. There are 231 cu. in. in 1 gal. How many cubic inches
in a bottle holding 2 qts. ?
11. How many cubic inches in a cistern holding 10 bbls. ?
12 bbls. ? 16 bbls. ?
12. In a jar that holds 2 gals., 3 qts. of water are placed.
How many cubic inches of the jar are unfilled?
13. From a barrel of vinegar a grocer fills 2 four-gallon jugs
and puts 3 gals, and 1 qt. in another jug. How many
gals, had he left?
14. A man sells 3 gals, and 2 qts. of molasses to one cus-
tomer; 2 gals, and 1 qt. to another customer, and 1 qt.
and 1 pt. to a third. How many, quarts did he sell in
all? How many gallons?
15. From a barrel full of rain water, 80 qts. were taken out at
different times. The water remaining in the barrel
measured 40 qts., the rest having evaporated. How
many quarts had evaporated?
214 RATIONAL ELEMENTARY ARITHMETIC.
16
1
2
3
4
B
6
16
32
48
64
80
ne
1. Add:
16
16
16
. 16
16 48
16
32
16
* 32
32 48
32
32
48
2. 16 x 3
16 v
5 -
16 X 2
16 v
6 -
16 X 4
3-. 16 is what part of 32? 48? 64?
80?
96?
4. 32 is how many
16
's? What part
of 48? Of 64? 80?
96?
5. 48 is how many
16
s? How many
32's? What part of
64?
Of 80?
96?
6. 64 is how many
16's? How many 32's? 48's? What
part of
80?
Of 96?
7. 80 is how many
16's? How many 32's? 48's? 64's?
What part of 96?
8. 96 is how many
16's? How many
32's? 48's? 64's?
9. A farm
of 96 acres was divided into
16 eq
ual i
mrts. How
many acres in each?
10. In a square mile of land there are 16 farms equal in size.
How many acre$ in each? If one of these farms is di-
vided into 3 fields, two of which contain 16 acres each,
what is the area of the third field?
11. From a bin containing 80 Ibs. of meal, 2 eight-lb. pack-
ages were taken. How many sixteen-lb. packages can
be made from the remainder?
PRODUCTS BY SIXTEEN. 215
t. A brick mason contracts to build a chimney for $72. If
it takes 10 days to do the work and he pays each of his
2 helpers $1.50 per day, what is his rate of pay per
day?
2. A man agreed to haul away 1560 cu. yds. of clay for $264.
He paid 4 teamsters $3.90 each per day for 13 days.
How much did he have left? What did each teamster
receive ?
3. If each teamster was paid at the rate of 130 per cu. yd.,
how many yds. did he haul to earn what he received?
4. A man hauls sand for 90 per cu. yd. If his wagon holds
1|- cu. yds. and he hauls 18 loads per day, what is
his daily pay ?
5. A newsboy buys his papers at the rate of 10 for 60 and
sells them for 10 each. How much will he gain if he
sells 75 papers? 120 papers?
6- He sells 45 on Monday, 54 on Tuesday, 81 on Wednes-
day, and 70 on Thursday. What does he gain in the 4
days?
7. On Friday he buys 100 papers and sells all but 5 that
are spoiled by the rain. What does he receive for his
work on Friday?
8. A newspaper prints 1 million copies in 6 days. At the
end of the week 13,526 copies had been given away
and 29,674 copies were left on hand. What was the
average daily circulation?
9. If -|- of these papers are sold by newsboys, how many
newsboys must there be, if each one sells 100 papers
every day?
10. A man divides 80 acres of land into streets and building
lots. The streets take up ^ of the land, and the
remainder is divided into blocks each containing 3 A.
How many blocks?
216 RATIONAL ELEMENTARY ARITHMETIC.
2 pt =1 qt. 4 pk. = 1 bu.
8 qt. = 1 pk. (peck)
1. Review pages 11 and 67 as oral work.
2. Add:
3 bu., 1 pk., 6 qt. 1 bu., 2 pk., 3 qt. 2 bu., 3 pk, 4 qt.
1 bu., 2 pk., 1 qt. 2 bu., 1 pk., 5 qt. 3 bu., 4 qt.
4 bu., 2 pk., 5 qt. 5 bu., 2 qt. 3 bu., 3 pk., 7 qt.
1 bu., 2 pk., 3 pk., 6 qt. 1 qt.
3. Subtract:
5 bu., 3 pk., 6 qt. 3 bu., 2 pk., 7 qt. 6 bu., 1 pk., 5 qt.
1 bu., 2 pk., 4 qt. 2 bu., 5 qt. 1 bu., 1 pk., 1 qt.
4 bu., 2 pk., 4 qt. 8 bu., 3 pk., 5 qt. . 12 bu., 2 pk., 6 qt.
1 pk., 4 qt. 2 bu., 2 pk., 2 qt. 7 bu., 4 qt.
4. Multiply.
2 bu., 2 pk., 3 qt. 3 bu., 1 pk., 3 qt. 4 bu., 1 pk., 1 qt.
2_ 3__ ^_
5. How many bushels in 128 pks. ? In 150 pks. ?
6. How many quart boxes will 1 bu. 3 pks. 2 qts. fill ?
7. Find cost of 3 pks., 6 qts., 1 pt. of nuts ; at 12^ a pint?
8. In 96 qts. how many pecks? How many bushels?
9. What part of 7 bu. are 7 pks. ? 7 qts. ?
10. How many quarts of cherries can be bought for $2, if 1
bushel of cherries is worth $3.20?
11. I bought 7 bu. 3 pks. of potatoes on Monday; 8 bu. on
Tuesday and 10 bu. 1 pk. 6 qts. on Wednesday. How
many potatoes did I buy in all ?
12. A teamster feeds his horses 36 qts. of oats a day. How
long will 120 bu. of oats last him ? What does it cost
him each day when oats are worth 27^ a bu. ?
APPLICATIONS OF DRY MEASURE. 217
1. From a sack of peanuts holding 3 bu., 25 qts. were taken.
How many bushels remained?
2. A bushel of plums is divided equally among 12 people.
How many quarts did each receive?
3. How many pecks of beans will a man sell who sells 3 qts.
to each of 8 customers?
4. A woman measuring out 2J qts. of flour uses a measure
holding ^ pt. How many times does she fill the meas-
ure?
5. A barrel of apples was sold in 3 lots. The first sale was
1 bu. and 2 pks. ; the second 2 pecks ; the third lit
bu. How many bushels were there in the barrel?
6. From 3 bushels of peas, a man sells \ peck to one cus-
tomer; 4 qts. to another, 1 pk to another. How many
has he left?
7. If one-half a peck of peaches when canned make 3 qts.,
how many bushels must be bought to make 36 qts. of
canned peaches?
8. A man bought at a feed store 5 bu. of corn, 2 bu. and 3
pks. of oats and 1J bu. of mixed feed. He had at home
in the bins, 3 pks. of corn, ^ bu. of oats and 1 pk. of
ground feed. How many bushels of feed did he have
in the bins after he received what he bought?
9. In one year a farmer's family used 50J bu. of potatoes.
He saved 9 bu. 3 pks. for planting and sold 117 bu.
and 3^ pks. How many bushels did he raise that year ?
10. 240 boxes of peaches, holding 1 pk. each, were shipped to
market. The fruit was picked in one-half bu. baskets.
How many baskets of fruit were there ?
11. A fruit dealer bought 2 crates of strawberries, each hold-
ing 24 qts. ; and 6 crates, each holding 32 qts. The
berries were put into pint boxes and sold for 10^ a
box. What did the dealer receive for the berries?
218
RATIONAL ELEMENTARY ARITHMETIC.
1
2
3
4
5
6
1. Add
161
16 X
50
66%
S3U
too
66}
161 16f 33}
2.
50
161
16}
161 X 3 =
161 X 2 -
161 X 4 =
161 X 6 -
16} X 6 =
66|?
66f ?
33}? 83?
83}? 100?
33^'s? What part of 66f'
50's?
3. 16} is what part of 50?
4. 33} is what part of 50?
5. 50 is how many 16}'s?
83}? 100?
6. 66} are how many 16}'s?
7. 83} are how many 16f 's?
8. 100 is how many 16|'s? 33^'s? 50's? 66|'s? 83}'s?
9. A man paid J of a dollar each for 15 books. What did
they cost him?
10. A boy 33} miles from home, rode } the distance on his
wheel. How many miles did he ride?
11. A piece of cloth 3 yds. long sold for 50#. What was the
price per yd.?
12. A girl picked 66| qts. of berries in 4 days. What was
the average amount per day?
13. A hundredweight of grain was divided into 6 equal
amounts. How many pounds in each?
14. From a tank of water, 16 1 gals, were drawn out, which
were } of the amount remaining. How many gallons
were left in the tank?
PRODUCTS BY SIXTEEN AND TWO-THIRDS. 219
1. A schooner brought 48, 1)72 spruce trees from northern
Michigan to Chicago at Christmas time. What are they
worth at 90^ a dozen?
2. A blacksmith shoes 42 horses at $2 each in 1 week. The
shoes and nails cost him $8, shop rent $12, and he pays
each of his two helpers $15 per week. What was his
share of the money received?
3. A teamster has his two horses shod all around, twice each
month, during December, January mid February, and
once a month the remainder of the year. What does it
cost a year at $2 per shoeing for each horse?
4. A cooper made 1000 butter tubs at 12^ each and 600 bar-
rels at 30^ each. If he paid J of the price for lumber
and -J- of it to his workmen, how much did he have left ?
5. If each tub holds 24 pounds, what will 1000 tubs of but-
ter be worth at 21^ per pound?
6. If each bbl. holds 3 bu. of apples, what will 000 bbls.
bring if sold at 30^ per peck?
7. There are 630 sq. yds. of lathing needed in a new house
and it can be done in 6 days. Will a man earn more
by doing it by the day at $3 per day or by the square
yard at 3# per sq. yd. ?
8. If 54 laths will cover 4 sq. yds. how many will be needed
for 600 sq. yds.? How many bundles of 50 laths each?
9. If each lath uses 6 nails, and 54 laths cover 4 sq. yds.,
how many nails will 600 sq. yds. use? How many
pounds allowing 400 nails to the pound ?
10. A carpenter works 5-J days in a week at $3 per day, but
breaks a saw worth $1.40 and loses a hammer worth 90^.
What is the week's work worth to him?
11. A painter has 3 helpers at $3.50 per day and 2 at $3.
What must he charge for a week's work so as to have
$25 for himself?
220 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 162 and 163.
2. What is the name of the first period?
3. What is the name of the second period ?
4. Hew many places are there in units' period?
5. Each period has three places.
Thousands. Units.
1 g 3 1 g t
w g 5 w o
246,123
6. Read the figures of each period as though they stood
alone and then add the name of the period.
246 thousands.
123 units, or ones.
7. If we multiply the number 246,123 by 10 we will have
the beginning of a new period, 2,461,230.
8. This will be read:
2 millions (this is the name of the new period).
461 thousands
230
9. The use of figures to represent numbers, as we have been
doing, is called ihe Arabic Notation or method of
writing numbers.
10. There is another method of writing numbers, in which
letters are used. This is the Roman Notation.
11. Fill out the following blanks with figures:
y
VI =
XT -
II =
VTT =
T, =
TTT -
VTTT -
n -
TV =
IX -
XT, =
V - .
X -
YH -
12. What is the equivalent in figures of I? V? X? L?
C? D? M?
READING AND WHITING NUMBERS. 221
1. If a letter is followed by one or more letters of equal or
less value, the sum of all is the value of the numbei
represented. Thus: VI = 6; XI == 11; XX = 20;
CLX == 160; DC = 600.
2. If a letter is followed by another of greater value, the
difference of the two is the value of the number
represented. Thus: IV = 4; IX = 9; XIX = 19;
XL = 40; CD = 400.
