ffSffESfe»'^«8*S||,5
WILSON. HINKliE ^ CO. |
CT .'.XTON. F •'■^- & HAFFELFINGBR. |
n^:W'^ORK: C MAYMA4P.. |
University of California • Berkeley
The Theodore P. Hill Collection
of
Early American Mathematics Books
Digitized by the Internet Archive
in 2008 with funding from
IVIicrosoft Corporation
http://www.archive.org/details/aryarithmetiprimOOwhitrich
IVHITE'.'S (1 R A O ED-SCHOOL SERIES.
A
PRIMARY
ARITHMETIC,
UNITING
ORAL AND WRITTEN EXERCISES
IN A
NATURAL SYSTEM OF INSTRUCTION.
By E. E. white, M. A.
WlLSOlNT, HlI^KLE & Co.,
CINCINNATI: NEW YORK;
137 WALNUT ST. 28 BONO ST.
WHITE'S GRADED-SCHOOL SERIES.
COMPLETE IN THREE BOOKS.
I, TIII3IARY AllITH3IETia
II, INTERMEDIATE AIIITH3IETIC,
III, C03irLETE ARITH3IETIC,
PLAN OF PEIMART ARITHMETIC.
Zessons I to XI develop the idea of numbers from one to ten and
combine groups of objects.
Zessons XI to XX teach the Addition and Subtraction of num-
bers—results not exceeding ten.
Zessons XX to XXIX teach the Addition and Subtraction of num-
bers—results not exceeding fifty.
Zessous XXX to XZII teach the Addition of numbers to amounts
not exceeding one hundred.
Zessons XLIIl to III teach the Subtraction of numbers— minu-
end in Oral Exercises not exceeding one hundred.
Zessons III to LXXIII teach the Multiplication of numbers-
product in Written Exercises not exceeding one thousand.
Zesso)is IXXTII to XC teach the Division of numbers— dividend
in Written Exercises not exceeding one thousand.
Zessons XC to XCII inclusive contain a General Review.
Entered, according to Act of Congres?, in the year 18GS. by
WILSON, HINKLE & CO.,
In the Clerk's Office of tlie District Court of the United States, for tlio
Southern District of Ohio.
ELECTROTYPED AT THE FRANKLIN TYPE FOUNDRY, CINCINNATI.
PREFACE.
The true method of imparting to a child a clear comprehension
of the value of numbers, the foundation of arithmetical knowl-
edge, consists of three steps, viz.: 1. The perception of numbers
represented by objects in sight. 2. The conception of numbers
applied to objects not in sight. 3. The conception of numbers
not applied to objects. A knowledge of the elementary combina-
tions of numbers is best communicated in the same manner.
A faithful observance of this natural order constitutes one of
the characteristic features of this first book in aritlimetic. Ab-
stract numbers and operations are reached, in practice as well as
in theory, as the final step. The plan every-where observed is,
first, Physical Objects (m sight or repref^ented by pictures); sec-
ondly, Concrete Numbers; and, thirdly, Abstract Numbers. In
this and other evident features, the book is a practical embodi-
ment of tlie simplest and most vital principles of the inductive
method of instruction.
But the distinguishing feature of the book, as well as of the
Series of which it forms a part, is the comp'ete uxiox of 3Tenfal
(Oral) and Writte^i Ari'hmetic. This is secured, not by scattering
a few miscellaneous slate exerci.ses through the work, but by
making every oral exercise preparatory to a written one, and by
uniting both as the essential complements of eacli other. Slate
and blackboard exercises are introduced at the very beginning
of the course, and are continued, increasing in number and diffi-
culty, to the end. P^ach lesson gives the pupil something to do,
as well as something to study.
Two other noticeable features of the book are the great variety
of exercises — the object being to make the pupil accurate and
rapid in combining small numbers — and their preeminently
progressive character. Attention may also be called to the pre-
sentation of converse operations, as Addition and Subtraction,
Multiplication and Division, in connection witli each other, as
well as sei)arately; to the converse forms of the tables and their
noil niemoriter character; and, also, to the superior typography,
and the number, beauty, and utility of the illustrations.
It is hoped that these and other features will commend the
work to all intelligent and progressive teachers.
Columbus, Ohio, May, 1868.
SUGGESTIOiNS TO TEACHERS.
The first thirty lessons of this book may be mastered in the
earlier part of the primary course. To this end, the pupils should
be advanced very slowly, and the exercises should be multiplied
until great rapidity and accuracy are secured.
The first step in every new combination is to combine groups
of objects, and, both in the pupil's study and the teacher's instruc-
tion, the pictorial illustrations should be supplemented by the use
of visible objects, as counters, blocks, beans, etc. The teacher should
also refer to other fomiliar objects in sight, as chairs, desks,
slates, etc. Attention should be called to the difference between
the pictures in the lessons, and the objects which they represent.
Pupils should be required to give answers in complete sentences.
Suppose the question to be, "How many tops are 5 tops and 4
tops?" The answer should be, "5 tops and 4 tops are 9 tops."
To secure rapidity, drills may occasionally be introduced in
which only results are given, as "9 tops." Nothing is gained
by requiring pupils to give reasons for answers to simple exam-
ples, and even problems which admit of a formal analysis should
be solved briefly and concisely. See page 51.
The written exercises are designed to go hand in hand with
the oral, and should be taught with equal thoroughness. They
are so easy and progressive that but little explanation will be
found necessary. They should not only be copied and performed
by the pupils on their slates, but they should also be used as
blackboard exercises. Such exercises are exceedingly valuable
both as a means of awakening interest and of imparting skill in
numerical calculations.
Blackboard exercises, affording a great variety of combinations,
and requiring but little labor in copying, may be easily arranged.
The following are given as illustrations :
0)
(2)
(3)
1
5
4
3 2
7 6
12 8
5 4
9 8
20 16
7 6
11 10
28 24
9 4 8
13 4 12
36 4 32
By pointing successively to the figures in the oblique rows
and to the figure between them, the first diagram will afford an
excellent drill in adding or in multiplying, the "4," or any otlier
figure in its place, being the number added or multiplied, as the
case may be. The second diagram will afford a good exercise
in subtraction, ana the third in division.
PRIMARY ARITHMETIC.
Touch your head. How many heads have you?
How many chins? Hold up one hand. Hold up
tAvo hands.
How many fingers do I hold up? Hold J^
up two fingers. Hold up one thumb. Hold ^
up two thumbs.
How many eyes have you? How many cheeks?
How many tongues ? How many lips ? How many
feet?
How many nuts do you see in
this picture? How many leaves?
j[\ How many stems has each nut ?
Brino; me one block. Brinpj me
two blocks. Take away one block.
How many blocks are left?
Hand me two books. Take one of them. How
many books have I left ? INIake two marks on your
slate.
Make the figure one on your slate^ uius : /.
^lake the figure two on your slate, thus : J'.
Make the figure 2 two times.
(5)
PRIMARY ARITHMETIC.
■bBSSOM n«
To Teachers. — Drill the pupils until they can tell the
number of objects in each group, and combine the groups, without
counting.
Hold up two fingers. Hold up two hands. M
How many fingers do I hold up? Hold up j^
three fingers. Hold up two fingers.
Here is a picture of a dog. How
many fore feet has he? How many
hind feet? How many of his feet
can you see?
Bring me two blocks. Bring me one more. How
many blocks have I now? Take one block. How
many blocks have I left? Make three marks on
your slate.
How many acorns in each of these groups? How
many in the third group more than in the first?
How many groups of rabbits do you see? How
mnny rabbits in the first group? How many rabbits
in the second group?
How many balls are ® ^ and ^ ?
^^ and ^p ^p are how many balls?
Make the figure three on your slate, thus: J.
IVIake the figures 1, 2, 3.
PRIMARY ARITHMETIC.
How many fingers do I hold up on
my right hand? How many on my
left hand? How many on both hands?
Hold up four fingers.
Plere is a picture of a fine ox.
How many horns has he? How
many ears
How
many
legs?
How many feet?
Bring me four blocks. Take one of them. How
many blocks have I now? Make three marks on
vour slate. Make four marks.
How many groups of pears do you see? How
many pears in the first group? How many in the
second group? How many in the third group?
How many pears in the second group more than in
the first ?
How many flowers in each of these groups ? How
many more flowers in the second group than in the
first?
How many blocks are If if HP and iifS ^
l^^» «P and ^ ^ are how manv blocks?
How many balls are ^ and ^ ^8 ^©*?
PRIMARY ARITHMETIC.
Make the figure foiir^ thus :
//.
Make the figure
4 four times. Make 1, 2, 3, 4.
To Teachers. — Multiply these exercises until the pupils
can add the groups instantly, without counting.
. >^J,- *«>«!.-« —
How many fingers do I hold up on
my right hand? How many on my
left hand? How many on both hands?
Hold up four fingers. Hold up five fingers.
How many geese do you
see in this picture ? How
many goslings ? If two gos-
lings should go aAvay, how
many would be left?
Place four blocks on the
table. Add one block more.
How many blocks are there now? Take away two
blocks. How many blocks are left?
How many groups of tops are here? How many
tops in the first group? How many in the third?
How many in the second?
How many horses in each of these groups? How
many in the first group more than in the second ?
PRIMARY ARITHMETIC. 9
Place three blocks on the table. Add two blocks
more. How many blocks are there?
How many balls are ^0 i^ ^0 and ^ ^02
and ^M ars hoAV many balls?
]\Iake the figure five, thus : J^ !Make the figure
5 five times. Make 1, 2, 3, 4, 5.
.^^J^H
How many fingers do I hold up on
my right hand? How many on my
left hand? How many on both hands?
Hold up five fingers. Hold up six fingers.
How many little chickens
do you see in this picture?
How many are near the old
hen's beak? How many are
near her right wing? How
many in both groups?
Place five blocks on the table. Add one block
more. How^ many blocks on the table now? Take
away three blocks. How many blocks are lefl?
Here are how many groups of girls ? How many
girls are in the first group? How many in the
second? How many more girls in the second group
than in the first?
10
PRIMARY ARITHMETIC.
How many kittens in each group below? How
many more in the first group than in the second?
How many stars are -)■- :|c -);- -/- -/- and -);-?
'!' -)r '!^ '!' ^i^d 'I- -)r ^I'e how many stars? How
many stars are -*'- -/- and -);- -)^-?
Make the figure six, thus : ^ Make 1, 2, 3, 4,
5, 6. How many figures have you made?
— -'^^»l^•;»3*;^?^ -
How many fingers do I hold up on m^ r^
my right hand? How many on my W \^
left hand? How many on both hands?
Hold up six fingers. Hold up seven fingers.
Here is a bird^s nest. How
many eggs are in it? If the
bird should lay one egg more,
how many eggs would there
then be in the nest?
Place six blocks on the table. Add one block
more. Six blocks and one block are how many
blocks ? Take away two blocks. How many blocks
are left on the table?
Here are two groups of beautiful acorns. How
many acorns in the first grou]) ? How many in the
PRIMARY ARITHMETIC.
11
second group? How many more in the second group
than in the first?
How many pears in each of these groups ? How
many more in the first than in the second ? If two
pears should be taken from the first group, how many
would be left?
How many blocks are iSlilifl and ilifl|pi ?
iiiPSlPijp and IfPiilr ^^^ how many blocks?
Make the figure seven, thus : /. Make the figure
7 seven times. Make 1, 2, 3, 4, 5, 6, 7.
How many fingers do I hold up on
my right hand? How many on my K\r
left hand? How many on both hands?
Hold up eight fingers. Put down two fingers. How
many fingers are now up?
Here are two fine rab-
bits. How many ears
have both of them?
How many legs has each
rabbit? How many legs
have they both?
Place four blocks on the table. Add four blocks
more. How many blocks are now on the table?
12 PRIMARY ARITHMETIC.
Place eight blocks on the table. Take away one
block. How many blocks are left? Take away two
blocks more. How many blocks are now left?
How many boys are in the first group? How
many in the second? How many in the third?
How many boys in the third group more than in
the first ?
How many tops are spinning in the first group?
How many in the second? How many in the first
more than in the second ? If two tops were taken
from the first group, how many would be left?
How many balls are #^#9 and ^9?
^^^^ and ^^^^ are how many balls?
Make the figure eight, thus: ^ Make 1, 2, 3/4,
5, 6, 7, 8. How many figures have you made?
How many fingers do I hold up on
my right hand? How many on my
left hand? How many thumbs do I
hold up? How many fingers and thumbs do I hold
up on both hands?
PRIMARY ARITHMETIC.
13
How many joints in each of your fingers? {Three
Joints.) How many joints in two fingers? How
many joints in three fingers ?
Here is a nice peach.
How many leaves are on the
limb? If there were two
leaves more, how" many would
there then be? If you should
pick two leaves, how many
Avould be left on the limb?
Place seven blocks on the table. Add tAVO blocks
more. Seven blocks and two blocks are how many
blocks? Take three blocks. How many blocks are
left?
How many quails in each group? How many in
the second group more than in the first?
Here are two rows of books. How many books
in the first row? How many in the second? How
many more books in the second row than in the
first?
How many stars are -)(- -/- -/- -/- -)(- -)'- and -)'- -)(- ?
-/c ')[- -.[- ai^d ■>[' •>/- -,[-', c -/c -/c ^re how many stars?
How many stars are -)'- -/- -/- -/- and -/- ->/- -/- -/- -/- ?
Make the figure nine, thus : J/^. Make the figure
9 nine times. Make 1, 2, 3, 4, 5, 6, 7, 8, 9.
14
PRIMARY ARITHMETIC.
1
How many fingers do I hold up?
How many thumbs? How many fin-
gers and thumbs counted together?
Here is a nice fan, and a pair
Wwf ^ X ^ of gloves. How many fingers has
each glove? How many fingers
have both gloves? How many
folds has the fan? Count them.
How many nails are on your right hand? How
many nails on your left hand? How many on both
hands?
How many keys in the first group? How many
in the second? How many in the third? How
many more keys in the third group than in the first ?
How many poplar trees in the first row? How
many in the second row? How many more trees in
the first row than in the second?
If ifijg
Place ten blocks in a row. Take away five blocks.
How many blocks are left? Take away five more.
How many blocks are now left?
^lake the character naught, thus : ^. This stands
for not any or nothing. Make ten, thus : /^. Make
0, 1, 2, 3, 4, 5, G, 7, 8, 9, 10.
PRIMARY ARITHMETIC.
15
Count the balls in each row from left to rio:ht and
from right to left. Count also the rows up and
down.
Naught,
i<Th
9®#®©g
One.
Two.
Three.
Four.
^ Five.
Six.
Seven.
Fight.
Nine.
Ten.
0 1
3 4 5 6 7
9 10
How many balls are in the lowest row? How
many in the third row from the top? How many
in the fifth row ? How many in the seventh ? Hoav
many horizontal rows are there? How many verti-
cal rows?