3. Bead the following numbers written in the Roman Nota-
tion:
IV VIII II IX
XIX XVI XIV XXXIX
XXXIV XLIV XXVII XI
XLIX LIV LXIX LXXVIII
XCIX CIX CLXIX LC
CCCXXVI MCLXXIV DIX MLV
4. Write the following numbers in the Roman Notation:
9 = 13 = 96 =
4 = 78 = 104 =
7 = 44 = . 199 =
6 = 83 = 335 =
14 = 59 = , 549 =
29 = 94 = , 2000 =
(Write answers to the following in Roman numerals.)
5. Columbus discovered America in MCDXCII; 20 years
later Florida was explored. In what year was Florida
explored ?
6. The first battle of the Revolution was fought in
MDCCLXXV; the last battle was fought 6 years later.
What was the year of the last battle?
7. Washington was elected President in MDCCLXXXIX;
Lincoln was elected 71 years afterward. In what year
was Lincoln elected?
222
RATIONAL ELEMENTARY ARITHMETIC.
1. Review page 129.
2. A farmer sold five tons of hay. The first load weighed
2,112 pounds, the second 1,936 pounds, the third 1,987
pounds, and the fourth 2,174 pounds. What did the
first load weigh?
3. Add:
(a)
(&)
(e)
(d)
w
(/)
7843
32765
25987
96875
81818
247
8789
89247
6586
40984
92193
91838
9576
76348
78379
50839
87689
9705
2589
20873
96468
9787
76434
87278
8956
94608
980
67898
68979
3849
3210
13495
20876
76580
37590
89878
7029
68950
67099
54777
89763
79929
47992
334
In long columns the number to be carried may be indicated by placing
the figure immediately underneath the column as in problem (a).
To prove your work, add the columns from the top, downward
4. Add the following problems in the usual way:
(a)
68
97
89
/TO
Oft 7
(
238
472
836
ot>n ?
W
237
48984
3789
PidOTfi ?
W)
24567
89012
4567
OQC7ft
9
30
78
83
29220
48
67
98
CQ om
JoU i
722
146
348
765 ?
897
305
969
070 9
O'iJ I U
500
3897
57878
36498 ?
9889
65847
678
QQ7AQ ?
OJ7OI U
54378
98989
24864
3099-
87655
98788
4890
&fi7fi7
?
9
oo
oo i UJ (
ou< U<
818
818
Another method of proof is to think the columns divided into shorter
columns, add the parts, as indicated in problem (a), and add these separate
RXKRCISES IN ADDITION AND SUBTRACTION. 223
1. 6384 The Minuend is the number subtracted from.
1945 The Subtrahend is the number subtracted.
4439 The Difference or Remainder is the result.
0384 The sum of the difference and subtrahend should
be the minuend. If so the work is correct.
2. Subtract the following and prove your work:
(l) (2) (3) (4) (5) (6)
8346 24890 36745 48234 57855 72180
5838 17901 17829 29018 29666 23092
(7) (8) (9) (10) (11) (12)
62387 83475 90281 38297 27666 87726
34299 56077 37345 19088 18785 68640
(13) (14) (15) (16) (17) (18)
418967 687240 723485 868240 927200 707241
229875 478119 438907 372906 418117 354438
(19) (20) (21) (22) (23) (24)
381487 592173 600840 821380 727248 917288
191598 394205 236450 291653 570649 129399
3. A man began business with $5,275.75; in five years he
had $22,794.50. How much had he gained?
4. One country road is 20 mi. 160 rds. long; another is 14
mi. 80 rds. long; how much longer is the first?
5. A cotton dealer bought 328,900 Ibs. of cotton one year,
and 715,600 Ibs. the next. How many more Ibs. did
he buy the second year?
6. One vessel is valued at $1,250,000; another at $975,800.
What is the difference in value?
7. A box containing 43,200 cu. in. was divided into two parts;
one holding 25,920 cu. in. How many cu. in. in the
second part?
224 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 37 and 142.
2. Multiply 892 Which number is the multiplicand? The
by 235 multiplier? The product?
To how many times 892 is the sum of 5 times 892 + 30
times 892' -h 200 times 892 equal?
Multiply 892 CONVENIENT FORM.
by 235 892
"4460 = 5 X 892 235
26760 = 30 X 892 4460
178400 = 200 X 892 2676
209620 = 235 X 892 1784
209620
NOTE: It will be noticed that the first figure of the products from
multiplying by the separate numbers of the multiplier is placed directly
under that figure of the multiplier. The remaining figures of the products
are written as usual to the left. See the multiplication of 892 by 235,
second form.
3. Multiply the following:
(1) (2) (3) (4) (5) (6) (7)
563 589 789 582 678 765 899
365 589 579 376 497 689 655
4. Multiply (a) 729 by 460; (6) 476 by 308.
" (a) (6)
729 476
460 308
43740 3808
2916 1428
5. Compare 4x5 with 5X4. Does 892 X 235 differ from
235 X 892? In multiplication why do we always use
the smaller number for the multiplier? Give a way of
proving that a product is correct.
PROBLEMS IN MULTIPLICATION. 225
1. Find the following products and prove results:
573 X 248 384 x 537 735 X 376 487 X 789
858 X 305 275 X 937 972 X 219 976 X 253
835 x 583 508 X 607 506 X 429 4005 x 129
968 X 675 651 X 234 309 x 150 2060 X 456
809 X 584 943 x 923 847 X 907 3070 x 250
548 X 394 475 X 406 653 X 295 1022 X 284
2. An elevator in a tall building goes up 165 ft. and down
the same distance each trip. How many feet does it
go in 152 trips?
3. If it cost 56# per word for a cablegram from Japan to
Chicago, what is the cost of a message of 1213 words?
4. If a steamer burns 378 pounds of coal in going 1 knot,
how many pounds will she burn in going 15,288 knots?
5. There are 40 street lamps on 1 mile of street, each burn-
ing 18 cu. ft. of gas every night. How much gas will
they burn in the month of April?
6. A library has in one case 276 books, which contain, on an
average, 304 pages each. How many pages of reading
matter in the bookcase?
7. There are 897 hills of corn in a single row and 364 such
rows in a field. How many hills of corn in the entire
field?
8. How many square feet in an acre? If ISO pounds of
water fall on one square foot in a year, how many pounds
will fall on an acre ?
9. There are 12 elevators in a building. They each make
94 round trips in a day and carry, on an average, 4
passengers each way. How many passengers make
single trips on all of them in a day ?
10. In a single layer in a wall there are 964 bricks. The
wall is 197 bricks high. How many bricks does it
contain ?
226
RATIONAL ELEMENTARY ARITHMETIC.
1. Divide 21,816 by 72.
303
72)21816
216
216
216
2. Divide 15,250 by 61.
250
61)15250
122
305
305
4. Divide 25,215 by 105.
240^
5.
21,816 -* 72 = 303; what will
303 X 72 = How, then, may
we prove the correctness of our
work in division?
3. Divide 5130 by 342,
15
342)5130
342
Proof:
1710
1710
105 divisor.
240 quotient.
4200
210
25200
15 rem.
25,215 dividend.
To prove the correctness of division, multiply the divisor
by the quotient, and add the remainder if there be one.
The result should equal the dividend.
Divide :
3767 - 38 99,684 * 234
7873 - 41 91,464 * 111
7692 - 32 94,770 -J- 135
67,654 - 53 95,928 -r- 806
26,754 - 64 90,750 -- 125
95,637 - 75 68,331 -=- 911
76,894 -=- 86 33,633 -5- 111
PROBLEMS IN DIVISION.
227
1. There were 23 cars in a trainload of cattle and 21 head
of cattle in each car. The entire weight of the cattle
was 645,502. What was the average weight per head?
2. An apartment building containing 48 apartments cost
$132,240. What was the average cost of each apart-
ment?
3. A farmer paid $20,000 for 324 acres of land. How much
did it cost him per acre?
4. Solve the following:
516)220332 718)92622 356)182984 729)91125
618)400276 317)687020 540)72689 720)840671
427)600000 825)872640 207)907060 421)117000
5027)702060 1702)347020 1202)987261 4800)960000
5200)987654 3702)587869 1234)765432 1067)987000
5. On a certain trip the traveling expenses for one person to
London and return were $325. How many such trips
would $9100 furnish?
6. What was the average cost per mile of a railroad 750
miles long which cost $33,750,000?
7. A proofreader counted the number of wojds in a book,
finding 88440 words on 268 pages. How many words
were there on each page?
8. A wealthy man gave to the 4 fire departments of a
village (each department employing 27 men) $32,400 as
a donation for the firemen. How much did each man
receive?
9. A lady donated $1701 to buy books for the school children
of a certain town. There were 567 school children in
the town. How much did each receive?
228 RATIONAL ELEMENTARY ARITHMETIC.
1. A lumber vessel carried 887,392 barrel staves. Allowing
16 staves to the barrel, how many barrels can be made
from them?
2. A ship traveled about 15,228 nautical miles in 66 days,
stopping 12 days on the way for coal and other sup-
plies. What was her average speed per hour?
3. The Danube Eiver is 1,725 miles long, the Ehine 600
miles and the Ehone 580 miles. How many times as
long as the Thames, 220 miles, is their united length ?
4. There are 102 counties in Illinois and the area of the
state is 56,650 square miles. What is the average size
of each county ?
5. Chicago's area is 119,689 acres. How many square miles
of land in Chicago?
6. A field of corn has in it 229,599 hills. There are 291
equal rows. How many hills in each row?
7. A rectangular farm contains 552,866 square yards. One
end of it is 563 yards long. How long is one side?
8. A field contains 926,156 square feet. One end of it is
679 feet long. How long is one side?
9. At a brick yard 3,276,224 bricks were made during the
season. They were hauled away in 824 equal loads.
How many bricks were hauled at a load?
10. $48,077.20 was divided equally among 709 men. How
much did each receive?
11. A merchant sold 999 bicycles for $41,793.72. What was
the average selling price of each bicycle?
12. In 312 days of the year a merchant sold $91,040 worth
of goods. What did his daily sales average ?
13. In four years a factory uses 1,434,160 pounds of coal.
What was the average amount used per week?
14. The Atlantic Ocean in the deepest part is 27,366 feet
deep. What is its depth in miles?
PRODUCTS BY TWENTY.
229
20
20
40
60
80
100
1. How many 20's in 40?
2. 40 is how many 20's?
3. 60 is how many 20's?
4. 80 is how many 20's?
5. 100 is how many 20's?
In 80? 60? 100?
What part of 60? Of 80? 100?
40's? What part of 80? 100?
40's? 60's? What part of 100?
40's? 60's? 80's?
6. A boy bought 80 papers for 44^. The next day he bought
20 papers at the same rate. What did they cost him ?
7. A train goes 40 miles in 55 minutes. At the same rate
how long will it take to go 80 miles?
8. A boy rode 9 miles in 1 hour. How far will he ride at
the same rate in 40 minutes?
9. 60 qts. of syrup cost $7.20. At the same rate what will
5 gal. cost?
10. A man puts 20 pounds of meal in one sack. How many
sacks will he need for 1 hundredweight?
11. ^ of a bu. of wheat weighs 20 pounds. How many bu.
weigh 60 pounds? 80 pounds? 100 pounds?
12. A toy bank holds $2 in dimes. How many weeks will it
take to fill it if 20^ are put in each week ?
13. Allowing 4 weeks to the month, how many terms of 20
weeks are there in 10 months of school? How many
terms does a boy spend in school who attends 25 school
months?
14. It takes a man 20 minutes to reach his office. What part
of an hour does it take him each day to go arid return ?
How many hours does it take him in 6 days?
15. A man bought 40 horses for $2880. At the same rate
what will l?e the cost of 100 horses ?
230 RATIONAL ELEMENTARY ARITHMETIC.
16 oz. (ounce) = 1 Ib.
100 Ib. = 1 cwt. (hundredweight).
20 cwt.or 2000 Ib. = 1 T. (ton).
1. How many ounces in 8 Ibs.? In 14 Ibs.? In 20 Ibs.?
In 25 Ibs.?
2. How many pounds in 3| cwt.? In 1\ cwt.? In 9i cwt. ?
3. How many pounds in 1 T. ? In 4 T. ? In 3J T. ?
4. How many ounces in J cwt. ? In 2^ cwt. ? In 3| cwt.?
5. How many ounces in \ T.? In 3| T.? In 2J T.?
6. How many hundredweights in J T. and in \ T. together?
7. 1 T. equals 10 cwt. and how many pounds?