To Teachers. — Make this table on the Hackboard, using
circles, squares, triangles or other simple figures, and drill tlie
pu{)ils in rapid counting, thus (pointing to the figures): One;
one, two ; two, one ; one, two, three ; three, tAvo, one, etc. — each
row being counted in two directions. Count first the horizontal
rows and then the vertical. The drill should be continued until
great rapidity and accuracy are secured.
16
PRIMARY ARITHMETIC.
ORAL EXERCISES.
To Teachers. — The object of this and the next eight lessons
is to teach the addition and subtraction of numbers not exceed-
ing ten. The first step is to add and subtract groups of visible
objects, or objects represented by pictures ; the second, to add and
.subtract groups of objects not in sight (concrete numbers); and
the third, to add and subtract the corresponding abstract numbers.
The exercises in each step should be multiplied until the results
are given by the pupils instantly, without counting. The tables
may be recited thus : 0 and 1 are 1 ; 1 and 1 are 2; 2 and 1 are 3,
etc.: and 1 from 1 leaves 0; 1 from 2 leaves 1, etc.
1. Here is a bird's nest and here is one. One
nest and one nest are liow many nests? Two nests
and one nest are how many nests?
2. One bird and one bird are how many birds?
Two birds and one bird are how many birds?
How many are 1 and 1 ? 2 and 1 ?
3. John caught three fishes, and then he caught
one more. How many did he catch in all? Four
fishes and one fish are how many fishes?
How many are 3 and 1? 4 and 1?
4. Charles has picked five fine clusters of cherries
and John one. Five clusters and one cluster are
PRIMARY ARITHMETIC.
17
how many clusters? Six clusters and one cluster?
How many are 5 and 1? 6 and 1?
5. If Charles should give one of his clusters to
Jane, how many would he have left? One cluster
from five clusters leaves how many clusters?
One from 5 leaves how many? 1 from 6?
6. Seven acorns and one acorn are how many
acorns ? Eight acorns and one acorn ?
How many are 7 and 1? 8 and 1?
7. Eight boys and one boy are how many boys?
Nine boys and one boy are how many boys? One
boy from nine boys leaves how many?
.&&
t
8. How many tops are 5 tops and 1 top? 6 tops
and 1 top? 3 tops and 1 top? 8 tops and 1 top?
7 tops and 1 top? 9 tops and 1 top?
9. One top from 3 tops leaves how many tops?
1 top from 5 tops ? 1 top from 7 to]is ? 1 top from
8 tops? 1 top from 6 tops? 1 top from 10 tops?
3^*:c
rojr
tunntf are
0
and
1?
1
and
1?
2
and
1?
3 and
1?
4
and
1?
5
and
1?
6
and
1?
7
and
1?
8
and
1?
9 and
1?
Tahe
from
from
from
from
from
from
from
from
from
from 10.
r. A.
1
T.IMARY ARITHMETIC.
10. How many are 2 and 1? 4 and 1? 6 and 1?
8 and 1 ? 9 and 1 ? 3 and 1 ? 5 and 1 ? 7 and 1 ?
11. One from 3 leaves how many? 1 from 5?
1 from G? 1 from 7? 1 from 9? 1 from 10?
1 from 8? 1 from 4?
ORAL EXI'RCISES.
1. How many fingers are one finger and one fin-
ger? One finger and two fingers?
2. How many clusk^rs of grapes are one claster
and two clusters ? Two clusters and two clusters ?
How many are 1 and 2? 2 and 2?
3. Jane has picked three violets and Kate two :
how . many violets have both picked ? Four violets
and two violets are how many violets?
How many are 3 and 2? 4 and 2?
4. Two violets from five violets leave how many
violets? Two violets from six violets?
Two from 5 leaves how many? 2 from G?
5. Here are five lambs, and here are two more.
How many lambs do you see?
PRIMARY ARITHMETIC.
19
6. Two lambs from six lambs leave how many
lambs? Two lambs from seven lambs?
Two from 6 leaves how many? 2 from 7?
7. How many robins do you see? Six robins and
two robins are how many robins? Seven robins
and two robins?
How many are 6 and 2 ? 7 and 2 ?
8. How many do two birds from eight birds leave?
Two birds from nine birds?
Two from 9 leaves how many? 2 from 8?
9. Here are eight shells in one group and two
shells in another. How many are eight shells and
two shells?
How many are 8 and 2? 7 and 2?
10. Jane found ten shells and gave two of them to
Willie: how many had she left?
Two from 10 leaves how many? 2 from 9?
D>»<C
Mow mm
?/ are
0 and
2?
1 and
2?
2 and
2?
3 and
2?
4 and
9?
5 and
2?
6 and 2?
7 and
2*?
8 and
2?
Take
from
from
from
from
from
from
from
from
from
20 PRIMARY ARITHMETIC.
11. How many are 2 and 2? 4 and 2? 3 and 2?
5 and 2? 6 and 2? 8 and 2? 7 and 2?
12. Two from 4 leaves how many? 2 from 3?
2 from 5? 2 from 7? 2 from 6? 2 from 8?
2 from 10? 2 from 9?
2
Add 2
2
4
2
_6
2
_8
2
7
2
5
(1)
From 4
Take 2
(2)
6
2
(3)
8
2
(4)
10
2
(5)
9
(6)
7
2
WRITTEX EXERCISES.
(1) (2) (3) (4) (5) (G) (1) (2) (3) (4) (5) (6)
12 2 112
12 2 2 2 2
12 2 12 1
12 2 2 12
Add 1. 2 1 4 3 2
To Teachers. — These exercises should be copied by the
pupils on their slates, added, and the results properly written
below. They, or similar exercises, should also be written on the
blackboard, and the class drilled on them until the results are
given instanthj. In adding the columns at the right, the results
only should be named; as, (Ex. 3) 1, 3, 5, 7, 9.
ORAL EXERCISES.
1. How many blocks are one block and two
blocks? One block and three blocks?
""^MM
2. How many horses do you sec? Two horses
and three horses are \\o\f many horses? Three
horses and thrcc horses?
PRIMARY ARITHMETIC.
21
3. Two marbles and three marbles are how many
marbles? Three marbles and three marbles?
How many are 2 and 3? 3 and 3?
4. A man has five horses : if he sell three of them,
how many will he have left?
Three from 5 leaves how many? 3 from 6?
5. How maiiy fawas are in these two gronps?
Five fawns and three fawns are how many fawns?
6. Four squirrels are running on a fence and three
are on a tree. How many are four squirreLs and
three squirrels ? Five squirrels and three squirrels ?
How many are 4 and 3? 5 and 3?
7. Six kittens and three kittens are how many kit-
tens? 7 kittens and 3 kittens?
8. How many boys are six boys and three boys?
Seven boys and three boys?
How many are 6 and 3? 7 and 3?
9. Tliree kittens from nine kittens leave how
many ? Three kittens from ten kittens ?
Three from 9 leaves how manv? 3 from 10?
^000(130
10. How many pears are 7 pears and 3 pears?
6 pears and 3 pears ? 5 pears and 3 pears ? 4 pears
and 3 pears? 3 pears and 3 pears?
22
PRIMARY ARITHMETIC.
11. How many caps are 1 cap and 3 caps? 3 caps
and 3 caps? 5 caps and 3 caps? 4 caps and 3 caps?
6 caps and 3 caps? 7 caps and 3 caps?
12. Three pears from 4 pears leave how many
pears? 3 pears from 6 pears? 3 pears from 8 pears?
3 pears from 10 pears? 3 pears from 7 pears?
Jlorv innny are
0 and 3?
1 and 3?
2 and 3?
3 and 3?
4 and 3?
5 and 3?
6 and 3?
7 and 3?
Take
3 from
3 from
3 from
3 from
3 from
3 from
3 from
3 from ]0.
13. How many are 1 and 3? 3 and 3? 2 and 3?
5 and 3? 4 and 3? 7 and 3? 6 and 3?
14. How many are 3 and 2? 3 and 1 ? 3 and 4?
3 and 5? 3 and 6? 3 and 3? 3 and 7?
15. Three from 4 leaves how many? 3 from 6?
3 from 5? 3 from 8? 3 from 7? 3 from 10? 3
from 9?
16. Three from 5 leaves how many? 2 from 5?
3 from 9? 2 from 9? 3 from 8? 2 from 8? 3
from 10?
(1) (2)
3 3
WRITTEN EXERCISES.
(4) (5) (fi)
3 3 3
A.dd 2
4
5
7
_6
3
(1)
(2)
(;>)
(i)
(5)
(0)
From 5
7
8
10
0
6
Take 3
3
3
3
3
3
ma
(2) (8) (4) (5) (6)
PRIMARY ARITHMETIC.
23
ORAL EXERCISES.
1, How many fingers are one finger and three fin-
gers? One finger and four fingers?
2. Here are two rabbits, and here are four more.
How many are two rabbits and four rabbits?
One and 4 are how many? 2 and 4?
8. If four of these six rabbits should run away,
how many would be left? Four rabbits from six
rabbits leave how many rabbits?
Four from 5 leaves how many? 4 from 6?
Hr<^ /^C /^^ ^W^ ^^
4. Heniy has bought three pine-apples, and Jane
four : how many pine-apples have they both ?
5. How many oranges are three oranges and four
oranges? Four oranges and four oranges?
Three and 4 are how many? 4 and 4?
G. How many acorns are five acorns and four
acorns? Six acorns and four acorns?
7. How many are five marbles and four marbles?
Six marbles and four mftrbles?
Five and 4 are how many? 6 and 4?
24
PRIMARY ARITHMETIC.
8. Nine robins are standing; on a limb : if four
should fly away, how many would be left?
9. Four robins from ten robins leave how many
robins? Four robins from nine robins?
Four from 9 leaves how many? 4 from 10?
10. Here are two rows of trees. How many trees
in both rows? How many are 3 trees and 4 trees?
5 trees and 4 trees? 6 trees and 4 trees?
11. How many are 2 doves and 4 doves? 4 doves
and 4 doves? 6 doves and 4 doves? 5 doves and
4 doves? 3 doves and 4 doves?
12. Four trees from 6 trees leave hoAV many trees?
4 trees from 8 trees? 4 trees from 10 trees? 4 trees
from 7 trees? 4 trees from 9 trees?
w
iiirrnj/ are
0
and
4?
1
and
4?
2
and
4?
3 and
4?
4
and
4?
5
and
4?
6 and
4?
Tnlte
4 from 4.
4 from 5.
4 from 6.
4 from 7.
4 from 8.
4 from 9.
4 from 10.
13. How many are 2 and 4? 4 and 4? 3 and 4?
5 and 4? 6 and 4?
14. How many are 4 and 1 ? 4 and 3? 4 and 5?
4 and 4? 4 and 2? 4 and G?
15. Four from five leaves how many? 4 from 4?
4 from 6? 4 from 7? 4 from 9?
PRIl^ARY ARITHMETIC.
25
16. Four from 6 leaves how many? 4 from 8?
3 from 8? 4 from 10? 3 from 10?
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (6) (1) (2) (8) (4) (5) (6)
444444 422122
Add 243561 214412
— — — — — — 212110
(1) (2) (3) (4) (5) (6) 14 0 2 2 3
From 6 8 7 9 10 5 ^^^ }_ _^ ^ ± ± ±
Take 4 4 4 4 4 4
ORAL EXERCISES.
1. HoAV many girls are one girl and five girls?
Two girls and five girls?
-i ^k -^ -^^ ^^ -«^ -s^
2. How many are two palm trees and five palm
trees? One palm tree and five palm trees?
How many are 1 and 5? 2 and 5?
3. A hunter saw six deer, and five of them ran
away: how many deer Avere left?
4. Five deer from six deer leave how many deer?
Five deer from seven deer?
Five from 6 leaves how many ? 5 from 7 ?
5. Here are two groups of flies. How many flies
are three flies and five flies ? Four flies and five flies?
26
PRIMARY ARITHM:ETIG.
6. How many rabbits are three rabbits and five
rabbits? Four rabbits and five rabbits?
How many are 3 and 5? 4 and 5?
7. Mr. Smith owns eight sheep : if he sell five of
them, how many sheep will he have left?
Five from 8 leaves how many? 5 from 7?
8. Kate has five pears in one basket, and five in
another : how many pears has she in both ?
9. How many are four stars and five stars? Five
stars and five stars?
10. Five pears from nine pears leave how many
pears? Five pears from ten pears?
Five from 9 leaves how many? 5 from 10?
11. How many quails are 2 quails and 5 quails?
1 quail and 5 quails? 3 quails and 5 quails? 5
quails and 5 quails? 4 quails and 5 quails?
12. Five l)irds from 6 birds leave how many
birds? 5 birds from 8 birds? 5 birds from 7 birds?
0 birds from 10 birds? 5 birds from 9 birds?
JTotv main/ are
0 and 5?
1 cand 5?
2 and 5?
3 and 5?
4 and 5?
5 .and 5?
Tahe.
from 5.
from 6.
from 7.
from 8.
from 9.
from 10.
PRIMARY ARITHMETIC.
27
13. How many are 1 and 5? 3 and 5? 2 and 5?
4 and 5? 5 and 5?
14. How many are 5 and 2? 5 and 1? 5 and 3?
5 and 5? 5 and 4?
15. Five from 5 leaves how many? 5 from 7?
5 from 6? 5 from 8? 5 from 9? 5 from 10?
16. How many are 3 and 3? 4 and 4? 5 and 5?
2 and 2? 4 and 3? 5 and 3? 7 and 3?
17. Two from 8 leaves how many? 4 from 8?
5 from 8? 3 from 8? 3 from 9? 4 from 9?
5 from 9? 2 from 9?
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (6)
(1) (2) (3) (4) (5) (6)
5
Add 2
5
5
5
_4
5
1
5
3
5
_0
(1)
From 7
Take _5
(2)
10
5
(3)
9
5
(J)
6
5
(5)
8
5
(6)
5
5
Add
5
2
2
1
8
1
1
1
1
5
1
3
1
1
1
1
2
1
2
1
3
1
1
2
1
5
2
1
2
2
—-.->»..- >^-*i^'^-
ORAL EXERCISES.
1. Jane picked one nice cluster of cherries^ and
Harry picked six clusters: how many clusters did
tliey both pick?
2. How many clusters" are one cluster and six clus-
ters? Two clusters and
SIX
clusters ?
How many are 1 and 6? 2 and 6?
28
PRIMARY ARITHMETIC.
3. IIow many clusters of cherries Avill remain if
you take six clusters from seven clusters? Six clus-
ters from eight clusters?
Six from 7 leaves how many? 6 from 8?
4. Charles found three shells on the sea-shore, and
John six: how many shells did both find?
5. How many pebbles are two pebbles and six
pebbles? Three pebbles and six pebbles?
How many are 2 and 6? 3 and 6?
G. How many shells w^ill remain if you take six
shells from nine shells? Six shells from eight shells?
Six from 9 leaves how many ? 6 from 8 ?
7. How many rabbits in each of these groups?
How many are four rabbits and six rabbits? Three
rabbits and six rabbits?
How many are 4 and 6 ? 3 and 6 ?
8. A hunter saw^ ten rabbits, and caught six of
them : how many rabbits got away ?
9. How many will remain if you take six marbles
from ten marbles? Six marbles from nine marbles?
Six from 10 leaves how many? 6 from 9?
10. How many blocks are 2 blocks and 6 blocks?
1 block and 6 blocks? 3 blocks and G blocks?
4 blocks and G blocks?
PRIMARY ARITHMETIC.
29
11. How many pears are 1 pear and 6 pears?
3 pears and 6 pears? 2 pears and 6 pears? 4 j)ears
and 6 pears?
12. Six blocks from 7 blocks leave how many
blocks? 6 blocks from 6 blocks? 6 blocks from
8 blocks? 6 blocks from 10 blocks? 6 blocks from
9 blocks?
:>^^c
Botv many are ]
0 and
6?
1 and
6?
2 and
6?
3 and
6?
4 and
6?
Take
6 from
6 from
6 from
6 from
6 from
13. How many are 1 and 6? 3 and 6? 4 and 6?
2 and 6 ? 6 and 1 ? 6 and 2? 6 and 4?
14. Six from 7 leaves Iioav many?
6 from 10? 6 from 9? 6 from 6?
15. How many are 4 and 3? 5 and 4?
G and 2? 4 and 5? 6 and 3? 5 and 3?
16. How many are 2 and 4? 3 and 6?
4 and 4? 6 and 4? 3 and 4? 4 and 5?
17. Two from 6 leaves how many? 3
5 from 10? 4 from 7? 4 from 9? 2
3 from 10?
6 from 8?
3 and 6?
5 and 3?
from 9?
from 8?
WRITTEN EXERCISES.
(1)
(2)
(3)
(-1)
(5)-
(1)
(2)
(3)
(4)
(5)
6
0
6
6
6
G
1
1
1
2
Add 3
2
4
1
0
1
1
0
3
3
—
—^
—
—
—
0
6
4
3
2
(1)
(2)
(3)
(^)
(5)
2
1
3
2
1
From 9
8
10
7
6
Add 1
1
2
1
1
Take 6
6
6
6
6
30
PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. How many pine-apples are one pine-apple and
seven pine-apples ? Two pine-apples and seven pine-
apples ?
2. A fruit dealer bought eight pine-apples, and
sold seven of them : how many had he left ?
3. Seven pine-apples from eight pine-apples lea\e
how many pine-apples?
4. How many are two apples and seven apples?
Two peaches and seven peaches? Two pears and
seven pears? Two plums and seven plums?
How many are 1 and 7? 2 and 7?
5. Seven apples from eight apples leave how man/
apples? Seven apples from nine apples?
Seven from 8 leaves how many ? 7 from 9 ?
6. Here are two rows of tops, and all are spinning..
How many tops are three tops and seven tops ? Tw >
tops and seven tops?
7. If seven of these tops should stop spinning, how
many would then be spinning? Seven tops from
ten tops leave how many tops? Seven tops from
nine tops?
Seven from 10 leaves how many? 7 from 9?
PRIMARY ARITHMETIC.
31
8. How many nuts are two nuts and seven nuts?
Three nuts and seven nuts? Three cakes and seven
cakes ?
How many are 1 and 7? 2 and 7? 3 and 7?
9. How many crowns are 1 crown and 8 crowns?
2 crowns and 8 crowns?
10. How many girls are one girl and eight girls?
Two girls and eight girls?
How many are 1 and 8? 2 and 8?
11. There are ten boys playing together : i^eight
of them go home, how many boys will be left?
Eight boys from ten boys leave how many boys?
Eight from 10 leaves how many ? 8 from 9 ?
12. How many chairs are 1 chair and 7 chairs?
1 chair and 8 chairs ? 2 chairs and 7 chairs ? 2 chairs
and 8 chairs?
13. How many crowns will remain if you take
7 crowns from 10 crowns? 8 crowns from 10 crowns?
7 crowns from 9 crowns? 8 crowns from 9 crowns?
8 crowns from 8 crowns?
— o<,^«^oo
Hoiv mnmf are
0 and 7?
1 and 7?
2 and 7?
, 3 and 7 ?
0 and 8?
1 and 8?
2 and 8?
14. How many are 2 and 7?
land 8? 1 and 7? 8 and 2?
Talze
7 from
7 from
7 from
7 from
7.
8.
9.
10.
8 from
8 from
8 from
8.
9.
10.
2 and 8?
3 and 7?
7 and 3?
32 PRIMARY ARITHMETIC.
15. Seven from 10 leaves how many? 7 from 8?
7 from 9? 8 from 10? 8 from 8? 8 from 9?
16. How many are 4 and 5? 4 and 6? 5 and 4?
6 and 4? 3 and 6? 3 and 5? 6 and 3? 5 and 3?
2 and 6? 4 and 3? 4 and 6? 2 and 5?
17. How many remain when yon take 3 from 7?
3 from 9? 4 from 10? 5 from 10? 6 from 10?
3 from 8? 5 from 8? 6 from 8? 4 from 8?
8 from 8? 7 from 9?
Add _2
3
1
1
^
_0
(1)
(2)
(3)
(4)
(5)
(6)
From 9
10
8
9
10
8
Take_7
7
7
8
8
8
WRITTEN EXERCISES.
(i) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (0)
777 888 771801
10 10 14
0 17 10 3
10 0 0 8 1
Add 1 2 1 1 1 1
EEVIEW.
1. John has 4 marbles in one hand, and" three mar-
bles in the other: how many marbles has he in both
hands ?
2. Jane has found a nest w^ith 7 eggs in it : if she
take 4 esfi^s from the nest, how many will remain?
3. Frank .had 5 cherries, and his mother gave
him 4 : how many cherries had he then ?
4. Willie has 3 apples in his hand, and 6 in his
basket: how many apples has he?
PRIMARY ARITHMETIC.
33
5. There are 8 pigeons sitting on a limb : if 5 fly
away, how many pigeons will be left ?
6. There are 9 men in a stage coach : if 4 get out
of the coach, how many men will be left ?
7. How many are 2 and 2? 2 and 2 and 2?
2 and 2 and 2 and 2? 2 and 2 and 2 and 2 and 2?
2 and 1? 2 and 3 and 5?
S. How many are 3 and 3 and 3? 3 and 1 and 3?
3 and 4? 3 and 4 and 2? 4 and 2? 4 and 2 and 3?
4 and 4 and 2?
9. How many will remain if you take 5 from 7?
5 from 9? 5 from 8? 6 from 8? 6 from 10? 6
from 9? 4 from 7? 4 from 9?
WRITTEN EXERCISES.
Add
(1) (2) (3) (4) (5) (6)
6 5 4 3 12
3 4 5 6 7 8
(1) (2) (3) (4) (5) (6)
From 9 8 7 10 6 5
Take 6 5 4 6 3 5
Add
(1)
(2)
(3)
(4)
(5)
(6)
2
2
1
1
2
0
2
0
1
0
4
1
2
2
0
3
1
1
4
2
2
2
1
1
3
1
2
3
1
^
0
REVIEW.
1. John holds up 5 fingers, and Henry 3: how
many fingers do both hold up?
2. Charles has placed 9 blocks on the table: if
Mary take away seven of them, how many blocks
will be left on the table?
P. A. 3.
84 PRIMARY ARITHMETIC.
3. Susan has made 8 figures on her slate: if she
should rub out 5 of them, how many figures would
be left?
4. There are 3 bottles in one row, and 5 bottles in
another : how many bottles in both rows ?
5. A farmer has 5 cows in one lot, and 4 cows in
another lot: how many cows has he in both lots?
6. Charles had 10 cents, and spent 7 cents for an
orange : how many cents had he left ?
7. Jane picked 9 peaches, and gave 6 of them to
her little brothers: how many peaches had she left?
8. How many are 4 and 4? 4 and 4 and 2?
4 and 3? 4 and 3 and 3? 5 and 3? 5 and 3
and 2? 2 and 3? 2 and 3 and 4?
9. How many will remain if you take 5 from 8?
5 from 9? 6 from 10? 6 from 8? 4 from 7?
4 from 9? 4 from 8? 3 from 10? 3 from 8?
10. Take 3 from 6. 3 from 9. 3 from 7. 4
from 8. 4 from 10. 4 from 7. 7 from 9. 7 from
10. 8 from 10. 6 from 10.
WRITTEN
EXERCISES.
(1)
(2)
(3)
(•1)
(5) (H)
(1)
(2)
(3)
H)
(5)
(8)
o
4
3
5
6 5
1
1
1
0
1
6
Add 7
5
6
4
3 2
1
3
0
1
1
1
— —
3
2
3
4
9
0
(1)
(2)
(")
(-1)
{■->) (G)
2
2-
1
1
2
1
From 6
Take 3
7
4
8
5
9
6
7 10
4 7
Add
1
2
1
1
_1^
2
1
1
PRIMARY ARITHMETIC.
35
ORAL EXERCISES.
To Teachers. — The object of this and the next lesson is to
develop the idea of each number from eleven to twenty inclusive,
to teach its name, and the mode of representing it by figures.
Make ten marks on the blackboard, and make beneath these,
successively, one mark, two marks, three marks, etc. Add the
lower group to the upper, and give the appropriate name to the
result, as to four and ten, fourteen. Blocks, beans, etc., may also
be used in a similar manner.
Before answering the three questions below the illustrations,
the pupil should, in each case, add and subtract the groups of
objects represented; thus: "Ten trees and one tree are eleven
trees; one tree from eleven trees leaves ten trees."
^J^ -^^ -^^ ^^^ -^^ -^^ -^^ ^^^
1. How many boys are 10 boys and 1 boy?
How many are 10 and 1? Write eleven, thus
One from 11 leaves how many?
//
i
2. How many stars are 10 stars and 2 stars?
How many are 10 and 2? Write twelve, thus :
Two from 12 leaves how many?
/J'.
3. How many balls are 10 balls and 3 balls?
How many are 10 and 3 ? Write thirteen, thus : /J.
Three from 13 leaves how many?
4. How many are 10 birds and 4 birds? 10 boys
and 4 boys?
36
PRIMARY ARITHMETIC.
How many are 10 and 4? Write fourteen, thus : /A.
Four from fourteen leaves how many?
A A -/^
5. How many pens are 10 pens and 5 pens?
How many are 10 and 5? AYrite fifteen, thus: /^.
Five from 15 leaves how many?
Write and read 10, 11, 12, 13, 14, 15.
6. How many stars are 10 stars and 6 stars?
How many are 10 and 6? Write sixteen, thus: /^.
Six from 16 leaves how many?
\
7. How many arrows are 10 arroAvs and 7 arrows?
How many are 10 and 7 ? Write seventeen, thus : //.
Seven from 17 leaves how many ?
8. How many soldiers are 10 soldiers and 8 sol-
diers?
How many are 10 and 8 ? Write eighteen, thus : /d^.
Eight from 18 leaves how many?
9. Ten knives and 9 knives are how many knives ?
PRIMARY ARITHMETIC, 37
How many are 10 and 9 ? AYrite nineteen, thus : /^.
JS^ine from 19 leaves how many ?
10. Ten pens and 10 pens are how many pens?
How many*are 10 and 10 ? Write twenty, thus: J'^.
Ten from 20 leaves how many?
Copy and read 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20.
Count from 10 to 20 forward and backward.
ORAL EXERCISES.
1. How many are 10 and 1? 10 and 2? 10 and
3? 10 and 4? 10 and 5? 10 and 6 ? 10 and 7?
10 and 8? 10 and 9? 10 and 10?
2. How many are 10 and 2? 10 and 5? 10 and
6? 10 and 4? 10 and 1? 10 and 7? 10 and 8?
10 and 10?
3. Ten from 12 leaves how many? 10 from 13?
10 from 14? 10 from 16? 10 from 15? 10 from
17? 10 from 18? 10 from 19?
4. How many will be left if you take 10 from 14?
10 from 16? 10 from 18? 10 from 20?
5. How many are 10 and 2? 10 and 5? 10 and
6? 10 and 7? 10 and 10?
6. How many are 10 and 3? 10 and 5? 10 and
7? 10 and 9? 10 and 8? 10 and 6?
38
PRIMARY ARITHMKTIG.
In the following table the first twenty numbers
are expressed by words, figures, and letters.
By 1
Words.
By Figures.
By Zettcrs.
ROMAN.
SCRIPT.
ROMAN
SCRIPT.
ROMAN.
ITALIC.
One.
^...
1
/
I
I
Two.
tyii^o.
2
J
II
II
Three.
'£/U.
3
J
III
III
Four.
W'^^i.
4
J
IV
IV
Five.
S5...
5
s
. Y
V
Six.
J4.
6
^
VI
VI
Seven.
Cfeve^n.
7
/
VII
VII
Eight.
^V''-
8
J>
VIII
VIII
Kine.
9
/
IX
IX
Ten.
^T^n.
10
/^
X
X
Eleven.
6p/ei'en.
11
//
XI
XI
Twelve.
tJ/we/i^€.
12
/J
XII
XII
Thirteen.
Z//u)Y€eii,
13
/J
XIII
XIII
Fourteen.
^'cal/een .
14
/J
XIV
XIV
Fifteen.
^W^^^H.
15
/s
XV
XV
Sixteen.
<y(lr/eej/.
16
//
XVI
XVI
Seventeen
.tJei'en/ccn.
17
//
XVII
XVII
Eighteen.
L^/a/i/een.
18
/<?
XVIII XVIII
Nineteen.
Sl^/ne/<;en .
19
/f
XIX
XIX
Twenty.
Kyicen^// .
20
^^
XX
XX
PRIMARY ARITHMETIC.
39
i^BssoH xxn,
ORAL EXERCISES.
1. Here is a fine farm, with a stream of water flowing
through it. How many cows are grazing in the pasture?
2. How many cows are 5 cows and 2 cows? 7 cows
and 2 cows? 9 cows and 2 coavs?
3. How many ducks are in the water? How many
are on the ground?
4. How many ducks are 7 ducks and 3 ducks? 8
ducks and 3 ducks? 9 ducks and 3 ducks?
5. How many sheep are lying down ? How many are
standing near the water?
40
PRIMARY ARITHMETIC.
6. How many are 6 sheep and 4 sheep? 8 sheep
and 4 sheep? 10 sheep and 4 sheep?
7. How many are 5 cows and 5 cows ? 6 cows and
5 cows? 7 cows and 5 cows?
How many are 5 and 5 ? 6 and 5 ? 7 and 5 ?
8. How many are 10 cows less 5 cows? 11 cows
less 5 cows? 12 cows less 5 cows?
9. How many are 8 ducks and 5 ducks? 9 ducks
and 5 ducks? 10 ducks and 5 ducks?