8. Add:
2 T. 17 cwt. 25 Ib. 1 T. 8 cwt. 60 Ib.
1 2 75 4 1 40
10 cwt. 25 Ib. 8 oz. 9 cwt. 20 Ib. 4 oz.
5 30 6 4 9 9
4 44 2 G 18 2
9. Subtract:
3 T. 15 cwt. 14 Ib. 2 T. 12 cwt. 9 Ib.
278 186
15 cwt. 75 Ib. 8 oz. 16 cwt. 43 Ib 12
8 35 5 14 23 8
10. Multiply:
3 T. 5 cwt. 15 Ib. 2 T. 3 cwt. 20 Ib.
4_ 5
2 cwt. 9 Ib. 2 oz. 4 cwt. 3 Ib. 4 oz.
8 4
11. Divide:
2)4 T. 18 cwt. 50 Ib. 3)6 T, 15 cwt 48 Ib.
PROBLEMS IN WEIGHING. 231
1. At 100 an oz. how much will 3 Ibs. of cinnamon cost?
44 Ibs?
2. What will a ton of hay cost at a pound?
3. A bushel of wheat weighs 60 Ibs. How many bushels in
a load of wheat weighing 1 T., cwt. and 40 Ibs. ?
4. A family uses 75 Ibs. of ice every day for 20 days. What
does it cost them at 350 per cwt. ?
5. From 10 cwt. of sugar a grocer sold 8 cwt., 40 Ibs., 12
oz. How much was left?
6. 60 Ibs., 10 oz. of tea were divided equally among 5 per-
sons. How much did each receive?
7. A man bought 3 Ibs., 8 oz. of meat at 160 a Ib. and 2 Ibs.,
12 oz. of butter at 200 a Ib. What was the total cost?
8. A bushel -of oats weighs 32 Ibs. How many bushels in
80 cwt. ?
9. From a keg of nails weighing 1 cwt., 15 Ibs. and 8 oz.
were taken at one time, 9 Ibs. and 12 oz. at another.
What was the weight of the remainder?
10. How many bales of cotton, each weighing 450 Ibs. may
be shipped on a vessel which can carry 2250 tons ? On
a vessel that can carry 3000 tons?
11. What will it cost to have 8 tons of coal hauled at 750 a
load of 3500 Ibs. ?
12. 500 bbls. of flour are shipped in 7 equal loads. How
many tons will each load weigh if 1 bbl. weighs 196
Ibs.?
13. A man hauled 8 loads of wheat, 35 bu. at a load. A
bushel of wheat weighs 60 Ibs. What was the weight
of the 8 loads? How many hundredweight in each
load?
14. A farmer owning 700 bu. of oats sold 9 loads of 2240 Ibs.
each. One bushel weighs 32 Ibs. How many bushels
had he left?
232 RATIONAL ELEMENTARY ARITHMETIC.
60 sec. (second) = 1 min
60 min. (minute) = 1 hr.
24 hr. hour) -Id. 5 ; wk ' l
_ . ,. / i / i N 12 mo.
7 d. (day) = 1 wk. (week).
1. Review page 109 as oral work.
2. How many months in J a yr.? In 3} yrs.? In 5 yrs. ?
3. How many minutes in 3 hrs. ? In 2J hrs. ? In 1^ hrs. ?
In J of an hr. ? In one day ?
4. In 4 yrs. how many days? In 2\ yrs.? In | of a yr.?
5. How many seconds in 5 min. ? In one hr. ? In \ an hr. ?
In J a day?
6. Add:
8 hr., 30 min., 15 sec. 3 mo., 4 wk., 7 d.
3 29 45 8 3 12
1 yr., 8 mo., 15 d. 2 yr., 6 mo., 10 d.
325 2 4 15
7. Subtract:
24 hr., 50 min., 30 sec. 4 yr., 8 mo., 15 d.
8 30 15 1 2 6
6 yr., 4 mo., 20 d. 5 yr., 9 mo., 6 d.
3 3 12 485
8. Multiply:
4 hr., 15 min., 30 sec. 3 hr., 15 min., 20 sec.
2 3
4 yr., 2 mo., 4 d. 5 yr., 2 mo., 3 d.
5 6
PROBLEMS IN TIME. 233
1. Divide:
2)6 hr., 45 min., 15 sec. 6)24 hr., 30 min., 18 sec.
2)4 yr., 8 mo., 12 d. 5)5 yr., 10 mo., 15 d.
2. Find the time between June 6, 1885, to Aug. 12, 1889.
The difference between dates is found by subtraction, using the num-
bers of the months named.
yr. mo. d.
Aug. 12, 1889 = 1889 8 12
June 6, 1885 = 1885 6 6_
426
3. Find the time from:
Jan. 2, 1865, to June 5, 1887.
Mar. 12, 1885, to May 21, 1889.
July 21, 1872, to Sept. 26, 1890.
Feb. 15, 1860, to Oct. 29, 1878.
Nov. 2, 1889, to Dec. 28, 1892.
Apr. 10, 1879, to Aug. 25, 1897.
4. If a boy works ^ of each day for 6 days at 20^ an hr.,
what is his week's salary ? If he works 9 hrs. overtime,
half of that time at 15^ a half hour and the rest at 20^
a half hour, what is his pay for 'the extra work?
5. A man leaves his office for home at 5.45 p. m., and arrives
45 min. later. What time does he reach home ? If he
takes the same time going and returning every day,
how many hours does he thus spend in ten days?
6. A fast mail train runs from Chicago to Burlington in 5
hrs. 20 min. 45 sec. and a freight train runs the same
distance in 9 hrs. 40 min. How much longer does it
take the freight train?
7. James was born September 18, 1887, and Willie was born
December 21, 1892. How much older is James?
234 RATIONAL ELEMENTARY ARITHMETIC.
1 . There are 319 pages in a book, how many pages are there
in 369 such books?
2. There are 18 windows on each side of a car. How many
windows are there in 397 cars?
3. In a 7 story building, there are on each of the sides, 27
windows on each story ; there are on each of the ends
16 windows on each story. How many windows in all ?
. A street paved with stone blocks contains 65 stones in
width and 786 in length. One man must buy half of
these. If they cost him If each, how much must he
pay for them ?
5. How many grains will 1,648 silver dollars weigh, if one
dollar weighs 412J grains?
6. A man deposits $372 in the bank each week day for 26
weeks. How much does he deposit in that time?
7. A man rides 116 miles a day on his bicycle. How far
from the city can he go and return in 12 days?
8. It is 195 feet between the telegraph poles. How much
wire is needed to put up 6 wires on 257 poles?
9. A merchant bought 97 rolls of carpet, 27 of them con-
taining 56 yards to the roll, 34 containing 59 yards to
the roll, and the remainder 63 yards to the roll. How
many yards did he buy?
10. A manufacturer sold 65 cases of shoes, each case contain-
ing 6 dozen pairs, at $2.75 a pair. What was the
amount of his sale?
11. A farmer had 2,365 bushels of wheat. He sold 1,240
bushels at 65^ a bushel, 643 bushels at 85^ a bushel,
and the remainder at 96^ a bushel. How much did he
get for the entire crop of wheat?
12. A merchant's sales were $127 each day for 23 days, $156
each day for 19 days, and $113 each day for 32 days.
How much were his sales for the entire time?
MISCELLANEOUS PROBLEMS. 235
1. It is 85 miles from Chicago to Milwaukee. A man
went from Chicago to Milwaukee and returned each
day for 26 days. How many miles did he travel?
2. A man lived 27 miles from Chicago. He came into the
city and returned 6 days each week for 14 weeks. How
many miles did he travel?
3. A manufacturer sold 687 bicycles at $47 each. How much
did he get for them?
4. An agent sold 163 reapers at $145 each. What was the
amount of his sale ?
5. The cost of one car is $965. A railroad company buys
235 such cars. What is the cost of the cars?
6. A square building is 115 feet high and 122 feet wide.
What is the area of one of its sides in square feet?
7. The same building is covered with a flat roof. How many
square feet in the roof?
8. 53 cars stand in a solid blockade on the street. 26 of
them are 32 feet long and the remainder 37 feet long.
How far is it from one end of the blockade to the other?
9. A street car company sold 540 horses at $62.25 each.
How much did it get for the horses?
10. A man works 8-J hours a day, 6 days in the week, for 26
weeks. How many minutes does he work?
11. For every 25 papers a boy delivered he received 13^.
If he delivered at this rate 175 papers a day each week
day for 2 weeks, how much money did he get?
12. The school year contained 40 weeks. Each week I
burned a quart of oil, which cost me 13^ a gallon.
What did my oil cost me for the school year?
13. An elevator boy received $13 a month as wages. At the
end of the year he had spent $19 for clothing, $32 for
car fare, $4.50 for books and had given his mother
How much money did he have left?
236 RATIONAL ELEMENTARY ARITHMETIC.
1. Review page 92.
2. A man had in his pocket one five-dollar bill, two two-
dollar bills, three one-dollar bills, two half dollars,
three quarters, four dimes, six nickels and three pen-
nies. How can he make even change for any one of
the following purchases:
3. A hat at $2.65 and a necktie at 5(V?
4. A vest at $3.50 and a dozen collars at 95^?
5. One book at $1.25 and another at 38^?
6. A box of paper at 50^, an inkstand at 65^ and a fountain
pen at $1.95?
7. A pair of shoes at $2.95?
8. Railroad fare at $4.42?
9. Hotel bill for 2J days at $2.50 a day?
10. A magazine, 35# ; a newspaper, 2#, and a sheet of paper,
envelope and stamp, 5^?
11. A bicycle suit at $6.70?
12. Repairing bicycle, $4.70?
13. A boy went to the bank to get change, at various times,
for the following amounts. How many of each piece
of money might be given him ?
14. A twenty-dollar bill so as to get five-dollar bills, one-
dollar bills and half dollars?
15. A ten-dollar bill, so as to get two-dollar bills, one-dollar
bills, half dollars and quarters?
16. A five-dollar bill, so as to get dollars, half dollars, quar-
ters and dimes?
17. A two-dollar bill, so as to get half dollars and dimes ?
18. A one-dollar bill, so as to get quarters, dimes, nickels and
pennies ?
19. A' half dollar, so as to get dimes, nickels and pennies ?
20. A quarter, so as to get pennies, nickels and any other coin
that he could get?
COUNTING PAPER. 237
2i sheets - one quire. 20 quires one ream.
1. How many sheets in J a quire? In f of a quire?
2. How many sheets in ^ of a ream ? In 2 reams ?
3. How many quires in 72 sheets? In 96 sheets? In 240
sheets ?
4. What is the cost of a quire of paper at 2$ a sheet?
5. What is the cost of a ream of paper when bought at 3
sheets for 10?
6. A man bought 1 box of paper containing 2 quires and
another containing 5 quires. How many sheets of
paper did he get?
7. If 12 sheets of paper cost 50, what is the cost of a ream
at the same rate?
8. I paid $1.20 for a ream of paper. What was the cost of
^ a quire?
9. How many boxes will hold a ream of paper if each box
contains 1-J quires? 1J quires?
10. A man bought paper at $1.50 a ream and sold it at 12
sheets for 5$. How much did he gain ?
11. A man bought paper at $2.75 a ream and sold it at 200 a
quire. What was his gain ? If he had paid $3 a ream
and sold it at 250 a quire, how much more would he
have gained?
12. A ream of paper is divided into 40 equal parts. What
part of a quire is each ?
13. From 3 reams of paper 1 J reams were sold at one time and
3 quires at another time. How many sheets remained?
How many quires? What part of a ream?
14. After collecting damaged lots of paper, a man found he
had 18 quires and 10 sheets of one kind, 11 quires
and 5 sheets of another kind, and 10 quires and 5
sheets of a third kind. He sold it at $1.25 a ream,
What did he get for all?
238 RATIONAL ELEMENTARY ARITHMETIC.
1. A man leaves his home each week day at 8.11 in the
morning and reaches his office at 8.27. He returns in
the evening, leaving his office at 5.45 and reaching his
home at 6.01. How many hours does he spend on the
way in a week? In the month of January, if there are
4 Sundays in a month?
2. A teacher leaves her home each morning at 8.20 and
reaches the school-house at 8.47. She returns, leaving
the school-house in the evening at 3.43 and reaching
her home at 4.05. How many hours does she spend on
the way in 4 weeks? How many hours in the school
year if there are 38 weeks of school in a year?
3. How far does she travel in 4 weeks if the school-house is
J of a mile from her home ? How far does she travel
in a school year of 40 weeks ?
4. A train leaves St. Louis at 11.31 in the evening and
reaches Chicago at 8 o'clock in the morning. It stops
11 minutes at stations on the way. What is the actual
running time from St. Louis to Chicago?
5. A train leaves Chicago at 9 o'clock in the evening and
arrives in St. Louis at 7.28 the next morning. Another
train leaves Chicago at 11.30 in the evening, reaching
St. Louis at 8.04 next morning. In how much less
time does one train run than the other, and which is
the faster train?
6. A train leaves Chicago at 6.30 in the evening and reaches
Omaha at 8.15 next morning. If 23 minutes are spent
in stopping at stations, what is the actual running time
from Chicago to Omaha?
7. A second train leaves Chicago at 10.30 in the evening
and reaches Omaha at 4 o'clock the next afternoon.
How much longer is this train on the way than the one
which left Chicago at 6.30?
MISCELLANEOUS PROBLEMS. 239
1. If a block containing 3 A. is '20 rods wide, "how Jong is it?
If it contains 10 lots, how many square rods in each?
2. A lot cost $200, the house cost 12 times as much as the
lot, and the fence | as much as the lot. What did the
house and the fence together cost?
3. The battle of Lexington was fought April 19th, 1775.
How many Aprils have there been from then to the
present day ?
4. The buildings for the Columbian Exposition were dedi-
cated October 12th, 1892. How many years, months
and days since then?
5. Nathaniel Hawthorne was born July 4th, 1809, and Texas
was admitted to the Union July 4th, 1845. What was
Hawthorne's age in months, when Texas became a state ?
6. Daniel Webster was born January 18th, 1782, and James
A. Garfield was born November 19th, 1831. How old
was Webster when Garfield was born?
7. Memorial Day was first celebrated by order of John A.
Logan, May 30th, 1868, and he was then 42 years, 3
months and 21 days old. When was he born ?
8. Gen. Grant was born April 27th, 1822, and was 41 years,
2 months and 7 days old when Vicksburg, Miss., was
captured. When did he capture Yicksburg?
9. Gen. Wm. T. Sherman was born Feb. 8th, 1820, and fin-
ished his great march through Georgia December 13th,
1864. How old was he on that day ?
10. Gen. Sheridan was born March 6th, 1831, and made his
famous ride from Winchester to the battlefield at Cedar
Creek, October 19th, 1864. What was his age then?
11. The area of Illinois is 56,650 square miles and the area
of the Philippine Islands is 114,326 square miles.
How much more than twice as large as Illinois are the
Philippines ?
240 RATIONAL ELEMENTARY ARITHMETIC.
1. A grain dealer bought 25,000 bu. of wheat at 97^5 per
bushel, and after 3 months sold it for $1.12 per bu.
He paid storage charges at the rate of -J^ per bu. each
month. What was his gain ?
2. A grain elevator holds 800,000 bu. If it is kept full for
6 months, what will storage charges amount to at fy
per bu. each month ?
3. Six vessels carry 800,000 bu. of grain from Chicago to
Buffalo. If 2 of them carry 160,000 bu. each, what is
the average load of the other four ?
4. "Wheat weighs 60 Ibs. to the bushel. What is the weight
in T. of 160,000 bu. ? In cwt. ?
5. At 6^ per cwt. what does it cost to ship 120,000 bu. of
wheat from Chicago to Buffalo?
6. An elevator containing 645,000 bu. of grain caught fire
and the grain was damaged. The grain was worth
81<p per bu. and was insured for $250,000. What was
the loss ?
7. The owner of the grain, after receiving the insurance
money, sold the damaged ^grain for feed at 13^ per
bushel. What was his actual loss ?
8. Corn weighs 56 pounds to the bushel. How many car
loads of 15 tons each will fill a vessel that can carry
90,000 bu. ?
9. At 10^ per hundredweight, what will it cost to ship 90,000
bu. of corn from Chicago to New York City?
10. A vessel owner agrees to carry 125,000 bu. of corn for
$3750. How much does he receive per hundred-
weight ?
11. A builder received $127.25 for making some repairs to a
house. He pays his 2 helpers $2.50 each per day for
the 12 days needed to do the work. What is his own
share of the money?
MISCELLANEOUS PROBLEMS. 241
1. How many caps worth 33^/ each, can be bought for $15?
For $24?
2. If the price of bread is raised from 5# to 6^ per loaf, how
much more will 700,000 loaves cost?
3. If a barrel of flour will make 196 loaves of bread, how
many barrels are required to make 700,000 loaves?
4. A rapid-fire gun shoots 100 shells per minute, how many
shells will 7 such guns shoot at the same rate in %
a minute? In 1-J- minutes?
5. If each shell weighs 1 lb., how many guns will it take to
fire a ton of shells in 1 minute?
6. If each shell uses up 6 ounces of powder, how much pow-
der will "be used by 15 guns in 1 minute?
7. A man earning $1.20 per day works 11 days in January,
17 days in February, 28 days in March, and 25 days
in each of the next three months. How much does he
earn in the six months?
8. A man working for $12 per week puts in J of a day over-
time each day, for which he receives double pay. How
much does he earn in 4 weeks if he works every work-
ing day?
9. What will the bricks for a wall 39 ft. high cost at $5.25
per thousand, if one thousand bricks will carry up the
wall 6 in. ?
10. A brick mason earning 50^ per hour, works 7 hours on
Monday, 5 hours on Tuesday, and full time 8 hours
a day for the rest of the week. What is his pay for
the week?
11. A gang of 20 men digging for a foundation are stopped
by rain from half past 9 to a quarter past 10 o'clock.
If they are working for 20^ per hour each, how much pay
does each one lose? How much would they all lose at
per hour?
242 RATIONAL ELEMENTARY ARITHMETIC.
1. Add 3 yd. 2 ft. 8 in., 4 yd. 1 ft. 4 in., and 3 yd. 2 ft. 6 in.
rd. yd. ft. in. Write the numbers in columns, put-
328 ting in. under in., ft. under ft., etc.
414 8 in. + 4 in. + 6 in. = how many
326 inches, or how many feet and inches?
2106 Where should the inches be written?
2 i What should be done with the 1 foot?
1 ft. + 2 ft. -f 1 ft. -f 2 ft. = how many feet, or how
many yards and feet? Where should the number of
feet be written? What should be done with the 2 yards?
2 yds. -h 3 yds. + 4 yds. + 3 yds. = how many yards,
or how many rods and yards? Where should the num-
ber of yards be written? The number of rods?
2. Subtract 2 yds. 2 ft. 8 in. from 4 yd. 1 ft. 10 in.
y d - ft - in - Write the numbers as in addition, 10 in.
4 1 10 8 in.= how many inches? 1 ft. 2 ft.
= ? How can 4 yd. and 1 ft. be changed
122 without changing their meaning? 4 ft.
2 ft. = how many feet? 3 yd. 2 yd. = how many
yards?
3. Multiply 1 yd. 2 ft. 5 in. by 3.
yd- ft - in - 3 times 5 inches = how many inches, or
how many feet and inches? Where should
the 3 inches be written? 3 times 2 ft. =
513 how many feet? How many yards? How
many feet were added from the first col-
umn? Where should the 1 foot be written? Where
should the 2 yards be written? 3 times 1 yard = how
many yds.? 3 yds. + 2 yds. = how many yds.?
4. Divide 7 yd. 2 ft. 8 in. by 2.
i of 7 yd. = how many yards, or how many yards
and feet? i of 5 ft. = how many feet or how many
feet and inches? J of 20 inches = how many inches?
DENOMINATE NUMBER EXERCISES. 243
1. Add 12 sq. yd., 4 sq. ft., 120 sq. in.; 4 sq. yd., 7 sq. ft.,
20 sq. in.; 6 sq. yd., 9 sq. ft., 16 sq. in.; 7 sq. ft, 4
sq. in.
2. Add 4 cu. yd., 9 cu. ft., 1200 cu. in. ; 3 cu. yd., 400 cu, in. ;
4 cu. ft., 600 cu. in. ; 5 cu. yd., 12 cu. ft.
3. Add 15 gal., 3 qt, 1 pt., 3 gi. ; 4 gal. 2 qt. ; 6 qt., 1 pt,
2gi.; 9 gal., 1 pt., 3 gi.
4. Add 3 bu., 3 pk., 7 qt., 1 pt. ; 4 bu., 2 pk., 6 qt. ; 3 pk., 4
qt, 1 pt ; 3 bu., 1 pk., 6 qt.; 1 pk., 2 qt, 1 pt.
5. Add 2 T., 16 cwt, 80 lb., 8 oz. ; 1 T., 8 cwt, 15 lb., 6 oz.;
3 T., 10 cwt, 50 lb., 8 oz. ; 18 cwt, 90 lb., 4 oz.
6. Add 4 hr., 45 min., 15 sec.; 6 hr., 30 min. ; 55 min., 45
sec.; 3 hr., 30 sec.
7. Subtract 16 sq. yd., 7 sq. ft, 44 sq. in., from 24 sq. yd.,
5 sq. ft, 120 sq. in.
8. Subtract 3 cu. yd., 9 cu. ft, 680 cu. in., from 12 cu. yd.,
6 cu. ft, 1240 cu. in.
9. Subtract 1 gal, 3 qt, 1 pt, 3 gi., from 4 gal., 2 qt, 1 pt,
Igi-
10. Subtract 2 bu., 2 pk., 5 qt, 1 pt, from 6 bu., 3 pk., 4 qt,
Ipt
11. Subtract 2 T., 15 cwt, 15 lb., 9 oz., from 4 T., 12 cwt ,
20 lb., 8 oz.
12. Multiply 9 cu. yd., 8 cu. ft., 640 cu. in., by 4.
13. Multiply 6 gal., 3 qt, 1 pt, 3 gi., by 5.
14. Multiply 5 bu., 3 pk., 7 qt, by 2.
15. Multiply 2 T., 10 cwt, 60 lb., 12 oz., by 3.
16. Multiply 4 hr., 40 min., 30 sec., by 5.
17. Divide 16 sq. yd., 3 sq_ft.,'141 sq. in., by 3.
ISf Divide .19 cu. yd., 1 cu. ft, 216 cu. in., by 9.
19. Divide 26 gal., 3 qt, 2 gi., by 6.
20. Divitie 12 bu., 1 pk., 3 qt, by 5.
21. Divide 12 T., 3 cwt, 50 lb., by 10,
244 RATIONAL ELEMENTARY ARITHMETIC.
1. A train traveled 32 mi., 120 rd., 7 yd., one hour, and 30
mi. 160 rd., 4 yd,,, the next. How far did it travel in
the two hours?
2. A man built 4 yd., 1 ft., 8 in., of walk at one time, and 3
yd., 2 ft., 6 in., at another. How much did he build?
3. One field contains 6 A., 80 sq. rd., and 40 sq. yd. ; the field
beside it contains 14 A., 120 sq. rd , 20J sq. yd. If
the fields are joined into one, how much land will it
contain ?
4. A building whose area is 30 sq. yd., 6 sq. ft., 72 sq. in., is
enlarged by an addition whose area is 9 sq. yd., 8 sq.
ft., 72 sq. in. What is the area of the entire building?
5. One room contains 185 cu. yd., 7 cu. ft., 192 cu. in. of
air; another 172 cu. yd., 4 cu. ft., 432 cu. in.; a third
864 cu. yd., 2 cu. ft., 192 cu. in. If the air in all the
rooms is entirely changed once every hour, how much
air will be required in 1 hour?