Eight and 5 are how many ? 9 and 5 ? 10 and 5 ?
10. How many are 13 ducks less 5 ducks? 14 ducks
less 5 ducks? 15 ducks less 5 ducks?
11. Ten less 5 is how many? 12 less 5? 14 less 5?
12. There are 13 sheep in a flock : if 5 of them should
be sold, how many would be left?
y>»iOc
to man
y are
0 and
5?
1 and
5?
2 and
5?
3 and
5?
4 and 5 ?
5 and
5?
6 and
5?
7 and
5?
8 and
5?
9 and
5?
10 and
5?
Take
13. How many are 5 and 5?
8 and 5? 10 and 5? 4 and 5?
14. How many are 5 and 6?
5 and 9? 5 and 7? 5 and 10?
15. Five from 10 leaves how
5 from 11? 5 from 13? 5 from 15?'
O lIUIll
5 from
6.
5 from
7,
5 from
8.
5 from
9.
5 from
10.
5 from
11.
5 from
12.
6 from
13.
5 from
14.
5 from 15.
7 and 5?
9 and 5?
6 and 5
?
5 and 4?
5 and 8?
many ?
5 from 12?
5
Add _5
5 5 5 5
6 8 _7 _9
5
4
(1)
From 10
Take j5
(2) (3) (4)
11 13 12
5 5 5
(5)
14
5
2
1
3
3
2
2
2
5
2
2
1
2
2
2
5
5
5
5
2
5
2
1
2
2
2
2
5
5
3
5
2
1
2
3
5
4
PRIMARY ARITHMETIC. 41
WRITTEN EXERCISES.
Copy and read 11, 13, 15, 17, 19, 18, 16, 14, and 12.
(1) (2) (3) (4) (5) (G) (1) (2) (3) (4) (5) (6)
Add
To Teachers.— The object of this and the next six lessons
is to teach the addition and subtraction of numbers not exceed-
ing twenty. The use of objects should be continued.
ORAL EXERCISES.
1. Here are two rows of trees. How many trees
are 4 trees and 6 trees? 5 trees and 6 trees?
2. How many houses are 4 houses and 6 houses?
5 houses and 6 houses?
Four and 6 are how many ? 5 and 6 ?
3. There are ten trees in a row: if 6 of thern
should be cut down, how many trees would remain
standing ?
4. How many clusters of oak leaves in each of
these two groups? How many leaves in both groups?
6 leaves and 6 leaves are how many leaves?
42
PRIMARY ARITHMETIC.
5. How many are 6 flags and 6 flags ? 7 flags and
G flags? 5 flags and 6 flags?
Six and 6 are how many? 7 and 6? 5 and 6?
Six from 12 leaves how many? 6 from 13?
6. How many tops are in these two rows? If 8
tops be taken away, how many Avill be left ?
7. Six tops from 14 tops leave how many tops?
6 tops from 15 tops?
8. How many balls are 8 balls and 6 balls? 9
balls and 6 balls? 10 balls and 6 balls?
Nine and 6 are how many? 10 and 6?
9. John found 15 peaches on one limb, and picked
6 of them : how many peaches were left on the limb ?
Six from 15 leaves how many? 6 from 16?
10. How many are 6 boys and 6 boys? 7 boys
and 6 boys? 8 boys and 6 boys? 9 boys and 6
boys? 10 boys and 6 boys?
11. How many are 4 trees and 6 trees? 6 trees
and 6 trees? 8 trees and 6 trees? 5 trees and 6
trees? 7 trees and 6 trees? 9 trees and 6 trees?
10 trees and 6 trees?
12. Six quails from 10 quails leave how many
quails? 6 quails from 12 quails? 6 quails from
14 quails? 6 quails from 16 quails? 6 quails from
13 quails? 6 quails from 11 quails?
PRIMARY ARITHMETIC.
43
Uuv mauy fire
0 and 6?
1 and 6?
2 and 6?
3 and 6?
4 and 6?
5 and 6?
6 and 6?
7 and 6?
8 and 6?
9 and 6?
10 and 6?
Tahe
6 from
6.
6 from
7.
6 from
8.
6 from
9.
6 from
10.
6 from
11.
6 from
12.
6 from
13.
6 from
14.
6 from
15.
6 from
16..
4 and 6?
6 and 6?
9 and 6?
8 and 6?
6 and 2?
6 and 4?
6 and 9?
6 and 8?
13. How many are 2 and 6?
5 and 6? 3 and 6? 7 and 6?
10 and 6? land 6?
14. Six and 3 are how many?
6 and 6? 6 and 5 ? 6 and 7?
6 and 10? 1 and 10?
15. How many will remain if you take 6 from 7?
6 from 9? 6 from 10? 6 from 14? 6 from 13?
6 from 15? 6 from 16?
16. How many will remain if you take 5 from 13?
6 from 13? 5 from 9? 6 from 9? 5 from 11?
6 from 11? 5 from 14? 6 from 14? 5 from 10?
6 from 10? 5 from 12? 6 from 12?
WRITTEN EXERCISES.
Copy and read 20, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30.
(1) (2) (3) (4) (o) (6)
(1) (2) (3) (4) (5) (6)
6
Add jl
6 6 6 6
8 6 7 9
6
_5
(1)
From 10
Take 6
(2) (3) (4)
14 12 13
& Q Q
(5)
15
6
Add
44
PRIMARY ARITHMETIC.
■bBSSOH XXIV.
ORAL EXERCISES.
1. How many are 4 raisins and 7 raisins? 5 rai-
sins and 7 raisins ? 6 raisins and 7 raisins ?
Four and 7 are how many? 5 and 7? 6 and 7?
2. John picked 12 pears, and gave 7 of them to
his sister: how many pears had he left?
3. Seven pears from 12 pears leave how many
pears? 7 pears from 13 pears? 7 pears from 10
pears? 7 pears from 11 pears?
Seven from 12 leaves how many? 7 from 13?
4. How many clusters in each of these groups? 7
clusters and 7 clusters are how many clusters?
5. How many hens are 5 hens and 7 hens ? 6 hens
and 7 hens? 7 hens and 7 hens? 8 hens and 7 hens?
Seven and 7 are how many? 8 and 7?
6. A merchant sold 9 forks to one man, and 7 forks
to another : how many forks did he sell ?
7. How many are 9 spoons and 7 spoons?
spoons and 7 spoons? 5 spoons and 7 spoons?
Nine and 7 are how many? 10 and 7?
10
PRIMARY ARITHMETIC.
45
8. There are 16 silver forks in the basket : if Jane
put 7 of them on the table, how many forks will be
left in the basket?
Seven from 16 leaves how many? 7 from 17?
9. How many are 3 shells and 7 shells? 4 shells
and 7 shells? 6 shells and 7 shells? 5 shells and
7 shells? 7 shells and 7 shells?
10. How many are 7 nails and 5 nails? 7 nails
and 7 nails? 7 nails and 9 nails? 7 nails and 6
nails? 7 nails and 8 nails? 7 nails and 4 nails?
7 nails and 3 nails?
11. How many are left when you take 7 figs from
10 figs? 7 figs from 12 figs? 7 figs from 14 figs?
7 figs from 16 figs? 7 figs from 15 figs? 7 figs
7 figs from 11 figs?
from 13 figs?
7 fi^
Hoiv many are
0 and
7?
1 and
7?
2 and
7?
3 and
7?
4 and
7?
5 and
7?
6 and 7?
7 and
7?
8 and
7?
9 and
7?
10 and
Take
from 7.
from 8.
from 9.
from 10.
from 11.
from 12.
from 13.
from 14.
from 15.
from 16.
from 17.
12. How many are 3 and 7? 5 and 7? 7 and 7?
8 and 7? 6 and 7? 9 and 7? 4 and 7? 7 and 8?
7 and 9? 7 and 6? 7 and 5? 7 and 4?
13. Seven from 10 leaves how many? 7 from 12?
46 PRIMARY ARITHMETIC.
7 from 11? 7 from 14? 9 from 13? 7 from 15?
7 from 9? 7 from 16? 7 from 15?
WRITTEN EXERCISES.
Copy and read 20, 22, 25, 21, 23, 24, 26, 27, 29,
28, 30.
(1) (2) (3) (4) (5) (6) (I) (2) (3) (4) (5) (6)
Add
ORAL EXERCISES.
1. If all these balls were together, how many balls
would there be in the group?
7
7
7
7
7
7
Add 4
6
8
5
i
9
(1)
(2)
(3)
(^)
(5)
(6)
From 11
13
15
12
16
14
Take 7
7
7
7
7
7
1
7
2
3
2
6
1
4
5
5
4
2
7
1
3
6
6
7
3
7
4
3
7
4
7
2
3
4
4
5
7
6
2
7
3
3
2. How many balls are 6 balls and 8 balls? 5
balls and 8 balls? 4 balls and 8 balls?
Six and 8 are how many? 5 and 8? 4 and 8?
3. Mr. Jones had 14 quails, and sold 8 of them:
how many quails had he left?
4. Eight quails from 14 quails leave how many
quails? 8 quails from 13 quails?
Eight from 14 leaves how many? 8 from 13?
5. How many spoons are 8 spoons and 8 spoons?
7 spoons and 8 spoons? 6 spoons and 8 spoons?
PRIMARY ARITHMETIC. 47
6. Eight desks and 8 desks are how many desks?
7 desks and 8 desks? 6 desks and 8 desks?
How many are 8 and 8? 7 and 8? 6 and 8?
7. Maria has 16 pens for the writing class: if she
give 8 pens to the girls, hoAV many will be left for
the boys?
Eight from 16 leaves how many? 8 from 15?
^^ ^¥ ^'v ^V <^
8. How many keys are 9 keys and 8 keys? 10
keys and 8 keys?
9. How many crackers are 9 crackers and 8 crack-
ers? 10 crackers and 8 crackers?
Nine and 8 are how many? 10 and 8?
10. Eight keys from 17 keys leave how many keys?
8 keys from 18 keys?
Nine from 17 leaves how many? 9 from 18?
11. How many boys are 2 boys and 8 boys? 4
boys and 8 boys? 6 boys and 8 boys? 8 boys and
8 boys? 10 boys and 8 boys?
12. How many are 1 step and 8 steps? 3 steps
and 8 steps? 5 steps and 8 steps? 7 steps and 8
steps? 9 steps and 8 steps? 6 steps and 8 steps?
8 steps and 6 steps?
13. Eight boys from 10 boys leave how many ?
8 boys from 1 2 boys ? 8 boys from 1 1 boys ? 8 boys
from 13 boys? 8 boys from 15 boys? 8 boys from
14 boys? 8 bovs from 16 bovs?
48
PRIMARY ARITHMETIC.
Ilotv many are 1
0 and
8?
1 and 8? 1
2 and
8?
3 and
8?
4 and
8?
5 and
8?
6 and
8?
7 and
8?
8 and
8?
9 and
8?
10 and
8?
Take
8 from 8.
8 from 9.
8 from 10.
8 from 11.
8 from 12.
8 from 13.
8 from 14.
8 from 15.
8 from 16.
8 from 17.
8 from 18,
14. How many are 3 and 8 ? 5 and 8 ? 2 and 8 ?
4 and 8? 6 and 8? 8 and 8? 7 and 8? 9 and 8?
5 and 8? 9 and 8? 7 and 8?
15. Eight and 2 are how many? 8 and 4? 8 and
3? 8 and 5? 8 and 7? 8 and 6? 8 and 8? 8
and 9? 8 and 7? 7 and 8?
16. How many will be left if you take 8 from 10?
8 from 12? 8 from 14? 8 from 16? 8 from 13?
8 from 15? 8 from 11? 8 from 10?
17. Six from 12 leaves how many? 7 from 12?
8 from 12? 6 from 14? 7 from 14? 8 from 14?
6 from 16? 7 from 16? 8 from 16?
WRITTEN EXERCISES.
Copy and read 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40.
a)
(2)
(3)
W
(•5)
(6)
(1)
(2)
(3)
W
(5)
(6)
8
8
8
8
8
8
1
2
2
1
7
6
Add 5
7
_6
_8
_9^
4
1
8
6
7
3
5
4
1
2
6
5
2
(1)
(2)
(3)
W
('i)
(6)
4
8
6
8
2
6
From 13
15
14
16
17
12
8
3
6
5
4
3
Take 8
8
8
8
8
8
Add
8
2
8
3
_8
4
PRIMARY ARITHMETIC. 49
ORAL EXERCISES.
1. How many clusters are 3 clusters and 9 clus-
ters? 4 clusters and 9 clusters? 5 clusters and 9
cl asters ? 6 clusters and 9 clusters ?
How many are 4 and 9 ? 5 and 9 ? 6 and 9 ?
2. JS^ine pears from 15 pears leave liow many pears?
9 pears from 14 pears ? 9 pears from 13 pears ?
Nine from 15 leaves how many? 9 from 14? 9
from 13? 9 from 12? 9 from 11?
3. How many arrows in each of these groups ?
How many in both groups?
AAAA A AAA
4. If there were 7 arrows in the first group, how
many would there be in both groups?
5. How many are 8 bows and 9 bows? 7 bows
and 9 bows ? 7 deer and 9 deer ?
Seven and 9 are how many? 8 and 9?
6. If you had 17 arrows, and should give away 9
of them, how many arrows would you have left ?
Kine from 17 leaves how many? 9 from IG?
7. AYilliam has 9 books, and Albert has 9 : how
many boolvs have they both?
P. A. 4.
50
PRIMARY ARITHMETIC.
8. If William had 10 books, and Albert 9, how
many would they then have?
Nine and 9 are how many? 10 and 9?
9. Nine books from 18 books leave how many?
9 books from 19 books?
Nine from 18 leaves how many? 9 from 19?
10. How many are 2 keys and 9 keys? 4 keys
and 9 keys? 6 keys and 9 keys? 7 keys apnd 9
keys? 8 keys and 9 keys? 10 keys and 9 keys?
11. How many are 3 girls and 9 girls? 5 girls
and 9 girls? 7 girls and 9 girls? 9 girls and 9
girls? 8 girls and 9 girls?
1 2. How many are left when you take 9 keys from
12 keys? 9 keys from 13 keys? 9 keys from 15
keys? 9 keys from 17 keys? 9 keys from 19 keys?
9 keys from 16 keys?
.oJ<X*:
Hoxiy mnny are
0 and 9?
1 and 9?
2 and 9?
3 and 9?
4 and 9?
5 and 9?
6 and 9?
7 and 9?
8 and 9?
9 and 9?
10 and 9?
TaliC
9 from 9.
9 from 10.
9 from 11.
9 from 12.
9 from 18.
9 from 14.
9 from 15.
9 from 16.
9 from 17.
9 from 18.
9 from 19.
13. How many arc 3 and 9? 6 and 9? 9 and 9?
2 and 9? 5 and 9? 7 and 9? 1 and 9? 4 and 9?