6. Before buying, a grocer had 2 gal., 2 qt., 1 pt. of vinegar;
he purchased 7 gal., 3 qt., 1 pt. more. How much had
he then ?
7. A farmer raised 56 bu., 3 pk. of Irish potatoes, and 24
bu., 2 pk. of sweet potatoes. How many had he
in all?
8. One family used 1 T. 13 cwt. 50 Ib. of ice in one summer,
another family used 1 T. 9 cwt. 75 Ib. How much did
they both use?
9. A steamship made the first half of a trip in 6 d. 10 hr.
45 min. and the return trip in 7 d. 3 hr. 15 min. If 2
d. 6 hr. 30 min. were spent in port before returning, in
what time did the ship make the entire trip?
10. A boy rode 10 mi. 80 rd. 4 yd. in 1 hour, and 2 mi. 120
rd. 3 yd. less the next hour. How far did he ride the
second hour?
DENOMINATE NUMBER PROBLEMS. 245
1. A man owning a farm of 740 A. and 78 sq. rd. sold 290 A.
and 98 sq. rd. How large was his farm then?
2. In a bin holding 7 cu. yd. 9 cu. ft. 576 cu. in. a partition
was placed separating a part holding 3 cu. yd. 18 cu. ft.
1152 cu. in. What were the contents of the remaining
part?
3. From a cistern holding 10 bbl. 14 gal. 1 qt. of waler, a
quantity was taken out, leaving 2 bbl. 8 gal. 3 qt. in
the cistern. . How much was taken out?
4. A grocer bought 12 bu. 1 pk. of potatoes and 4 bu. 3 pk.
less of apples. How many apples did he buy?
5. From a load of grain weighing 2 T. 14 cwt. 30 lb., 1 T.
18 cwt. 80 lb. were removed. What was the weight of
the remaining part?
6. One train made a trip in 14 hr. 15 min. 25 sec. ; another
train made the same trip in 1 hr. 50 miri. 45 sec. less
time. In what time was the trip made by the second
train?
7. Two boats left the same port at the same time, one sailed
21 mi. 5^ yd. while the second sailed twice as far. How
far did the second one sail ?
8. A building whose area was 27 sq. yd. 3 sq. ft. 72 sq. in.
was torn down and another built whose area was three
times that of the old one. What was the area of the
new building?
9. In digging a cellar, 24 cu. yd. 3 cu. ft. 576 cu. in. of earth
were excavated; it was then determined to make the
cellar three times as large. How much more earth was
removed? How much in all?
10. A book dealer shipped 3 boxes of books. One weighed 1
cwt., 90 lb., 8 oz. ; the second weighed twice as much
as the first, and the third as much as both the others
together. What was the weight of each?
246 RATIONAL ELEMENTARY ARITHMETIC.
(COPY OF BILL.)
Bought of JOHN SAMPLE, BOOKSELLER
3
Boolt/^ @ .35
$1
1
05
2
cJOAMyt/fc&y @ 10
20
4
f t/YVCAA/b-' @ 05
20
3otoi
1
45
(COPY OF RECEIPTED BILL.)
, Jdu>. 23,
Bought of PRINCE'S TOY STORE
,sn
,54
Scvta/t
2
la
38
U
35
SI
BILLS AM) ACCOUNTS.
247
Copy, find amounts due on the following accounts, and
recei pt.
J. MANNING,
In account with D. L. FARMER, Dr.
1898.
Jan.
2
To 75 Ibs. Kice @
1 .04
(4
2
" 330 Ibs. Sugar @
.05
it
7
" 50 Ibs. Java Coffee @
.32
-
7
" 45 Ibs. Tea @
.00
Amount due,
JAMES OILMAN,
In account with GEO. JOHNSON, Dr.
1898.
May
6
To 5 Days' Work
@ 12.50
13
" 12 Ibs. Nails
@ .03
a.
14
" 7 Panes of Glass
@ .40
June
11
" 10 gals. Paint
1.00
18
" Job Work on House
275
00
Amount due,
-
248 RATIONAL ELEMENTARY ARITHMETIC.
1. Make bills for the following:
Feb. 4, Mrs. J. K. Brown bought of White, Jones & Co.:
10 Ibs. of Sugar @ $.05
20 " Flour @ .04
2 " Tea @ .60
Jan. 11, L. B. Hall bought of Smith Bros. :
20 pr. Boys' Boots @ $1.75
15 " Slippers @ 1.50
25 " Ladies' Shoes 2.75
25 " Rubbers @ .50
June 4, Messrs. Black & Co. bought of Marshall Field
& Co. :
3 bolts of Velvet @ $100.00
3 " Muslin @ 37.00
2 " Calico @ 10.00
May 5, L. French bought of Browne, Steele & Co. :
5 yds. of Silk @ $1.75
3 " Eibbon @ .75
12 " Gingham @ .12
7 " Velvet @ 4.50
15 " Calico @ .05
4 papers Pins @ .07
2 " Needles @ .08
Sept. 1, J. C. Hill bought of Birch & Son:
8 Histories @ $1.25
15 Spellers @ .25
9 Readers @ .40
12 Grammars @ .60
20 Arithmetics @ .55
Oct. 21, O. F. Horn bought of Taylor & Co. :
5 Coal Stoves @ $20,00
10 Oil ^Stoves @ 8.00
25 Ibs. Nails .04
BILLS AND ACCOUNTS. iM'.i
1. Make out bills, supplying names, find the amounts, and
receipt:
9 Ibs. of Ham $.16
8 " Veal @ .12
12 " Mutton .12J
16 " Beef .14
4 " Pork .08
13 Ibs. of Dried Beef $.12
25 " Codfish .11
16 " Mackerel .06J
18 " Bacon .12
30 yds. of Cassimere @
70 Spools Thread
64 yds. Sheeting
45 " Calico @
$1.75
.12
.04
5 Table Cloths
2.50
112 bbl. Flour
$ 6.20
108 tons of Hay
250 bu. Wheat
14.00
.92
130 " Corn @
QO 1
Oa9
75 " Barley @
.85
12 doz. Eggs @
12 Ibs. Kice
$.12^
.04"
48 " Coffee
.33J
15 " Butter @
.22
32 " Cheese @
.14
6 rolls of Wall Paper
8 qts. Paint
6 " Oil
$.20
.30
.15
250 RATIONAL ELEMENTARY ARITHMETIC.
1. Charles sleeps J of the 24 hours, is in school \ of the 24
hours, works for his mother ^ of the 24 hours, and
uses iV of the 24 in eating. How many hours does he
sleep? Go to school? Work for his mother? Use
in eating? Use in other ways?
2. Tom read J of a book on Sunday, } on Tuesday, and I
on Wednesday. What part was read in these 3 days?
What part was not read?
3. If Tom 7 s book had in it 324 pages, how many pages did
he read on Sunday? On Monday? On Tuesday?
How many pages were left unread?
4. Fred bought 1J dozen eggs on Monday, and 3 times as
many on Tuesday. On Wednesday he sold 2} dozens.
How many dozens had he left?
5. Felix had a small fruit-stand. He bought at different
times: 2J dozen oranges; If dozen oranges; 3 dozen
oranges, and 5J dozen oranges. How many oranges
did he buy each time ? How many in all ? How many
dozens in all?
6. A clerk in a small grocery store sold these quantities of
sugar: 4 pounds 4 ounces; 3J pounds; 5 pounds 12
ounces; 7f pounds. How many ounces did he sell
each time ? How many pounds and parts of a pound
did he sell in all?
7. A woman asked the meat-market clerk for a 6-pound
roast. When he had weighed it he charged her $.78,
and the meat was 12 cents a pound. How much did it
weigh? How much more did it weigh than it should
have weighed?
8. When butter is 32 cents a pound, what is the difference in
price between 4J pounds and 4J pounds?
9. A rug 15 feet long is J as wide as it is long. How many
feet wide is it?
PROBLKMS IN FRACTIONS. 251
1. Mary bought \ pound of chocolate creams, and Anna
bought \ of a pound more than Mary. What part of a
pound did Anna buy? Did both girls buy?
2. Charles bought \\ pounds of sweet potatoes one day, 1J
pounds the next day, and 2 pounds another day.
How many pounds of sweet potatoes did he buy in the
3 days?
3. Ellen used 1J yards of ribbon for her hair, 1 yards for a
neck ribbon, and 3 1 yards for a sash. In all how many
yards of ribbon did she use?
4. Ross had a kite string 30J yards long. He gave Carl 13J
yards of it. How many yards were left for Ross?
5. Grace bought 7{- yards of ribbon; she gave 2J yards to
Bessie, and 1J yards to May. How many yards did
Grace give away? How many yards had she left?
6. Carl had $15J, and he bought a football suit for $5J.
How many dollars and parts of a dollar had he left?
7. Nellie's mother canned 3f gallons of pears, If gallons of
peaches, 2J gallons of plums, and 5 gallons of different
kinds of berries. How many gallons of fruit did she
can in all?
8. From a keg having in it 2J gallons of cider, If gallons
were sold. How many gallons were unsold?
9. Four sizes of jars were on a shelf. The first size held \
pint; the second held \\ times as much as the first; the
third held twice as much as the second, and the fourth
held 4 times as much as the first. How much did the
second hold? The third? The fourth? How much
did 4 of the jars, 1 of each size, hold?
10. Walter spent f of an hour studying his arithmetic, J as
long studying his spelling, and twice as long studying
his geography as studying his spelling. How many
hours and parts of an hour did he spend on the 3 studies?
252
RATIONAL ELEMENTARY ARITHMETIC.
A B C I> E
D?
J?
1. Into how many parts is A divided, and what is one part
called?
2. How many parts, and what is one called, in B? C? D?
E? F? G? H? I? J?
3. One part of A equals how many parts of B? C?
E? G? I? J?
4. One part of F equals how many parts ofG? H? I?
D? E?
5. The number below the line of a fraction is the denom-
inator, and indicates into how many equal parts any-
thing is divided. Thus, as one of the parts of B is ,
the denominator, T , shows that B is divided into 4
equal parts; as one part of G is ^, the denominator, ,
shows that G is divided into 6 equal parts; etc.
6. The number above the line is the numerator, and indicates
how many parts are taken. Thus, in |- of B, the numer-
ator, -2-, shows that 2 of the 4 equal parts are taken; in
| of G, the numerator, -2-, shows that 2 of the 6 equal
parts are taken; etc.
What is the sum of % and |? % and -J-? -J- and
7.
8. How did you add \ and -J-?
9 It has already been seen that fractions, in order to be
added, must have the same denominator.
EXERCISES IN FRACTIONS. 253
1. Add J and i Study Figure G, p. 242.
2. In J- there are "how many J' 8 ? ^ n i there are how
many -J' 8 ?
3. How many ^'s are there in and together?
4. What is the difference between and ^?
5. What is the difference between and ^ ?
6. What is the difference between -^ and j ?
7. What is the difference between and -J-?
8. What is the sum of , | and ^ ?
9. What is the sum of , -{ and ?
10. What is the sum of J and -J-?
11. What is the sum of -J and ?
12. What is the sum of , -J and |?
13. What is the difference between J and ^?
14. What is the difference between J and J^?
15. What is the difference between \ and f ? Between f and
? Between f and ^? Between | and ? Between
I and i?
16. If f of a yard of ribbon costs 21^, what is the cost of \ of
a yard? The cost of | of a yard equals what part of
the cost of J of a yard?
17. John worked of the day Monday, ^ of the day Tues-
day, and ^ of the day Wednesday. How many days did
he work altogether ?
18. A girl having f .of a yard of ribbon bought \ more. What
part of a yard had she then?
19. If from -J of a gallon of milk ^ of a gallon is taken, what
part of a gallon is left?
20. A boy studied 1^ hours Monday, 1^ hours Tuesday, and
1 hours Wednesday. How long did he study during
the three days? How much longer Monday than
Tuesday? How much longer Wednesday than either
Monday or Tuesday?
254 RATIONAL ELEMENTARY ARITHMETIC.
1. If -| of a yard of cloth cost $.96, how much will ^ of a
yard cost?