10 and 9? 8 and 9? 9 and 8?
PRIMARY ARITHMETIC. 51
14. How many are 9 and 2? 9 and 5? 9 and 8?
9 and 9? 9 and 1 ? 9 and 6? 9 and 4? 9 and 3?
9 and 7? 7 and 9? 6 and 9?
15. How many are left when you take 9 from 12?
9 from 14? 9 from 16? 9 from 18? 9 from 15?
9 from 13? 9 from 11? 9 from 10?
38, 40.
9
9
9
9
9
9
Add 5
_6
7
_8
4
9
(1)
(2)
(3)
(4)
(•'>)
(6)
From 14
15
16
17
13
18
Take 9
9
9
9
9
9
7
3
.5
4
3
1
4
6
4
2
6
9
6
9
5
4
8
4
2
2
9
6
6
3
9
3
4
5
3
9
9
6
2
3
3
4
WRITTEN EXERCISES.
Copy and read 30, 32, 34, 31, 33, 36, 35, 37, 39,
EO.
(1) (2) (3) (4) (5) (G) (]) (2) (3) {4) (5) (6)
Add
REVIEW.
To Teachers. — The pnpil should not be required to give a
formal logical analysis of these problems. All that is necessary
is a correct statement of the answer and the operation. Take,
for example, the second problem below. The solution may be
given thus:
3rary found 12 eggs: 4 eggs and 8 eggs are 12 eggs. Or, 4 eggs
and 8 eggs are 12 eggs : Mary found 12 eggs.
1. John has 6 phmis in one hand, and 5 phims in
the other : how many phmis has he in both hands ?
2. Mary found 4 eggs in one nest, and 8 eggs in
another : how many eggs did she find ?
52
PRIMARY ARITHMETIC.
3. Alice gave 4 nice cherries to her brother Ed-
ward, and 7 cherries to her cousin William : how
many cherries did she give to both ?
4. There are 8 quails on the
fence, and 9 on the ground : how
many quails in the flock?
5. There are 6 windows in the
ends of a house, and 9 windows in
the sides: how many windows in the house?
6. How many are 2 and 5? 4 and 5? 7 and 5?
5andG? 5 and 8? 5 and 7?
7. How many are 3 and 6? 3 and 8? 3 and 9?
4 and 3? 7 and 3? 9 and 3? 10 and 3?
8. How many are 5 and 4? 6 and 4? 8 and 4?
9 and 4? 4 and 7 ? 4 and 5? 4 and 10?
9. How many are 4 and 7? 4 and 7 and 6? 5
and 7? 5 and 7 and 9? 6 and 8?
•
WRITTEN EXERCISES.
(1)
6
Add 5
(2)
6
7
(3)
6
8
(4)
6
9
(5)
5
8
(6)
6
7
(7)
5
6
(8)
5
9
(1)
5
Add 6
(2)
7
6
(3)
6
7
(4)
8
(5)
4
(6)
9
5
(7)
7
5
(8)
6
5
(1)
5
Add 6
(2)
8
7
(3)
9
_5
(-1)
8
9
(5)
7
6
(6)
6
_9
(7)
6
_8
(8)
4
_9
(1)
2
Add 9
(2)
3
8
(3)
4
7
i-i)
5
6
6
5
(6)
7
4
(7)
8
3
(8)
9
2
PRIMARY ARITHMETIC. 53
EEVIEW.
1. Mary found 12 eggs, and broke 5 of them in
climbing the fence: how many eggs had she left?
2. Charles has 15 cents: if he give 8 cents for a
lead pencil, how many cents will he then have?
3. Albert saw 13 blackbirds on a small tree, but
6 of them soon flew down to the ground : how many
were then on the tree?
4. Susan wrote 17 words on her slate, and then
erased 8 of them : how many words were left ?
5. Frank caught 14 trout,
and sold 9 of them : how
many trout had he left?
6. Four from 10 leaves how
many? 4 from 12? 4 from
14? 4 from 13? 4 from 11?
7. Five from 10 leaves how many? 5 from 12?
5 from 14? 5 from 9? 5 from 15? 5 from 13?
WRITTEN
EXERCISES.
(1)
(2)
(3)
{^)
(5)
(6)
(7)
(8)
From 9
10
12
14
11
15
13
16
Take _6
6
6
6
6
_6
_6
'_6
(1)
(2)
(3)
(J)
(o)
(6)
(7)
(8)
From 10
12
14
16
13
15
17
11
Take • _7
7
7
_7
7
7
7
_7
(1)
(2)
(3)
(-1)
(5)
(6)
(7)
(8)
From 10
12
14
13
16
18
17
15
Take _8
8
8
8
8
8
8
3
54
PRIMARY ARITHMETIC.
To Teachers. — Copy this diagram on the blackboard, using,
in place of the star, a letter, a circle, a triangle, a square, or
some other simple figure, and drill the class in rapid counting
to one hundred, first by ones ; then by tens, as 10, 20, 30, etc. ;
and then by fives, as 5, 10, 15, 20, etc.
\/ N/ \t \t \/ \» \t \f \/ \f
t\ /\ /\ /\ /\ /\ /\ /\ /\ /\
\t \/ \t \f \f \t \/ \t \/ \t
/> /N /<» /\ /\ t\ /\ t\ t\ 0 S
\t \f \> \/ \/ \/ \/ \f \t \*
*\ 0% l\ /\ t\ <\ *\ f\ /N /\
\f \t \f .\/ \/ \/ \t \f \/ \/
/> /\ t\ /\ f\ f\ t\ t\ t\ t\
\f \/ \/ \/ \/ \/ \/ \/ \f \/
/\ /\ /\ /V /\ l\ t\ t\ /\ *\
J"- J'> -^'- J*'- J'_ JL J"- J"_ *'" J*'-
\t \f \t \» \/ \f \/ \/ \t \/
/\ /\ /\ t\ t\ t\ /N *\ *\ t\
- '_ J* - J"_ J^'. _^'L *'■' J"L J^l J^'- -'-
*S l\ t\ tC 0\' 'l"* /\ tC ts" tC
^i, \/ \/ \f \t \t ^/ \/ \/ \/
'l^ #\ i\ ts t\ /v t\ t\ t\ t\
\/ \/ \/ \/ \/ \/ \f \/ \/ \*
/V /S /\ /> • /\ /\ /\ t\ f\ 0\
10
20
30
40
50
60
70
80
90
100
WRITTEN EXERCISES.
1. Copy and read the following numbers
20
80
40
50
60
70
80
90
21
31
41
51
61
71
81
91
22
32
42
52
62
72
82
92
23
33
43
53
63
73
83
93
24
34
44
54
64
74
84
94
25
35
45
55
65
75
85
95
26
36
46
56
66
76
86
96
27
37
47
57
67
77
87
97
28
38
48
58
68
78
88
98
29
39
49
59
69
79
89
99
2. Copy and read 21, 26, 33, 36, 38, 40, 44, 45, 48.
3. Copy and read 27, 36, 26, 37, 46, 48, 43, 55, 59.
4. Copy and read 61, 63, QQ, 64, 75, 73, 77, 78, 80.
PRIMARY ARITHMETIC.
DO
5. Copy and read 84, 83, 85, 87, 90, 94, 96, 97, 100.
6. Copy and read 18, 27, 3G, 48, 54, 67, 75, 8G, 94.
7. Beo:in Avith 5 and count to 100 by fives.
8. Begin with 10 and count to 100 by tens.
ADDITION
ORAL EXERCISES.
To Teachers. — The object of this and the next eleven les-
sons is to teach the addition of any number less than 10 to any
number less than 100. The exercises are so arranged as to lead
the pupil to add first the units. In finding the sum of 19 and 2,
29 and 2, or 39 and 2, for example, the 9 and 2 are first added.
This gives the unit figure, and by adding 1 to the left hand figure
the sum is obtained.
The Written Exercises should be used both as slate and
blackboard exercises. The columns of figures should be added
both up and down.
1. Charles has 9 cents in one hand, and 2 cents in
the other : how many cents has he in both liands ?
2. Mary has %Yritten 8 words : if she write 2 words
more, how many words will she have written?
3. A farmer has put 10
sacks of flour in his wagon :
if he put in 2 sacks more,
how many sacks will there
be in the wagon?
4. How many are 5 boys
and 2 boys? 15 boys and
2 boys ? 35 boys and 2 boyS ? 25 boys and 2 boys ?
45 boys and 2 boys?
56 PRIMARY ARITHMETIC.
5. How raany trees are 7 trees and 2 trees? 17
trees and 2 trees? 27 trees and 2 trees? 37 trees
and 2 trees? 47 trees and 2 trees?
6. How many are 8 and 2? 18 and 2? 28 and
2? 38 and 2? 58 and 2? 48 and 2?
7. How aiiany are 9 and 2? 19 and 2? 39 and
2? 29 and 2? 49 and 2? 59 and 2 ?
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)
22122 12222
Add 89976 12221
— — — — — 12211
(1) (2) (3) (4) (5) 12 2 2 2
22212 12222
Add 15 17 16 19 18 12 2 2 2
— — ~ —■ 12211
(1) (2) (3) (4) (5) 12 2 2 1
22222 12221
Add 18 29 27 38 26 12 2 12
— — ~- ~ ~ 12 212
(1) (2) (3) (4) (5) 12 2 2 2
22122 12211
Add 19 28 39 37 48 Add 12 12 2
ORAL EXERCISES.
1. Charles has 8 marblzs in one hand, and 3 marbles
in the other : how many marbles has he in both ?
2. Frank has 18 cherries: if his mother give him
3, how many cherries will he then have?
3. Mary has picked 17 phims: if she pick 3 more,
how many plums will she then have?
PRIMARY ARITHMETIC.
57
4. There are 9 birds on one
tree, and 3 birds on another:
how many birds on both trees?
5. Harry had 19 cents, and
his father gave him 3 cents:
how many had he then ?
6. How^ many are 12 eggs and 3 eggs? 14 eggs
and 3 eggs? 18 eggs and 3 eggs? 15 eggs and 3
eggs? 19 eggs and 3 eggs? 17 eggs and 3 eggs?
7. How many are 5 and 3? 15 and 3? 35 and
3? 55 and 3? 25 and 3? 45 and 3 ?
8. How many are 7 and 3? 17 and 3? 37 and 3?
57 and 3? 27 and 3? 47 and 3? 67 and 3?
9. How many are 8 and 3 ? 28 and 3 ? 18 and 3 ?
38 and 3? 48 and 3? 68 and 3?
10. How many are 9 and 3? 29 and 3? 19 and
3? 49 and 3? ^39 and 3? 59 and 3?
WRITTEN EXERCISES;
(1) (2) (3) (4)
3 3 3 3
Add 18 27 29 28
(1)
(2)
(3)
(4)
3
3
3
3
Add
17
36
29
38
(1)
(2)
(3)
(4)
3
3
3
3
Add
19
25
37
47
(1)
(2)
(3)
(4)
3
2
1
2
Add
16
49
39
28
(1) (2) (3) (4) (5) (6)
Add
3
3
1
3
3
1
3
3
3
3
2
2
3-
3
3
3
2
2
3
3
1
3
3
3
3
3
3
3
2
3
3
3
3
3
3
2
3
3
1
3
2
1
3
3
3
3
2
3
3
3
1
3
3
2
3
3
1
3
3
1
3
3
3
3
2
3
3
3
1
3
3
2
3
1
3
2
2
3
58 PRIMARY ARITHMETIC.
■bBssoH :kxx.h«
ORAL EXERCISES.
1. There are 8 horses in one field, and 4 horses in
another: how many horses in both fields?
2. Thomas received 15 cents for picking ten quarts
of cherries, and 4 cents for selling them : how many
cents did he receive in all?
3. There are 18 cows in one field,
'^^ ''"^^'**'^^ and 4 cows in another: how many
cows in both fields?
4. There are 19 boys and 4 girls in
a class : how many pupils in all ?
5. How many are 6 pears and 4 pears? 16 pears
and 4 pears? 36 pears and 4 pears? 26 pears and
4 pears? 46 pears and 4 pears?
6. How many are 5 and 4? 15 and 4? 35 and 4?
45 and 4? 25 and 4? 55 and 4?
7. How many are 7 and 4 ? 17 and 4 ? 37 and 4 ?
57 and 4? 47 and 4? 27 and 4? 67 and 4?
8. How many are 9 and 4 ? 19 and 4 ? 29 and 4 ?
49 and 4? 69 and 4? 59 and 4? 39 and 4?
9. How many are 8 and 4? 18 and 4 ? 48 and 4?
38 and 4? 28\md 4? 58 and 4?
10. How many are 9 and 2? 19 and 2? 39 and
2 ? 29 and 2 ? 59 and 2 ? 49 and 2 ? 69 and 2 ?
11. How many are 8 and 3? 18 and 3? 38 and
3? 48 and 3? ^28 and 3? 58 and 3? 47 and 3?
67 and 3? 57 and 3? 37 and 3? 27 and 3?
PRIMARY ARITHMKTIG.
59
(1)
(2)
WRITTEN EXERCISES.
(3)
(4)
(1) (2) (3) (4) (5) (6)
Add 16 24 28 36
(1)
(2)
(3)
(J)
4
4
4
4
Add 27
35
39
37
(1)
(2) "
(3)
{^)
4
4
4
4
Add 17
38
26
47
(1)
(2)
(3)
{4)
3
2
3
3
4
4
4
2
2
4
4
4
2
2
4
4
4
2
2
4
4
4
4
4
4
4
4
4
2
4
4
4
2
1
4
4
4
2
4
4
4
4
2
2
4
4
4
4
2
4
4
4
4
1
4
4
4
2
1
4
4
4
4
2
2
Add 19
28 38 47 Add 4
4 2 2 1
ORAL EXERCISES.
1. A garden contains 8 peach trees, and 5 pear
trees : how many trees of both kinds in the garden ?
2. Harry sokl three oranges for 18 cents, and two
lemons for 5 cents : how many cents did he receive ?
3. A drover bought 19 hogs of
one farmer, and 5 hogs of another :
how many hogs did he buy?
4. A man paid 17 dollars for a
cow, and 5 dollars for her calf:
how much did he pay for both?
5. How many are 8 stars and 5 stars? 18 stars
and 5 stars? 16 stars and 5 stars? 19 stars and
5 stars? 17 stars and 5 stars?
6. How many are 6 and 5 ? 16 and 5? 36 and 5?
56 and 5? 26 and 5? 46 and 5?
60 PRIMARY ARITHMETIC.
7. How many are 7 and 5? 17 and 5? 37 and 5?
27 and 5 ? 47 and 5 ? 57 and 5 ?
8. How many are 8 and 5 ? 18 and 5 ? 38 and 5 ?
48 and 5 ? 28 and 5 ? 58 and 5 ?
9. How many are 9 and 5? 19 and 5? 49 and 5?
29 and 5? 59 and 5? 39 and 5?
10. How many are 5 and 5? 15 and 5? 35 and
5 ? 55 and 5 ? 25 and 5 ? 45 and 5 ?
WRITTEN
EXERCISES,
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
(^)
(6)
5
5
5
5
5
5
1
5
5
5
Add 26
27
25
28
5
5
5
5
2
5
—
—
5
5
5
5
2
5
(1)
(2)
(3)
(4)
5
5
5
5
5
5
15
15
15
15
5
5
1
5
5
5
Add 16
26
20
28
5
5
5
5
5
2
— •
—
—
—
5
5
1
5
2
2
(1)
(2)
(3)
(4)
5
5
1
5
5
2
25
25
25
25
5
5
5
5
2
1
Add 37
45
39
43
5
5
5
5
2
2
5
5
1
5
5
2
(1)
(2)
(3)
(4)
5
5
1
5
2
2
14
37
23
23
Add
5
1
5
2
2
1
Add 26
14
28
39
—
—
—
—
—
ORAL EXERCISES.
1. How many are 5 and 6? 5 and 16? 5 and 36?
5 and 26? 5 and 46?
2. How many are 4 and 6 ? 4 and 16 ? 4 and 36 ?
4 and 46 ? 4 and 26 ? 4 and 56 ?
3. How many are 2 and 2 and 3 and 1 and 4 and
3 and 5?
PRIMARY ARITHMETIC. 61
4. How many are 5 and 4 and 3 and 2 and 1 and
2 and 3 and 4 and 5?
5. Begin with 2 and count to 50 by adding 2 suc-
cessively, thus : 2, 4, 6, S, 10, 12, etc.
6. Begin with 1 and coimt to 51 by adding 2 suc-
cessively.
7. Begin with 3 and count to 42 by adding 3 suc-
cessively, thus : 3, 6, 9, 12, 15, 18, etc.
8. Begin with 2 and count to 41 by adding 3 suc-
cessively.
WRITTEN EXERCISES.
(1)
(2)
(3)
(1)
(2)
(3)
(^)
(5)
(6)
(7)
(8)
5
4
3
5
5
5
4
4
4
5
4
Add 16
27
28
5
3
2
4
3
2
5
5
—
—
5
5
1
4
4
3
5
5
(1)
(2)
(3)
5
3
2
4
3
4
5
4
25
15
35
5
5
5
4
4
2
5
4
Add 26
25
27
5
3
3
4
3
3
5
4
—
—
■
5
5
5
4
4
2
5
5
(1^
(2)
(3)
5
3
5
4
3
1
5
5
35
25
45
5
5
3
4
4
2
5
4
Add 18
19
20
5
3
2
4
3
3
5
4
—
—
5
5
1
4
4
4
5
5
(1)
(2)
(3)
5
3
2
4
3
3
5
4
14
13
25
5
5
3
4
4
2
5
5
Add 26 37 35 Add _3_3_5_3_3J._4_4
ORAL EXERCISES.
1. Frank has 7 sour apples, and 6 sweet ones:
how many apples has he?
2. Jane's father gave her 8 cents, and her mother
gave her 6 cents : how many cents did she receive ?
62
PRIMARY ARITHMETIC.
3. Jane read 9 verses, and
Mary 6 verses more than Jane :
how many did Mary read?
4. In a certain orchard
there are 19 apple trees, and
6 peach trees : how many trees
in the orchard ?
5. How many are 5 raisins and 6 raisins? 15 rai-
sins and 6 raisins? 14 raisins and 6 raisins? 17
raisins and 6 raisins? 19 raisins and 6 raisins?
6. How many are 5 and 6 ? 15 and 6 ? 35 and 6 ?
55 and 6? 45 and 6? 25 and 6? 65 and 6?
7. How many are 7 and 6 ? 17 and 6 ? 37 and 6 ?
57 and 6? 47 and 6? 27 and 6?
8. How many are 9 and 6 ? 19 and 6 ? 39 and 6 ?
59 and 6? 29 and 6?
9. How many are 8 and 6 ? 18 and 6 ? 48 and 6 ?
58 and 6 ? 68 and 6 ? 38 and 6 ? 28 and 6 ?
WRITTEN EXERCISES.
a)
(2)
(3)
(1) (2)
(3)
(^)
(5)
(6)
(7)
(8)
6
6
6
6 6
6
8
3
6
4
6
Add 7
9
8
6 6
6
8
2
4
6
5
—
—
— ■
6 6
2
6
3
6
4
6
(1)
(2)
(3)
6 6
1
3
6
4
6
5
6
16
26
6 6
6
6
2
4
1
6
Add 16
38
25
6 6
1
3
6
6
2
5
■ — ■
— ■
—
6 6
6
6
3
4
3
6
(1)
(2)
(3)
6 6
6
6
6
4
4
5
16
86
26
6 6
6
6
2
6
6
5
Add 15
24
48
6 6
6
6
3
6
6
6
—
—
—
6 6
6
6
1
6
4
6
(1)
(2)
(3)
6 6
6
6
2
6
3
6
24
85
47
6 6
6
6
3
6
2
6
Add 65
46
26
Add
6 1
2
3
6
4
1
5
PRIMARY ARITHMETIC. 63
ORAL EXERCISES.
1. Five and 6 are how many? 6 and 15? 35
and 6? 6 and 45? 6 and 25?
2. Nine and 6 are how many? 6 and 19? 6 and
39? 14 and 8? 8 and 24?
3. How many are 7 and 4? 17 and 4? 18 and 5?
28 and 5 ? 36 and 6 ? 6 and 36 ?
4. How many are 8 and 4? 18 and 6? 35 and 7?
42 and 4? 41 and 5? 23 and 9?
5. How many are 3 and 4 and 5 and 6 and 2 and 3?
6. How many are 4 and 3 and 6 and 5 and 2 and
5 and 6 and 2?
7. Begin with 1 and count to 49 by adding 4 suc-
cessively.
8. Begin with 2 and count to 52 by adding 5 suc-
cessively.
WRITTEN EXERCISES.
(1) (2) (3) (4) (1) (2) (3) (4) (5) (6) (7)
16 15 27 46 2 2 5 4 4 5 3
Add 46 37 45 17 3 113 4 6 4
—
—
—
—
2
2
2
4
4
1
5
(1)
(2)
(3)
(4)
3
3
3
4
4
2
6
24
23
44
35
1
4
4
5
5
3
4
Add 18
27
48
27
2
4
5
5
5
4
3
—~
—
— ■
—
2
4
5
4
5
5
2
(I)
(2)
(3)
(i)
3
4
5
3
5
6
1
36
46
26
44
2
4
5
2
5
1
6
Add 14
35
25
47
3
3
4
1
6
2
5
—
—
—
2
3
4
2
6
3
3
(1)
(2)
(3)
(4)
3
3
4
3
6
4
4
36
26
45
55
2
3
4
4
6
5
6
Add 43
62
37
36
Add 1
3
4
5
6
6
5
64 PRIMARY ARITHMETIC.
]bBssaM xx:Kvn.
ORAL EXERCISES.
I. John has 8 marbles, and Charles 7: if Charles
should give all of his marbles to John, how many
marbles would John then have?
2. There are 6 chickens in
one brood, and 7 chickens in
another; how many chickens
are there in both broods?
3. There are 9 forks in the
basket, and 7 on the table :
how many in both places?
4. A boy gave 18 cents for a slate, and 7 cents for
a pencil: how many did he give for both?
5. How many are 8 pins and 7 pins? 18 pins
and 7 pins? 16 pins and 7 pins? 14 pins and 7
pins? 17 pins and 7 pins? 19 pins and 7 pins?
6. How many are 4 and 7 ? 14 and 7 ? 34 and 7 ?
54 and 7 ? 44 and 7 ? 24 and 7 ?
7. How many are 6 and 7 ? 16 and 7 ? 46 and 7 ?
36 and 7? 56 and 7? 26 and 7?
8. How many are 8 and 7 ? 18 and 7 ? 38 and 7 ?
28 and 7? 48 and 7? 58 and 7? 78 and 7?
9. How many are 7 and 7 ? 17 and 7 ? 37 and 7 ?
27 and 7 ? 47 and 7 ? 57 and 7 ?
10. How many are 6 and 7? 16 and 7? 7 and
16 ? 36 and 7 ? 7 and 36 ? 7 and 25 ?
II. How many are 28 and 3? 28 and 5? 28 and
8? 28 and 4? 28 and 6? 28 and 8?
PRIMARY ARITHMETIC. 65
WRITTEN EXERCISES.
(1) (2) (3) (4) (1) (2) (3) (4) (5) (6)
7 17 27 37 7 7 2 7 3 4
Add 14 2G 38 46 7 2 7 3 7 7
(1)
('-')
(-)
W
17
27
87
47
Add 17
23
45
39
(1)
(2)
(3)
(4)
33
24
25
13
21
32
44
55
7
7
1
7
3
4
7
2
2
7
7
7
7
7
7
7
3
4
7
7
1
7
7
4
7
7
2
3
3
7
7
7
2
7
7
4
1
7
7
7
3
4
7
7
2
7
7
7
Add 17 27 37 27 Add 7 2 2 3
ORAL EXERCISES.
1. How many are 5 and 7 ? 7 and 15 ? 7 and 35 ?
6 and 35? 5 and 35? 8 and 35?
2. How manv are 7 and 16? 6 and 16? 5 and
16? 7 and 33 ? 6 and 33 ? 5 and 38 ?
3. How many are 13 and 7? 7 and 13? 33 and
7 ? 7 and 43 ? 53 and 7 ? 63 and 7 ?
4. How many are 4 and 5 and 6 and 7 and 3 and
4 and 2 and 7?
5. How many are 1 and 3 and 5 and 7 and 6 and
4 and 6 and 3 and 5 and 6?
6. Begin with 2 and count to 52 by adding 5 sue-
ces.sively.
7. Begin witli 3 and count to 51 by adding 6 suc-
cessively.
8. Begin with 0 and count to 49 by adding 7 suc-
cessively.
P. A. 5.
66
PRIMARY ARITHMETIC.
9. Begin with 3 and count to 51 by adding 4 suc-
cessively.
WRITTEN EXERCISES.
(1)
(2)
(3)
(4) (1)
(2)
(3)
(4)
(5)
f^
23
54
46
35 7
3
4
7
4
3
Add 46
29
17
28 5
4
7
6
7
4
—
—
—
7
5
4
7
5
5
(1)
(2)
(3)
(4) 5
7
5
6
6
6
36
44
66
25 5
5
7
7
7
7
Add 25
55
14
37 7
7
4
6
2
6
—
—
—
— 7
5
3
7
3
5
(1)
(2)
(3)
(4) 7
7
7
7
4
4
36
45
23
14 7
5
3
7
5
3
41
33
43
54 7
7
4
7
6
2
Add 12 16 18
27
Add 5
5 6 7
~--»Tv5»i;;^^te«^!-«^ — -
ORAL EXERCISES.
1. "VYilliam walked 12 miles before dinner, and S
miles after dinner: how many miles did he walk?
2. A school-house has 9 windows in the sides, and
8 windows in the ends: how many Avindows has it?
3. Mary wrote 7 lines in her copy-book, and 8 lines
on a piece of paper : how many lines did she write ?
4. Albert gave 15 cents for
a top, and 8 cents for a pen-
cil: how many cents did he
pay for both?
5. How many are 8 boys
and 8 boys? 18 boys and 8
boys? 16 boys and 8 boys?
14 boys and 8 boys? 15 boys and 8 boys?
PRIMARY ARITHMETIC. 67
6. How many are 4 and 8 ? 14 and 8 ? 34 and 8 ?
24 and 8? 44 and 8? 64 and 8?
7. How many are 6 and 8 ? 16 and 8 ? 36 and 8 ?
56 and 8? 46 and 8? 26 and 8?
8. How many are 5 and 8? 15 and 8? 45 and 8?
65 and 8 ? 55 and 8 ? 35 and 8 ?
9. How many are 7 and 8? 17 and 8? 37 and 8?
67 and 8? 47 and 8? 27 and 8?
10. How many are 9 and 8? 19 and 8? 8 and
19 ? 8 and 29 ? 49 and 8 ? 8 and 49 ?
WRITTEN EXERCISES.
(1)
(2)
(3)
(4) (1)
(2)
(3)
(4)
(5)
(6)
28
38
18
48 8
2
2
8
8
4
Add 14
26
38
42 8
8
8
3
3
5
—
—
—
— 8
2
2
2
4
6
(1)
(2)
(3)
(4) 8
8
8
1
2
7
18
28
58
38 8
2
2
8
8
8
Add 25
17
23
19 8
8
1
2
3
7
—
—
— 8
8
2
3
4
6
(I)
(2)
(3)
(4) 8
8
8
8
8
5
44
43
35
18 8
8
8
8
8
4
25
34
27
46 8
8
8
8
8
3
Add 18
18
28
28 8
8
8
8
8
2
~"
~ Add 8
1
2
3
4
1
ORAL EXERCISES.
1. How many are 3 and 5 and 7 and 4 and 6 and
8 and 2 and 8?
2. HoYv^ many are 8 and 7 and 5 and 3 and 2 and
4 and 6 and 7?
68 PRIMARY ARITHMETIC.
3. How many are 9 and 5 ? 48 and 4 ? 53 and 7 ?
45 and 8 ? 27 and 8 ? 44 and 6 ?
4. How many are 15 and 6? 44 and 7? 36 and
8? 26 and 5? 18 and 3? 47 and 6?
5. How many are 16 and 5? 26 and 5? 46 and
5? 17 and 8? 37 and 8? 57 and 8?
6. How many are 15 and 7? 25 and 7? 55 and
7? 14 and 6? 34 and 6? 44 and 6? 18 and 3?
28 and 3? 48 and 3?
7. A boy bought a slate for 25 cents, a piece of
rubber for 8 cents, and a lead pencil for 5 cents : how
many cents did he pay for all?
8. Begin with 3 and count to 51 by adding 6 suc-
cessively.
9. Begin with 5 and count to 54 by adding 7 suc-
cessively.
10. Begin with 0 and count to 48 by adding 8 suc-
cessively.
11. Begin with 4 and count to 52 by adding 8 suc-
cessively.
WRITTEN
EXERCISES.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
(5)
(6)
35
44
27
36
8
3
6
6
2
8
Add 44
46
38
47
5
8
8
1
3
6
" —
8
4
6
8
4
4
(1)
(2)
(3)
(4)
5
8
8
2
5
1
41
34
56
44
8
1
6
8
8
2
Add 13
26
27
29
8
8
8
3
6
3
—
8
2
6
8
7
4
(1)
(2)
(3)
(4)
8
8
8
4
8
5
17
25
33
17
8
3
6
8
8
6
53
29
36
18
8
4
8
5
8
7
Add 26 43 28 45 Add 5 5 6 6
PRIMARY ARITHMETIC. 69
ORAL EXERCISES.