2. A girl walked -f of a mile, and after resting walked J of a
mile farther. What part of a mile did she walk in all ?
3. A man traveled 1-J milQs east, returned, and then went |
a mile west. How far did he travel ?
4. From a piece of cloth 24f yds. long, 6J yds. were sold to
one customer and 8^ yds. to another. How many yards
remained ?
5. One box weighs 5|- Ibs., a second box, 3 times as much as
the first, and a third, ^ as much as the second. What
is the weight of the second and the third box ?
6. A family uses 3J cwt. of ice one week, 2^ cwt. the next
week. How much do they use in the 2 weeks ?
7. How many jars holding ^ of a gal. each can be filled from
3| gals, of water?
8. A boy attends school | of the yr. ; ^ of his vacation is
spent in the country. What part of the year does he
spend in the country?
9. A grocer having 4^ crates of berries sold ^ of them.
How many had he left ?
10. A milkman sells f of a pt. of cream and 1^ qts. of milk
a day to each of 2 families. How much cream does
he sell to both in four days? How much milk?
11. One girl was absent from school -g^of a month; another
girl was absent ^ as long. What part of the month
was the second girl absent?
12. How many bean bags, each requiring -J- of a yd. of cloth,
can be made from ^ of a yd. ? From ^ a yd. ? From
| of a yd. ? | of a yd. ?
13. A man when traveling spent of a yr. in England ; ^ of
a yr. in France, J of a yr. in Germany, and |- of a yr.
in Italy. How many yrs. in all ?
PROBLEMS IN FRACTIONS. 255
1. A woman bought 4^ qt. of berries, 3-J^ qt. of currants,
and 2 qt. of cherries. How many quarts of fruit did
she buy?
2. In making a garden, a man planted ^ A. in cabbages, J A.
in peas, -^g A. in beans, and -fa A. in tomatoes. How
much land did he plant in all?
3. A girl spent ^ of the summer in the country, | of it in
the mountains, and the rest of it at home. What part
of the summer was she at home?
4. While canning peaches, a woman cut 12 peaches into
halves and 12 into thirds. How many halves were
there? How many thirds? How many more thirds
than halves? How many thirds equal four halves?
Six halves ? Eight halves ? Ten ? Twelve ?
5. A man traveled | of a certain distance by boat, \ by train,
and walked \ the remaining distance. What part of
the distance did he walk?
6. From a lot of 5J doz. pairs of shoes, 2 doz. were sold at
one price, and the rest at another price. How many
dozen were sold at the second price?
7. A man built 4^ yd. of fence one day and 1 T ^ yd. less the
next. How many yards did he build the second day ?
8. The area of a building was 30| sq. yd. ; an addition ^ as
large as the building, was made. What was the area
of the addition ?
9. How many square feet of tile will be needed for the floors
of two rooms, each containing 18-J sq. ft. ?
10. A boy spent f of every year at college, for 4 years. How
much time did he spend there in all ?
11. A carpenter bought 528 ft. of lumber, used \ of it, sold \
of the remainder, and stored what was left. What part
did he sell ? What part did he keep ? How many feet
did he keep?
256
RATIONAL ELEMENTARY ARITHMETIC.
2. Show J of the rectangle A; of it; f;
i; I; f. Show how many sixths
there are in J of the rectangle; in
of it.
3. Show how many J's there are in f and
of the rectangle A; in of the rectangle.
f ' + -
4. In the same way find
l;
5. Find also f + A; f + A; i - A; t - A-
6. Find the sums, using a divided rectangle if necessary:
(l)i + i; (5)*+i; (9)f + A; (13) f +
(2)4 + 1; (6H + i; (10)4 + A;
(4) J + I ; (8) f + A; (12) 1 + h ; (16) ! + A.
7. Find the differences, using rectangle when needed
(1) f - J; (5) ! - i ; (9) I -A; (13) f - A;
(2) f - f ; (6) f - J; (10) 1 - A J (14) T 6 y- A;
(7)i-t; (ID -A; (15) A- A;
(8) A - T S O ; (12) J - 2 V; (16) if- A.
8. f + J=? i- = ?
Show J of the rectangle; f of it; |; J; f.
Into how many squares is the rectangle
divided? One of these squares is
what part of the rectangle?
How many yVs are there in J of the rectangle? in J? in
in J? in | + J? in J
-
ADDING AND SUBTRACTING FRACTIONS. 257
1. Find the following sums and differences, using a rectangle
when needed:
(1) f + };
(6) * - 3;
(11)*+*;
(Wl+f;
(2) 3 + f ;
(7)!-f;
(12)! + -?;
(17)1-4;
(3) { + !;
(8) 1 - \;
(13)1--!;
(18)*+ I;
(4) J+i;
(9)1 + ?;
CM)t-H;
(19)4 + 1;
(5) | - I;
(io) t - 1;
rt*)l-|{
(20) A + f .
Notice that to add or subtract two fractions as J arid f , that is to find
| -|- | and g |, we could more quickly do this:
4 2. 4X3 2 X_5 j i g
and 6 3 5X3 3x5 i? Is iff*
2. In this way find these sums and differences:
(1)1+1; (6)f-i; (ll)H-i; (16)
(2)|-f; (7)i+Jj
(3) fH; (8)*-i; (13)H-A; (18)3J + H;
(4) !-i; (9) iV+|; (14) H+A; (19) 8J - 6i;
(5)f+t; (10) I -f; (15) T \-!; (20)101-7].
A number like 8|, which is made up of a whole number and a fraction,
is called a mixed number.
To add or subtract such numbers, first add or subtract the fractions,
then add or subtract the whole numbers and add the two results. Thus :
3. Add:
9| = 9^ 2 9f = 9 T V and 6| = &&. T ' f and A = f J =
6j = ey, I T V 9-
16fV = 15|| 15 + 1 A = 16 T V
4. Subtract: Since f = }| and | = f|, 1 or |- is taken
9f = 8J = 8|| from the 9 and added to f , giving J. 9f is
6| = 6U then the same as 8J or 8||. if taken
2|-g from |E leaves J-J and 6 from 8 leaves
2. The difference is 2JJ.
258
RATIONAL ELEMENTARY ARITHMETIC.
1. Solve these exercises like those on p. 257:
(1) 6| + 2|- ? (5) 8}- 5}=? (9) 18J + 6 T 9 , - ?
(2) 5} -h 3} = ? (6) 10} - 8| = ? (10) 20| - 15| - ?
(3) 4J-2}=? (7) 12} -6}=? (11) 33} -16}=?
(4) 12} - 6J = ? (8) 15| + 7J = ? (12) 66} - 6* = ?
2. 2 X } of the rectangle equals what part of the rectangle?
3. 2 X | = ? 3 X i = ? 4 x | = ? 6Xi= ? 7 X & = ?
4 X f - ? 16 X f = ?
Such an expression as J X f means f of f , but it is usually
read "} times f "
4. } x f, or } of t = ?
Show | of the rectangle; f of it; * of it; }.of i of it.
What part of the whole rectangle is one of the small
squares? How many of these squares in J of | of the
rectangle?
What part of the whole rectangle is J of I of the rec-
tangle? f of | of it? } X t = ?
5. fx I = ?
Divide a rectangle into 6 equal parts by lines running
across it one way and into 4 equal parts by lines run-
ning across it the other way; and show first what part of
the whole rectangle J of f of it is and then what part J
of f of it is. f X f = ? A quick way is to do this :
f X | = !| = If, or |. Show on a rectangle that }} = |.
MULTIPLYING AND DIVIDING FRACTIONS. 259
1. Solve these exercises:
2.
(1)
(2)
I
I
X
X
I
= ?
?
(6)
(7)
T P * X f =
?
(11) if x -H =
(12) X -
?
f
(3)
\
X
I
?
(8)
ft
r X
! -
?
(13) I x { -
?
(4)
2
x
I
?
(9)
4
I
X
T\ =
?
(14) J x =
^
(5)
I
X
5
7
?
(10)
1
x
ft =
?
(15) UX 11 =
?
I,*
2
5
=
?
3
Q?fc
means
i<
livided by
| equals what?
Solution:
f io 15 twentieths.
1 2 8 o 8 twentieths.
15 twentieths -r- 8 twentieths =1 8 8
The work may be arranged thus:
H _ 15 twentieths _ 15
/o 8 twentieths ~ 8
Notice the 20 is found by multiplying together the
numbers below the line (the denominators). The 15 is
found by multiplying the 3 by the 5 and the 8 by
multiplying the 2 by the 4.
3. Solve these exercises
a) *-*-$=?
(2) -
-J = ?
(3) !-
-!=?
(4) !-
-!=?
() -
-1=?
(6) *-
-i = ?
(7) 1-
-!=?
(8) 4-
-f=?
(9) A-
-}=?.
(10) f-f = ?
1
t=?
1*1
4 =?
(11)
(12)
(13)
(14)
(15)
(16)
(17) H-
(18)
(19)
(20) H- I =
260 RATIONAL ELEMENTARY ARITHMETIC.
1. What part of a dollar is 500? 250? 100?
2. How do you write 10 as a fraction of a dollar? How do
you write it with the dollar sign ($) ?
3. How do you write 100 as a fraction of a dollar? With the
dollar sign?
4. How do you write 250 as c fraction of a dollar? With
the dollar sign ? 500 as a fraction of a dollar ? With
the dollar sign ?
$.01 = ^ of a dollar?
.10 =s ^^ or ^ of a dollar?
25 = ^ of a dollar?
.50 = ^ or 7^ of a dollar?
5. The period used between figures when writing dollars and
cents is called the decimal point.
6. It is much easier to write cents with the decimal point
than as fractions of a dollar.
10 yi-g- of a dollar .01 of a dollar,
100 = ^ (or 1 V) of a dollar = .10 (or .1) of a dollar.
250 = T 2 ^. of a dollar = .25 of a dollar.
500 = -ffo (or T 5 ) of a dollar = .50 (or .5) of a dollar.
7. Numbers when written with the decimal point are road
exactly as when written as fractions.
y-J-3 of a dollar is read one-hundredth of a dollar.
.01 of a dollar is read one-hundredth of a dollar.
^-Q of a dollar is read one-tenth of a dollar.
.1 of a dollar is read one-tenth of a dollar.
-nro f a dollar is read twenty -five-hundredths of a dollar.
.25 of a dollar is read twenty -five-hundredths of a dollar.
-^- ff of a dollar is read five-tenths of a dollar.
.5 of a dollar is read five-tenths of a dollar.
8. From this it is seen that the first figure following the
decimal point is read as tenths; the second figure as
hundredths.
DECIMAL FRACTIONS. 2bl
1. Read the following numbers as parts of a dollar:
.05 .45 .23 .3
.6 .93 .8 .44
.18 .06 .75 .02
.72 .15 , .9 .12
2. Write each of the above decimal fractions in the form of
common fractions.
3. Express the following common fractions in the form of
decimal fractions:
OF bu. T\ ft. iV hr.
T 4 (F gal. rVo ton.
i. Write as decimal fractions the following:
TW A TITO
A TTHF Tiro
A 8 o AV A
To T 5 o TITO" A
5. A boy spent .25 of a dollar; how many cents did he spend?
.01 of a dollar = If.
.25 of a dollar = 25 X If = 25^.
6. From a flock of 350 sheep a farmer sold .3 of them. How
many did he sell?
7. A piece of cloth 10 yd. long was sold to two customers,
one buying .5 of it, the other buying the rest. How
many yards did each one take?
8. A boy traveled 100 miles, going .2 of the way by boat.
How many miles did he go by boat?
9. From a cistern holding 500 gal., .07 of its contents were
drawn off. How many gallons were drawn off?
10. A man bought .75 of a quantity of grain measuring 400
bu. How many bu. did he buy?
162 RATIONAL ELEMENTARY ARITHMETIC.
1. Begin on the right and add as with whole numbers.
12.24 Place the decimal point (.) in the sum just
16.32 beneath the points in the addends (numbers to
8.12 be added).