1. There are 7 cows in one pastnre, and 9 cows in
another: how many cows in both pastures?
2. John saw 9 pigeons on a tree, and 6 pigeons on
the ground : how many pigeons did he see ?
3. Wallace caught 8 fishes, and Willis caught 9:
how many fishes did both catch?
4. A farmer gave 6 dollars for a
yoke, and 9 dollars for a chain :
how many dollars did he give for
both?
5. How many are 5 plums and
9 plums? 15 plums and 9 plums? 17 plums and
9 plums? 13 plums and 9 plums? 16 plums and
9 plums? 14 plums and 9 plums?
6. How many are 3 and 9 ? 13 and 9 ? 43 and 9 ?
53 and 9 ? 23 and 9 ? 33 and 9 ?
7. How many are 5 and 9 ? 15 and 9 ? 45 and 9 ?
25 and 9 ? 35 and 9 ?
8. How many are 7 and 9 ? 17 and 9 ? 37 and 9 ?
57 and 9? 27 and 9? 47 and 9?
9. How many are 9 and 9 ? 29 and 9 ? 19 and 9 ?
49 and 9? 59 and 9?
10. How many are 8 and 9? 9 and 18? 35 and
9 ? 9 and 35 ? 24 and 9 ? 9 and 24 ?
11. How many are 6 and 9? 26 and 9? 9 and
26? 46 and 9? ' 9 and 46? 37 and 9? 9 and 37?
43 and 9? 9 and 43?
70 PRIMARY ARITHMETIC.
AdditioBft is the process of finding the sum of two
or more numbers.
The number obtained by adding two or more num-
bers is called the Sum or Amount,
WRITTEN EXERCISES.
(1) (2) (3) (4) (1) (2) (3) (4) (5) (G)
19 29- 89 49 9 2 3 9 3 4
Add 44 36 28 12
(1)
(2)
(-3)
(4)
14
5
13
14
15
14
22
15
24
13
19
16
23
25
16
18
Add 19
39
29
29
9
2
2
3
9
9
9
9
3
9
4
5
9
2
9
4
5
9
9
9
3
9
9
6
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
2
3
4
5
6
Add
WRITTEN EXERCISES IN ADDITION.
Copy and add the following examples :
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
2 3 323786 3 8
3 24365 3 306
1325 548944
223436439 2.
3 3 2 5 4 3 5 4 8 1
214327892 3
3 2 32167815
2345653737
32 3 1546299
1115 3 3 2 3 4 2
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
22
13
24
25
28
16
25
17
32
34
25
27
15
29
26
38
24
22 ■
16
18
24
28
19
15
21
27
34
29
27
27
27
26
PRIMARY ARITHMETIC. 71
Copy and read the following numbers :
(1)
(2)
(3)
(^)
(o)
(6)
100
110
120
100
122
135
101
111
121
110
133
134
102
112
122
120
144
136
103
113
123
130
155
164
104
114
124
140
166
167
105
115
125
150
177
177
106
116
126
160
188
186
107
117
127
170
199
185
108
118
128
180
200
144
109
119
129
190
125
163
Copy and add the following examples
(1)
(2)
(3)
W
(5)
(6)
46
43
63
125
146
149
54
55
42
248
186
127
37
36
57
105
137
136
82
44
69
123
123
144
63
61
43
149
145
133
45
38
4^
208
233
245
(7)
(8)
(9)
(10)
(11)
(12)
207
218
158
248
145
222
247
243
236
339
127
333
283
239
317
216
308
246
195
216
245
138
299
184
Copy and read the following numbers
(1)
(2)
(3)
(4)
(5)
(6)
200
210
204
214
324
420
300
320
305
325
446
325
400
420
405
425
66G
840
500
530
501
531
533
945
600
630
601
631
440
630
700
740
702
742
567
738
800
840
807
847
836
545
900
940
906
947
924
456
72
PRIMARY ARITHMETIC.
SUBTRACTION.
ORAL EXERCISES.
1. Here is a beautiful picture. What are the men
doing? How many are making the fence?
2. How many are 5 men less 2 men? 7 men less
2 men? 9 men less 2 men? 11 men less 2 men?
3. How many horses are 6 horses less 2 horses? 8
horses less 2 horses? 10 horses less 2 horses?
4. How many is 6 less 2 ? 8 less 2? 10 less 2?
5. How many fence-posts do you see? How many
are 5 posts less 3 posts? 7 posts less 3 posts?
PRIMARY ARITHMETIC. 73
6. The farmer has 10 sheep, but only 3 of them are
in sight. How many are 10 sheep less 3 sheep? 11
sheep less 3 sheep? 12 sheep less 3 sheep?
7. How many is 10 less 3? 11 less 3? 12 less 3?
8. How many are 11 men less 2 men? 21 men less
2 men ? 41 men less 2 men ? 61 men less 2 men ?
9. How many are 12 sheep less 3 sheep? 22 sheep
less 3 sheep? 32 sheep less 3 sheep? 52 sheep less
3 sheep?
10. Two from 11 leaves how many? 2 from 21?
2 from 41 ? 2 from 31 ? 2 from 51 ?
11. Three from 12 leaves how many? 3 from 22?
3 from 42 ? 3 from 32 ? 3 from 52 ? 3 from 62 ?
12. How many is 10 less 2 ? 20 less 2 ? 40 less 2 ?
30 less 2 I 60 less 2 ? 50 less 2 ?
13. How many is 11 less 3 ? 21 less 3 ? 41 less 3?
51 less 3 ? 31 less 3 ? 61 less 3 ? 81 less 3 ?
To Teachers. — The object of this and the next seven lessons
is to tench the subtraction of any number less than 10, from any
number not exceeding 100. The pupil should first be taught
to take the smaller number from tlie larger number as a whoL.
WRITTEN
EXERCISES.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
From 11
21
41
52
31
61
82
72
92
Take 2
2
2
2
3
3
3
3
3
(1)
(2)
(3)
(4)
(5^
(6)
(7)
(8)
(9)
From 13
23
41
51
66
74
72
49
29
Take 3
3
3
3
2
2
2
3
o
(1)
(2)
(3)
(4)
(5)
(C)
(7)
(8)
(9)
From 10
20
30
40
50
60
70
80
90
Take 1
1
2
2
2
3
3
3
3
74 PRIMARY ARITHMETIC.
]b]BSSOM :KIaIV«
ORAL EXERCISES.
1. Mary has 12 raisins: if she eat 4 of them, how
many will she have left?
2. Susan has picked 11 peaches and 4 pears: how
many more peaches has she than pears?
3. Mr. Smith has 13 hogs: if he
sell 4 of them to a drover, how
many will he have left?
4. Four pears from 11 pears leave
how many? 4 pears from 21 pears?
4 pears from 41 pears ? 4 pears from 31 pears ?
5. Four from 12 leaves how many? 4 from 22?
4 from 42? 4 from 32? 4 from 52?
6. Four from 7 leaves how many? 4 from 17?
4 from 37? 4 from 57? 4 from 47? 4 from 27?
4 from 67? 4 from 77?
7. How many is 13 less 4? 23 less 4? 43 less
4? 33 less 4? * 63 less 4? 53 less 4?
8. How many is 11 less 4? 21 less 4? 41 less
4? 61 less 4? 31 less 4? 51 less 4?
9. Begin with 36 and count back to 0 by subtract-
ing 4 successively, thus: 36, 32, 28, 24, etc.
10. Begin with 43 and count back to 3 by sub-
tracting 4 successively.
11. Begin with 33 and count back to 0 by sub-
tracting 3 successively.
12. Begiji with 35 and count back to 1 by sub-
tracting 2 successively.
PRIMARY ARITHMETIC.
iO
WRITTEN
EXERCISES.
(1)
(2)
(3)
(4)
(•^)
(6)
(7)
(8)
(9)
From 17
27
47
3(3
56
88
35
49
44
Take 4
4
4
_4
J
J
_4
4
J
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
From 12
22
42
62
13
23
43
63
53
Take 4
_4
4
4
4
4
4
4
4
(1)
(2)
(3)
W
(5)
(6)
(7)
(8)
(9)
From 11
21
41
61
14
13
23
43
33
Take 4
_4
4
jl
_4
_4
4
4
4
(1)
(2)
(3)
(4)
(5)
(G)
(7)
(8)
(9)
From 46
27
48
66
37
78
88
.96
66
Take 14
14
24
44
24
24
55
74
44
]L.]BSSOH XI..V.
ORAL EXERCISES.
1. In a spelling exercise^ Martha wrote 12 words
on her slate, and misspelled 5 of them: how many
words did she spell correctly?
2. A farmer has 13 chickens: if
he sell 5 of them, hoAV many will
■&^^^^^^^'- ^^ have left?
3. Alice made 14 figures on her
slate, and then erased 5 of them :
how many figures were left?
4. Five stars from 11 stars leave how many? 5
stars from 21 stars? 5 stars from 31 stars? 5 stars
from 51 stars?
5. Five from 12 leaves how many? 5 from 22?
5 from 42? 5 from 62? 5 from 32?
76 PRIMARY ARITHMETIC.
6. How many is 14 less 5? 24 less 5? 44 less
5? 34 less 5? 54 less 5? 64 less 5?
7. How many is 27 less 5? 38 less 5? 42 less
5? 61 less 5? 59 less 5?
8. Five from 13 leaves how many? 5 from 23?
5 from 43? 5 from 63? 5 from 53? 5 from 33?
5 from 63? 5 from 83?
9. How many is 19 less 5? 29 less 5? 49 less
5? 39 less 5? 53 less 5? 63 less 5? 73 less 5?
43 less 5? 33 less 5?
10. Begin with 43 and count back to 3 by sub-
tracting 5 successively.
11. Begin with 52 and count back to 2 by sub-
tracting 5 successively.
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (G) (7) (8) (9)
From 14 24 44 12 22 42 23 43 63
Take 55555 5555
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
From 45
67
54
39
77
65
57
64
89
Take 23
45
53
25
55
45
45
33
47
(1)
(2)
(3)
(-1)
(5)
(C)
(~)
(8)
(9)
From 21
31
33
32
50
44
48
53
54
Take 15
15
15
15
25
25
25
35
35
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
From 32
42
52
33
43
53
22
32
52
Take 13
14
23
24
24
35
13
24
35
To Teachers. — Teach the pupil how to proceed when the
lower unit figure is greater than the upper. Let him first learn
the hair and afterward the irhy.
PRIMARY ARITHMETIC. 77
ORAL EXERCISES.
1. Harry bought 15 slate pencils, and gave 6 of
them to his sister : how many had he left ?
2. A farmer has 13 oxen in one
field, and 6 in another: how many
oxen in the first field more than in
the second?
3. Jane is 14 years old, and her
brother is 6 years younger : how old is her brother ?
4. Six raisins from 12 raisins leave how many rai-
sins? 6 raisins from 22 raisins? 6 raisins from 42
raisins? 6 raisins from 11 raisins?
5. Six from 13 leaves how many? 6 from 23?
6 from 43? 6 from 33? 6 from 63?
6. Six from 18 leaves how many? 6 from 28?
6 from 48? 6 from 58? 6 from 7*8? 6 from G8?
7. How many is 15 less 6? 25 less 6? 45 less
6? 65 less 6? 35 less 6? 55 less 6?
8. How many is 14 less 6? 34 less 6? 54 less
6? 24 less 6? 44 less 6? 64 less 6?
9. How maay is 14 less 6? 23 less 6? 35 less
6? 21 less 6? 42 less 6? 53 less 6?
10. Begin with 36 and count back to 0 by sub-
tracting 6 successively.
11. Begin with 33 and count back to 3 by sub-
tracting 6 successively.
12. Begin Avith 42 and count back to 0 by sub-
tracting 6 successively.
78
PRIMARY ARITHMETIC.
WRITTEN EXERCISES.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(0)
From 15
25
35
14
34
54
13
43
63
Take 6
6
6
_6
_6
6
_6
_6
6
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
From 25
35
45
34
54
64
33
43
63
Take 16
26
26
16
26
36
26
36
56
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0)
From 22
44
31
43
25
54
62
63
31
Take 14
35
16
26
16
45
13
34
14
(1)
(2)
(3)
(4)
(.^)
(6)
(7)
(8)
From 137
257
146
188
296
267
168
149
Take 24
45
36
45
56
44
55
38
ORAL EXERCISES.
1. Alice is 14 years old, and her brother is 7 year^
younger than she: how old is her brother?
2. There are 16 knives in a basket : if 7 of them
be placed on the table, how many knives will re-
main in the basket?
3. A hen has 11 chickens, but a
hawk carried off 7 of them : how
many chickens were left?
4. Seven apples from 12 apples
--»i3ti^ leave how many ? 7 apples from
22 apples ? 7 apples from 42 apples ? 7 apples from
52 apples? 7 apples from 32 apples?
5. Seven from 15 leaves how many? 7 from 25?
PRIMARY ARITHMETIC.
79
7 from 55? 7 from 85? 7 from 65? 7 from 45?
7 from 35? 7 from 75?
6. How many is 16 less 7? 36 less 7? 26 less
7? 46 less 7? 66 less 7? 56 less 7?
7. How many is 14 less 7? 44 less 7? 54 less
7? 64 less 7? 84 less 7? 34 less 7? 74 less 7?
24 less 7? 84 less 7?
8. How many is 19 less 7? 29 less 7? 59 less
7? 68 less 7? 38 less 7? 32 less 7? 44 less 7?
33 less 7? 35 less 7?
9. Begin with 35 and count back to 0 by sub-
tracting 7 successively.
10. Begin with 40 and count back to 5 by sub-
tracting 7 successively.
WRITTEN EXERCISES.
(1)
From 16
Take 7
(2)
36
7
(3)
46
17
(4)
21
7
(5)
• 41
17
(6)
61
27
(7)
25
_7
(8)
55
17
(9)
75
47
(I)
From 73
Take 47
(2)
45
27
(3)
84
57
(4)
87
67
(5)
55
37
(6)
66
47
(7)
63
27
(8)
50
37
(9)
44
27
(1)
From 145
Take 36
(2)
247
143
(3)
365
246
(4)
473
344
(5)
586
277
(6)
693
475
(7)
287
176
(8)
364
246
(1)
From 234
Take 143
(2)
344
153
(3)
454
284
(4)
364
246
(5)
474
187
(6)
284
167
(7)
204
185
(8)
354
245
(1)
From 205
Take 127
(2)
333
227
(3)
415
345
(J)
616
508
(•5)
427
276
(6)
384
279
(7)
532
348
(8)
516
347
80 PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. Charles found 13 quinces on a quince-tree, and
picked 8 of them : how many were left ?
2. John found 15 nuts, and ate 8
of them : how many had he left ?
3. Kate had 22 problems to solve,
and she has solved 8 of them : how
many has she to solve ?
4. John bought 25 oranges, and sold 8 of them
before dinner: how many had he left?