9.67
3.25
2. Add:
(1) 623.21 (2) 4561.38 (3) 685.329
68.75 28.17 27.602
90.66 191.76 7.001
8.32 9.68 .868
(4) 365.250
.168
90.027
106.995
4.00 3125.88 12.789 78.200
67.75 .98 1.896 9.375
3. Begin on the right and subtract as with whole numbers
and place the point beneath the points in the subtra-
hend and minuend.
a)
(5)
(9)
4. Divide 25 by 10 and express the quotient in decimal form.
10)25 or 10)25^
2A=2.5 ^5
5. Divide 256 by 100 and give the quotient in decimal form.
100)256 or 100)256
86.3
7.9
(2)
(6)
(10)
60.9
14.7
(3)
35
21
.16
.87
(4)
(8)
(12)
30.16
3.95
806.302
99.809
201.06
99.98
476.001
96.993
(7)
(ID
108
69
.08
.89
36.004
9.735
1008.90
86.96
101
90
.010
.909
600.006
589.099
2.56 2.56
6. Multiply 2.5 by 10; multiply 2.56 by 10; by 100.
7. What part of 35 is 3.5? .35?
MULTIPLYING DECIMALS. 263
1. How many times 3.5 is 35? What part of 3.5 is .35?
2. What part of 325 is 32.5? 3.25? .325?
3. How many times .325 is 3.25? 325?
4. How may you quickly divide a number by 10 by merely
changing the decimal point? by 100? by 1000?
5. How may you quickly multiply a number by 10? by 100?
by 1000?
6. Multiply 68 by 27; by 2.7; by .27.
10 X 2.7 = ? 100 x.27.
i ** What part of 27 is 2.7? .27?
rt What part of 68X27 is 68 X
2.7? 68 X.27?
476 476 476 T ... , . . .
136 136 136 In fi (6) h W m ^ y deC ""*
1836 1833 1836 figures are m the product?
in (c)?
7. Multiply 6.8 by 27; by 2.7; by .27.
What part of 68X27 is 6.8X
(a) (6) (c) 27? 6.8X2.7? 6.8X.27?
6.8 6.8 6.8 How many decimal places in
27 2.7 .27 (a)? in (6)? in (c)?
476 476 How many decimal places in
136 136 both the multiplicand and
18.36 1.836 multiplier?
How may one quickly tell by
looking at multiplicand and multiplier how many
decimal places the product must have?
8. Knowing that 1235X321 = 396435, give the answers to
'all these questions without multiplying:
(1) 1235X32.1=? (5) 1.235X321=?
(2) 1235X3.21=? (6) 12.35X.321 = ?
(3) 123.5X32.1 = ? (7) 1.235X3.21 = ?
(4) 12.35X3,21 = ? (8) 1.235 X. 321 = ?
264 NATIONAL ELEMENTARY ARITHMETIC.
1. Solve the exercises:
(1) 32 X 2.5-?
(2) 45 X 3.8-?
(3) 63X.28-?
(4) 3.9 X 4.5=?
(5) 8.5 X. 48-?
(6) 5.8X.75-?
(7) 28.6X32.5-?
(8) 2.86 X 3.56-?
(9) 28.6 X 3.56-?
(10) 6.85X41.6-?
(11) 6t85X4.61-?
(12) 6.85 X. 475=?
2. Divide 894.24 by 24.3.
36.8, Quotient
Divisor, 24.3)894.24, Dividend
729._
165.2
145.8
19.44
19.44
As with whole numbers,
we say 24 in 89, 3 times.
Write 3 above 9. 24.3 X
30 - 729. 894 - 729 -
165. Bring down the 2
of the dividend, giving
165.2. Then 24 in 165,
6 times. Write 6 in the
quotient, and so on.
Remainder. Keep the decimal points
in a vertical line.
2. Solve the following exercises:
(1) 86.4-24;
(2) 64.8-36;
(3)249.1-53;
(4) 327.6 - 63;
(5)251.6-74;
(6)104.8-3.6;
(7) 140.4 - 5.4;
(8)148.8-6.2;
(9) 167.5 - 4.8;
(10)425.6-7.6;
(11)
(12)
(13)
(14)
(15)
(16)
101.34
215.536
13.312
83.781
246.015
396.435
(17) 4418.904
(18) 843.505
(19) 850.335
(20) 449.35
3.6;
7.8;
4.16;
2.61;
3.15;
32.1;
36.28;
6.83;
12.45;
18.92.
PERCENTAGE. 265
1. In one dollar how many cents?
2. What part of one dollar is 1 cent? 12 cents? 23 cents?
3. Another term for hundredths is per cent.
15 hundredths of a dollar = 15 per cent of a dollar.
7 hundredths of a dollar = 7 per cent of a dollar.
4. Instead of the word per cent, the sign $ is often used.
15$ of a dollar = 15 per cent, or hundredths, of a dollar.
7$ of a dollar = 7 per cent, or hundredths, of a dollar.
5. Since anything may be divided into 100 equal parts, any
number of such parts may be called so many hundredths
or per cent.
of a bu. = 15$ of a bu.
of a bu. = 7$ of a bu.
6. Since 15$ is the same as y^V, it may be written as a deci-
mal fraction exactly as y^ may be written decimally,
.15; 7$, the same as y^ may be written .07.
7. Write first with per cent sign, then as decimal fractions:
8 (> -.13. 3 3
TTTO TSU" 100 TT5TT
TUT TTTO" TOT TTTo"
20 50
TOT TOT
60 4_5 66
TOT TOO T~0~0~
8. Write first as common, and then as decimal fractions:
25$ 64$ 12|$
20$ 53$ 33$
3$ 50$ 2$ 16|$
5$ 75$ 45$ 66|$
9. Write as common fractions:
.8 .25 .7 .09
.5 .14 .04 .85
.16 .75 .65 .01
.33 3.1 2.25 1.03
266 RATIONAL ELEMENTARY ARITHMETIC.
1. Review pages 178 and 218.
2. How many cents in | of a dollar? In | of a dollar? f of
a dollar? of a dollar? | of a dollar? f of a dollar?
3. What per cent of a dollar is J of a dollar? f ? 1? ?
f? I? I?
4. Instead of one dollar, find the same parts and per cents of
one gallon. One bushel. Of any unit. Of $8. Of $24.
Of 40 marbles. Of 84 acres.
5. 25% of any number is what fractional part of it?
6. Answer similar questions regarding the other per cents
used.
7. How many cents is J of a dollar? | of a dollar? ^ of a
dollar? | of a dollar?
8. What per cent of a dollar is -} of a dollar ? | of a dollar ?
9. Instead of one dollar, find J and | of one yard. Of one
foot.
10. What per cent of a foot is -J of a foot? -jj of a foot? | of
afoot? | of a foot?
11. What per cent of a yard is -J of a yard? | of a yard? i
of a yard ? | of a yard ?
12. Find 16f $ of 18 pigeons. Of 24 marbles. Of 30 boys.
Find 83|$ of the same. 33 \%. 66 \%.
13. 33|$ of 12 is ? | of 12 is ? 33#& of 12 and | of 12
are the same.
14. Make statements about the other per cents.
15. 50$ of Fred's money is 15 cents. How much money has
he?
16. 75$ of the milk one family uses in a week is 9 quarts.
How much milk is used? What part of the quantity
used is 9 qts. ?
17. 33^$ of the horses in a livery stable is 21. How many
horses in all? What part of the whole number of
horses is 21 horses?
PERCENTAGE. 267
1. A man set out 150 fruit-trees and 28% of them died.
How many died?
150 The base is the number on which the percentage
28 is to be found.
1200 The rate is the per cent to be found. It may be
300 written as a decimal.
42.00 The percentage is a certain number of hundredths
of the base. Here it is .28.
To find the percentage :
2. Solve the following exercises:
(1) 12% of 35=? (6) 36% of 80=? (12) 95% of 1200=?
(2) 18% of 65=? (7) 38% of 75=? (13) 85% of 1000 = ?
(3) 30% of 68=? (8) 43% of 60=? (14) 85% of 150=?
(4) 45% of 90 = ? (9) 65% of 350=? (15) 25J% of 600=?
(5) 24% of 45=? (10) 70% of 460=? (16) 37J% of 800=?
(11) 75% of 650=?
To find the rate:
3. The base is 320 and the percentage is 48. Find the rate.
.15, rate
base, 320)48.00, percentage Diyide the percentage by the
1600 base '
1600
4. Find the rate in the following exercises:
(1) base = 240, percentage = 72;
(2) base = 120, percentage = 6;
(3) base = 65, percentage = 13;
(4) base = 96, percentage = 24;
(5) base = 104, percentage = 26;
(6) base = 144, percentage = 48;
(7) base = 160, percentage = 80;
(8) base = 80, percentage = 10.
268 RATIONAL 'ELEMENTARY ARITHMETIC.
To find the base:
1. The percentage is 87 and the rate is 25; find the base.
348, base
rate, .25)87.00, percentage
75 Divide the percentage by
120 the ra te per cent ex-
100 pressed as a decimal.
^~
200
2. Find the base in the following exercises :
(1) per cent age =96, rate =12; (8)percentage= 44.8, rate= 7;
(2) percentage =75, rate=15; (9) percentage = 10.88, rate =17;
(3)percentage=15, rate= 3; (10) percentage = 32.2, rate=35;
(4) percentage =37, rate=10; (ll)percentage= 92.4, rate=24;
(5) percentage =48, rate = 6; (12)percentage= 97.2, rate=45;
(6) percentage =42, rate =14; (13) percentage = 12.8, rate= 8;
(7) percentage =54, rate=18; (14) percentage =291. 84, rate=32.
3. Find the amounts in each exercise of problem 4, p. 267.
4. 16-J% of my pens are 42. 42 pens is what part of the
whole number? How many pens have I?
5. A boy lost 16|% of his marbles, and had 30 marbles left.
What part was lost? How many were lost? How
many had he at first?
6. In an orchard of 156 trees, 16f % are pear, and 83J% are
apple. What part of the whole number of trees is
pear? Apple? How many of each?
7. A man bought a bicycle for $45 and sold it so as to gain
25%. What was the selling price?
8. 87J% of the butter in a dairy is 84 pounds. What is the
whole number of pounds? If sold at 23 cents per
pound, how many dollars will the dairyman receive?
PROBLEMS IN INTEREST. 269
1. Charles loaned William one dollar, charging him 6 cents
for using it one year. At the same price, how much
would William pay for using $2 for one year? $5? $25?
2. Charles put SI in the bank for one year and the banker
paid him 6 cents (or 6%) for the use of it. At the end
of the year Charles told the banker he could use $1 for
6 months longer at the same price (or rate) for using it.
How much did the banker pay Charles for the use of
$1 for 6 months? For one year and six months?
3. The charge or price paid for the use of money is interest.
4. At 6 cents (or 6%) interest on one dollar, how much will
it cost Mr. Andrews to borrow $35 for one year?
5. At 6%, how much interest will Mary have to pay a bank
for using $75 of its money for one year?
6. 6% (or 6 cents) on each dollar is a common price or rate
of interest to pay for the use of a dollar for one year.
This makes 6% interest on $1 how much for 6 months?
For 3 months?
7. Clara borrowed $15 from her brother for 6 months at 6%.
How much did she pay for the use of the money?
8. Mr. Tanner borrowed $95 for 4 months at 6%. How
much interest did he pay?
9. Allen's father loaned him $50 for one year and six months
at 6%. How much did his father receive for the use
of the money?
10. John loaned his sister $17 for one year and three months
at 6%. How much interest did she pay him at the
end of that time?
11. A grocer borrowed $200 for 3 years and 6 months at 6%
interest. What did the use of the money cost him?
12. A father loaned each of his two sons $125.00 for 5 years
and three months at 6%. How much did the father
receive for the use of the money?
270 RATIONAL ELEMENTARY ARITHMETIC.
1. At 6%, what is the interest on $245 for one year? For
6 months? For 3 months? For one year and 6 months?
For one year and 3 months? For one year and 9
months?
2. William's uncle loaned him $25 for one year at 6%. How
much interest did William pay at the end of the year?
How much did he pay to rid himself of the whole debt?
3. Henry loaned John $125 for 5 years and 6 months at 6%.
At the end of that time how much money did John
pay Henry?
4. Annette borrowed $220 from her mother for 7 years and
3 months at 6%. What was the whole sum of her debt
at the end of that time?
5. A janitor borrowed $321 from his employer for 3J years
at 6%. What was the whole sum (or amount) of his
debt at the end of that time?
6. What is the interest on $25 for one year? What is the
amount due at the end of that time?
7. What is the interest and the amount on $5 for 7 years
and 3 months?
8. How much money must John lend at 6% to earn 6 cents
in one year?
9. How much money must Clara lend at 6% to earn 60 cents
in one year?
10. What sum of money must Kate lend to Mary at 6% to
earn 90 cents in one year?
11. What sum can Amos loan his father at 6% to earn $1.50
in one year?
12. The sum of money upon which the interest is found is
the principal.
13. What is the principal which Mary must lend at 6% so
that she may gain 30 cents in one year?
14. What principal at 6% will bring $7.20 in one year?
PROBLEMS IN INTEREST. 271
1. What principal at 6% will bring $1.80 in one year?
2. What would the same principal at the same interest gain
in 6 months? In 3 months?
3. What principal must John loan to Will at 6% to gain
$1.35 in 6 months?
4. What principal must Charles loan the bank at 6% if he
.. receive for his money $1.95 in 3 months?
5. How long will it take $1 at 6% to earn 6 cents?
6. At 6%, how long will it take $5 to earn 60 cents?
7. How long must Kate lend John $75 at 6% to have it gain
$22.50?
8. Samuel borrowed $40 at 6%. In how long a time would
he have to pay $16.80 for interest?
9. Henry borrowed $2400 at 6% for 3 years and 6 months.
What was the interest?
10. What was the principal of Henry's debt? What was
the interest? What was the amount? What was the
time? What was the rate?
11. Elizabeth borrowed $50 at 6% for 4 years and 3 months,
what was the interest?
12. What was the principal of Elizabeth's debt? What was
the interest? The amount? The time? The rate?
13. Find the interest, the amount and the rate on $2000 bor-
rowed for 5 years and 6 months at 6%.
14. Name the interest and the amount in the following cases
at 6%:
(a) $255 borrowed for 4 years and 9 months.
(b) $275 borrowed for 5 years and 2 months.
(c) $821 borrowed for 6 years and 3 months.
(d) $445 borrowed for 10 years and 6 months.
(e) $4450 borrowed for 5 years and 6 months.
(/) $7725 borrowed for 20 years and 3 months.
(g) $8726 borrowed for 9 years and 2 months.
272 RATIONAL ELEMENTARY ARITHMETIC.
To find the interest and the amount:
1. Examine problem 14, p. 271, and make a rule for finding
the interest, when the principal, rate, and time, in
years, are given.
2. Make a rule for finding the amount.
3. Find the interest and amount in the following problems:
(a) principal = $450, rate = 4%, and time =3J years;
(6) principal = $236, rate = 6%, and time =2J years;
(c) principal $175, rate = 7%, and time =1 years;
(d) principal = $1260,rate = 8%, and time =3 T 6 T years;
(e) principal = $1080,rate = 5%, and time = T \ year.
To find the principal :
INTEREST.
In Interest problems the base is called the principal, the
rate is called rate of interest, or rate, and the percentage
is called interest for one year.
To find the interest for a longer or shorter time than 1
year the interest for 1 year is multiplied by the time
expressed in years.
4. Morgan lent Henry $55.00 for a year at 6% interest.
At the end of the year how much interest did Henry
owe Morgan? What was the whole amount that Henry
owed Morgan at the end of the year ?
5. Find the interest and amount of $180.00 at 8% for 2J
years?
6. A man owed $875.00 for 3 yr. and 6 mon. on which he
paid 5% interest. What was whole amount of his debt
at the end of this time?
7. I borrowed $2400.00 for 4 yr. 9 mon. at 6J%. What
was the interest and what the amount I owed at the end
of the time ?
PRINCIPLES OF INTEREST. 273
8. Which is the greater and how much greater, the interest
on $1250 at 6-J-% for 4 years, or the interest on $1800
at 5% for 4 years and 9 months ?
9. A boy earns $3.00 a week and $3900.00 are lent at
4%. Which brings in the more money, the boy or the
$3900 ?
10. A man earns $83 J- a month and $20,000 are lent at 4J%,
interest. Which produces UK; larger income in a year ?
How much larger ?
11. How many $1200 sums of money lent at 7% will it
take to bring in enough to support a family whose
expenses are $42 a month ? How many such sums
will it take if they are lent at 5% and the family's
expenses are $50 a month ?
12. Which brings in the more interest, $750 at 7J% in 2 1 ,
years, or $1350 at 4J% in 2 T y years ? How much
more ?
13. On the first day of January a boy lends his father $20
from his savings the year before. On the first of the
next January he lends his father another $20. He
continues this for five years. His father pays him 12%
on each sum after he has had it a year. How much
interest does the boy receive at the end of the 1st
year ? Of the 2nd year ? Of the 3rd year ? Of the 4th
year ? Of the 5th year ? In all 5 years ?
14. The father pays the boy all the money he has borrowed
at the end of the 5th year. If the boy has saved all
his interest how much money has he now from all the
$20 loans and interest ?
15. A man's tax amounted to $175.85. He failed to pay it for
5 years. He was charged 6% interest for each year
he failed to pay. What was the whole amount he had
to pay ?
274
RATIONAL ELEMENTARY ARITHMETIC.
Without measuring, make a list of the following estimates in the drawing.
1. Height of whole mantel. Width of whole mantel.
2. Shelf to top of tiling.
3. Top of tiling to top of grate iron.
4. Width of upper part of grate iron.
5. Width of open space from grate iron to grill.
6. Width of upper grill; of lower grill.
7. Width of whole mantel.
8. Width of board behind each pillar.
9. Width of each pillar.
10. Width of tiled space at each side of grate iron.
11. Width of side iron of grate.
12. Measure all these distances and compare the measure-
ments with your estimates.
SCALE DRAWING OF MANTEL. 275
The drawing on the opposite page is made to the scale of } in. to 1 foot.
Add to the list of measurements of the drawing on the
opposite page, the measurements of the mantel ac-
cording to the scale.
1. What is the area of the board below the shelf? The
board back of each pillar? The tiling above the
grate? At each side of the grate? Both grills? The
iron around the grate?
2. Find the diameter of each post.
3. If the grate is 12 in. deep, how many cu. ft. are there
in the open space of the grate?
4. At $.60 a sq. ft., what was the cost of tiling this mantel?
5. The price of this mantel was $75, but the merchant gave
the purchaser a discount of 2%. What did the mantel
really cost?
6. The grate has 8 rows of gas pipe in it, each row containing
10 sets of holes, 5 rows in a set. How many gas jets
are there in the mantel?
7. Each row of gas pipe in the grate reaches from side to
side of the entire open space. How many feet of pipe
are in the grate?
8. The mantel occupies 10% of the wall it is in. How many
square feet are in the wall?
9. A tiled hearth occupies the entire space in front of the
mantel and is 2 feet wide. What was the cost of
tiling at 35# a square foot?
10. From catalogues obtain prices of tiling, grill work, wood-
work, etc., an^l make problems similar to those on this
page.
276
RATIONAL ELEMENTARY ARITHMETIC.
MULTIPLICATION TABLES.
IX 1= 1
2X 1= 2
3X 1= 3
4x 1= 4
IX 2= 2
2X 2= 4
3X 2= 6
4X 2= 8
IX 3= 3
2X 3= 6
3X 3= 9
4X 3 = 12
IX 4= 4
2X 4= 8
3X 4=12
4X 4=16
IX 5= 5
2X 5 = 10
3X 5 = 15
4X 5=20
IX 6= 6
2X 6=12
3X 6=18
4X 6=24
IX 7= 7
2X'7=14
3X 7=21
4X 7 = 28
IX 8= 8
2X 8=16
3X 8=24
4X 8=32
IX 9= 9
2X 9=18
3X 9=27
4X 9=36
1X10=10
2X10=20
3X10=30
4X10=40
1X11 = 11
2X11=22
3X11=33
4X11 = 44
1X12=12
2X12=24
3X12=36
4X12=48
5X 1= 5
6X 1= 6
7x 1= 7
8X 1= 8
5X 2=10
6X 2=12
7X 2 = 14
SX 2 = 16
5X 3=15
6X 3=18
7X 3=21
8X 3=24
5X 4=20
6X 4=24
7X 4=28
8X 4=32
5X 5=25
6X 5 = 30
7X 5 = 35
8X 5 = 40
5X 6=30
6X 6=36
7X 6=42
8X 6=48
5X 7=35
6X 7=42
7X 7=49
8X 7=56
5X 8=40
6x 8=48
7X 8=56
8X 8=64
5X 9=45
6x 9=54'
7X 9=63
8X 9=72
5X10=50
6X10=60
7X10=70
8X10=80
5X11=55
6X11 = 66
7X11 = 77
8X11=88
5X12=60
6X12=72
7X12=84
8X12=96
9X 1= 9
10X 1= 10
11X 1= 11
12X 1= 12
9X 2 = 18
10X 2= 20
11 X 2= 22
12 X 2= 24
9X 3= 27
10X 3= 30
11 X 3= 33
12 X 3= 36
9X 4= 36
10 x 4= 40
11 X 4= 44
12 X 4= 48
9X 5= 45
10X 5= 50
11X 5= 55
12 X 5= 60
9X 6= 51
10 X 6= 60
11 X 6= 66
12X 6= 72
9X 7= 63
10X 7= 70
11X 7= 77
12X 7= 84
9X 8= 72
10X 8= 80
11 X 8= 88
12X 8= 96
9X 9= SI
10X 9= 90
MX 9= 99
12 X 9 = 108
9X10= 90
10X10=100
11X10=110
12Xlo=120
9X11= 99
10X11 = 110
11X11 = 121
12X11 = 132
9X12=108
10X12 = 120
11X12=132
12X12 = 144
TABLES OF WEIGHTS AND MEASURES. 277
LIQUID MEASURE DRY MEASURE
4 gills (gi.) =1 pint (pt.). 2 pints (pt.) = 1 quart (qt.).
2 pints =1 quart (qt.). 8 quarts = 1 peck (pk.).
4 quarts = 1 gallon (gal- ). 4 pecks = 1 bushel (bush.
1 gallon = 231 cubic inches. 1 bushel = 2150. 42 cubic inches.
31 J gallons = 1 barrel (bbl.).
AVOIRDUPOIS WEIGHT
16 ounces (oz. ) = 1 pound (lb.).
2000 pounds = 1 ton (T.).
LINEAR MEASURE
12 inches (in ) = 1 foot (ft.). 5J yards, or 16$ feet = 1 rod (rd.).
3 feet = 1 yard (yd. ). 320 rods, or 5280 feet = 1 mile (ra. ).
SQUARE MEASURE
144 square inches (sq. in.) = 1 square foot (sq. ft.).
9 square feet = 1 square yard (sq. yd.).
" (sq. rd.).
160 square rods = 1 acre (a.).
640 acres = 1 square mile (sq. m.).
SOLID OR CUBIC MEASURE
1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).
27 cubic feet = 1 cubic yard (cu. yd. ).
WOOD MEASURE
16 cubic feet = 1 cord foot (cd. ft.).
8 cord feet, or ) i A / A \
128 cubic feet f =
TIME MEASURE MISCELLANEOUS TABLES
60 seconds (sec.) = 1 minute (m.). 12 units = 1 dozen.
60 minutes = 1 hour (h.). 12 dozen = 1 gross.
24 hours = 1 day (d.). 20 units = 1 score.
7 days = 1 week (wk.). 24 sheets = 1 quire.
365 days 1 common year (c. yr.). 20 quires = 1 ream.
366 days = 1 leap year (1. yr.).
100 years = 1 century (C.).
YB 17239
M3055T79
QA i
THE UNIVERSITY OF CALIFORNIA LIBRARY