5. How many are 14 nuts less 8 nuts? 24 nuts
less 8 nuts? 44 nuts less 8 nuts? 34 nuts less 8
nuts? 54 nuts less 8 nuts?
6. How many is 12 less 8? 32 less 8? 52 less
8? 62 less 8? 42 less 8? 22 less 8?
7. How many is 16 less 8? 26 less 8? 46 less
8? 36 less 8? 56 less 8? 76 less 8? 66 less 8?
8. Eight from 15 leaves how many? 8 from 35?
8 from 40? 8 from 30? 8 from 59?
9. Begin with 40 and count back to 0 by sub-
tracting 8 successively.
10. Begin with 45 and count back to 5 by sub-
tracting 8 successively.
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
From 13 33 53 12 42 62 17 27 57
Take 8 18 28 8 18 38 8 18 38
PRIMARY ARITHMETIC.
81
(1)
From 25
Take 18
(2)
55
28
(3)
65
38
(4)
24
18
(5)
44
28
(6)
63
38
(7)
83
58
(S)
51
36
(9)
71
25
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
From 148
256
198
273
366
354
275
486
Take 65
76
76
65
84
55
_87
_92
(1)
(2)
(3)
(4)
(o)
(G)
(7)
(8)
From 422
433
344
555
866
477
688
399
Take 364
225
256
367
276
248
586
157
ORAL EXERCISES.
1. Clara had 17 words to write, and she has written
9: how many words has she yet to write?
2. John has 15 marbles, and Samuel has 9 less
than Jolm : how many marbles has Samuel ?
3. A grocer has 25 sacks of flour : when he has
sold 9 sacks^ how many will he have left?
4. Sixteen birds lit on a
tree, and 9 of them soon flew
Jf9 1!^^^^^^^^/ ^^ ^^^^ ground : how many
^r-' • ^iM^'^^^wh were left on the tree?
5. How many will remain
if you take 9 pins from 13
pins? 9 pins from 23 pine?
9 pins from 63 pins?
35 less 9?
^^^'^^^:>m
9 pins from 43 pins?
6. How many is 15 less 9?
9? 45 less 9?"^ 65 less 9?
7. How many is 18 less 9? 38 less 9?
9? 58 less 9? 78 less 9? 68 less 9?
P. A. 6.
55 less
48 less
82
PRIMARY ARITHMETIC.
8. Begin with 45 and count back to 0 by sub-
tracting 9 successively.
9. Begin with 40 and count back to 4 by sub-
tracting 9 successively.
(1)
From 17
Take 9
(2)
37
19
WRITTEN EXERCISES.
(3) (4) (5) (6) (7)
47 26 6G 86 35
29 19 29 49 19
(8)
45
29
(9)
55
39
(I)
(2)
(3)
ii)
(5)
(6)
(7)
(8)
(9)
From 24
44
64
53
63
83
42
52
72
Take 9
19
29
39
29
59
29
49
59
(1)
(2)
(3)
W
(5)
(6)
(T)
(8)
From 236
135
344
4-33
363
172
284
464
Take G7
118
226
225
244
154
155
336
(1)
(2)
(3)
(-J)
(5)
(6)
(-)
(S)
From 344
456
265
237
473
686
468
557
Take 283
367
187
178
358
496
279
328
REVIEW.
1. Three from 31 leaves how many? 5 from 31?
7 from 31 ? 9 from 31 ? 6 from 31 ?
2. Four from 43 leaves how many? 6 from 43?
8 from 43? 7 from 43? 9 from 43?
3. Five from 44 leaves how many? 7 from 44?
9 from 44? 6 from 44? 8 from 44?
4. How many is 52 less 4? 52 leas 6? 52 less
8? 52 less 3? 52 less 5? 52 less 7? 52 less 9?
PRIMARY ARITHMKTIG. 83
5. How many is 55 less 6? 55 less 8? 55 less
5? 55 less 7? 55 less 9? 55 less 10?
6. How many is 60 less 3? 60 less 7? 60 less
9? 60 less 4? 60 less 6? 60 less 8? 60 less 5?
Subtraction is the process of finding the diifer-
ence between tAvo numbers.
The number obtained by subtracting one number
from another is called the Difference or Remainder.
WRITTEN EXERCISES.
(1)
From 6
Take 3
(2) (3)
8 9
_5 _6
(J)
7
4
(5)
9
5
(6)
7
3
(7) (8)
8 6
4 2
(9)
9
7
(10) (u;
7 8
_5 J
) (12)
9
_8
(13)
From 13
Take J
(14)
15
7
(15}
14
_6
(16)
16
7
(17)
15
8
(18)
17
_9
(19)
16
7
(20)
19
8
(21)
From 22
Take 16
(22)
23
17
(23)
44
28
(24)
55
29
(25)
46
28
(26)
34
16
(27)
35
17
(28)
42
25
(29)
From 122
Take _46
(30)
233
57
(31)
148
68
(32)
255
79
(33)
249
67
(34)
234
46
(3.5)
159
67
(36)
249
85
(37)
From 232
Take 145
(.38)
344
276
(39)
356
218
(40)
438
347
242
126
(42)
459
339
(43)
387
258
(44)
346
185
(45)
From 433
Take 227
(46)
545
366
(47)
573
383
(48)
999
(49)
796
669
(50)
307
249
(51)
606
546
(52)
704
665
(53)
From 581
Take 309
(54)
494
305
(55)
301
129
(56)
409
227
(57)
603
542
(58)
350
169
(59)
270
165
(60)
600
321
84 PRIMARY ARITHMETIC.
PROMISCUOUS ORAL EXERCISES.
1. Harry is 12 years old, and Charles is 9: what
is the sum of their ages ?
2. Mary is 15 years old, and Kate is 8: what is
the difference between their ages?
3. Mr. Jones luas 20 pears in his basket: if he
give a little boy 4 of them, how many pears will
remain in the basket?
4. Frank sold four oranges for 16 cents, and a pint
of nuts for 4 cents: how many cents did he receive?
5. If you add 9 urns and 6
urns and 5 urns, what will the
sum be?
6. If you take 6 tops from 15
tops, what will the difference be ?
7. A farmer has 16 cows in one pasture, and 7
in another : how many cows in both pastures ?
8. There are 25 eggs in a basket, and 8 in a nest :
how many more eggs in the basket than in the nest?
9. Mr. Gray has 15 peach trees in his orchard, and
6 in his garden : how many more peach trees in the
orchard than in the garden?
10. Clara has 16 pearl beads, and Jane has 9: if
Jane should give hers to Clara, how many beads
would Clara then have?
11. What is the number obtained by adding two
or more numbers together called ?
PRIMARY ARITHMETIC. 85
12. What is the sum of 27 and 8? 27 and 4?
25 and 4? 25 and 8? 25 and 6?
13. What is the amount obtained by adding 32
and 8? 36 and 7? 44 and G?
14. What is the number obtained by subtracting
one number from another called?
15. What is the difference between 9 and 15? 8
and 24? 6 and 21?
16. What will be the remainder if you take 7 from
33? 6 from 42?
17. When we take one number from another udiat
is the process called ?
18. Subtract 7 from 15. 7 from 35. 8 from 36.
19. What is the sum of 8 and 45? What is their
difference ?
20. Willis has 15 plums: how many more must
he pick to hav^e 25 plums ?
21. How many blocks must you add to 16 blocks
to make 23 blocks ?
22. A coat cost 25 dollars, and a vest 16 dollars:
how much did the coat cost more, than the vest ?
23. How many are 5 and 4 and 6 and 8 less 9?
24. How many are 8 and 9 less 6 less 5?
25. How many are 8 and 5 and 6 less 3 less 4
less 6 ?
26. How many are 5 and 6 and 7 less 4 less 5
less 3?
27. How many are 23 and 5 and 8 and 4 less 5
less 6 less 7?
86
PRIMARY ARITHMETIC
MULTIPLICATION
£.BSSOjM lAlu
\j2'ir2^ "^ /-^
ORAL EXERCISES.
1. What season of the year does this picture repre-
sent ? What are the boys doing in the orchard ?
2. How many boys are twice 1 boy? 3 times 1 boy?
3. How many barrels are empty? How many are 4
times 1 barrel?
How many are twice 1 ? 3 times 1 ? 4 times 1 ?
4. How many apple trees in sight? How many are
5 times 1 tree? 6 times 1 tree?
How many are 5 times 1 ? 6 times 1 ?
PRIMARY ARITHMETIC. 87
5. How many are 7 times 1 apple ? 8 times 1 apple ?
9 times 1 apple? 10 times 1 apple?
How many are 7 times 1 ? 8 times 1 ? 10 times 1 ?
To Teachers. — Develop the idea of multiplication, using
visible objects, as books, blocks, pencils, etc. Division may be
taught orally in connection with multiplication.
tv tnatty are
1 time 1? .
.
1
2 times 1? .
.
1 1
3 times 1? -
.
4 times 1 ? .
5 times 1? -
6 times 1? .
7 times 1 ? -
8 times 1? .
1
9 times 1 ? .
. I
1
10 times 1 ? .
1 1
1
0>*<00
ORAL EXERCISES.
1. How rfiaiiy boys are in the field? How many are
twice 2 boys?
2. How many barrels are filled with apples? How
many are 3 times 2 barrels ?
How many are twice 2 ? 3 times 2 ?
3. How many are 4 times 2 barrels? 5 times 2 bar-
rels? 6 times 2 barrels?
4. How many are 4 times 2 ? 5 times 2 ? 6 times 2 ?
5. How many are 7 times 2 apples ? 8 times 2 apples ?
6. How many are 7 times 2 ? 8 times 2 ?
v. How many are 9 times 2 trees? 10 times 2 trees?
88 PRIMARY ARITHMETIC.
8. How many are 9 times 2 men? 9 times 2
deer? 10 times 2 men? 10 tim_es 2 deer?
How many arc 9 times 2? 10 times 2?
9. How many are 3 times 2 tops? 4 times 2 tops?
2 times 2 tops? 5 times 2 tops? 7 times 2 tops?
6 times 2 tops? 8 times 2 tops? 10 times 2 tops?
9 times 2 tops?
To Teachers. — Show the pupil, that 3 times 2 is the sum of
three 2's; that 4 times 2 is the .siuu of four 2's, etc.; and when
the table is studied or recited, require the corresponding number
of 2's at the ripjht to be added. The subsequent tables should be
studied in the same manner.
Moni tnany are
1 time 2? 2
2 times 2? , 2 2
3 times 2? 2 2 2
4 times 2? 2 2 2 2
5 times 2? 22222
G times 2? 222222
7 times 2?.... 2222222
8 times 2?... 222 2 2222
9 times 2?. .222222222
10 times 2?. 22222222. 22
10. How many are 2 times 2? 4 times 2? 3
times 2? 5 times 2? 7 times 2? 6 times 2? 9
times 2? 10 times 2? 8 times 2?
11. How many are 5 times 1? 5 times 2? 7
times 1? 7 times 2? 9 times 1? 9 times 2? 6
times 1? G times 2?
12. How many are 4 times 1? 4 times 2? 8
times 1? 8 times 2? 7 times 1? 7 times 2?
13. How many times 2 are 4? 6? 8? 10? 12?
14? IG? 18? 20?
PRIMARY ARITHMETIC.
89
WRITTEN EXERCISES.
(1)
(2)
(3)
(^)
(5)
(6)
(T)
(8)
Multiply 2
2
2
2
2
2
2
2
Bv . . . 3
5
4
6
9
8
V
2
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Multiply 1
1
2
1
2
2
1
1
By . . . 6
9
/
8
4
6
7
5
(1)
(2)
(3)
(4)
(5)
(6)
Multiply
22
21
12
22
11
21
By . . .
4
_3
J
3
8
_4
(1)
(2)
(3)
(4)
(5)
(6)
Multiply
11
22
11
12
20
10
By . . .
6
4
9
3
4
9
ORAL EXERCISES.
1. A cart has 2 wheels: how many wheels have 4
carts?
Solution. — 4 times 2 toAeefe are 8 wheels : 4 carfe have 8 wheels.
2. A drayman earns 2 dol-
lars a day : how many dollars
will he earn in 6 days?
3. John bought 5 lemons
at 2 cents apiece : how many
cents did they cost?
4. If one bag hold 2 bush-
els of oats, how many bushels will 8 bags hold ?
5. What will 6 ]:)ushels of apples cost at 1 dollar
a bushel ? At 2 dollars a bushel ?
90 PRIMARY ARITHMETIC.
6. If 2 boys can sit at one desk, how many can
sit at 8 desks? How many at 10 desks?
7. If 1 step is 2 feet, how many feet are there in
7 steps? In 5 steps? In 6 steps?
8. If 2 horses make a span, how many horses will
make 4 span? 8 span?
9. Albert saw 5 yoke of oxen: how many oxen
did he see?
WRITTEN EXERCISES.
Copy and complete these tables:
3Iodel.
(1)
(2)
(3)
(4)
(5)
1X1-=1
2X1
2X2
2X2
5X1
5X2
1X2 = 2
2X2
2X4
4X2
1X7
4X2
1X3 = 3
2X3
2X6
6X2
7X2
6X2
1X4=4
2X4
2X8
8X2
2X6
8X2
1X5=5
2X5
2X3
3X2
1X5
7X2
1X6 = 6
2X6
2X5
5X2
8X1
9X1
1X7 = 7
2X7
2X7
7X2
2X5
9X2
1X8 = 8
2X8
2X1
9X2
4X2
8X1
1X9 = 9
2X9
2X9
9X1
3X2
4X1
To Teachers. — Teach the pupil that the sign of multiplica-
tion ( X ) when placed between two numbers, shows that the
number before it is to be multiplied by the number after it.^ 3X2
is to be read 3 multiplied by 2, which is the same as 2 times 3.
3X2=6 may be read, for convenience, 3 t'mies 2 equal 0.
ORAL EXERCISES.
1. How many leaves arc 2 times 3 leaves? 3
times 3 leaves? 4 times 3 leaves?
PRIMARY ARITHMETIC.
91
2. Two times 3 figs are how many figs ? 3 times
4 times 3 figs?
3 figs?
How many are 2 times 3 ?
3 times 3? 4 times 3?
3. James has found 5 times 3 shells: how many
shells has he found?
4. How many are 5 times 3 pebbles? 6 times 3
pebbles? 5 times 3 marbles? 6 times 3 marbles?
How many are 5 times 3? 6 times 3?
5. Alice has j^icked 7 oak twigs, and each twig has
3 leaves : how many leaves has she j)icked ?
6. How many times 3 books do you see here? 8
times 3 books are how many books? 9 times 3
books? 10 times 3 books?
How many are 8 times 3 ? 9 times 3 ? 10 times 3 ?
7. How many are 3 times 3 pens? 5 times 3
pens? 7 times 3 pens? 9 times 3 pens? 10 times
3 pens? 8 times 3 pens? 6 times 3 pens?
Soic inaiiy are
1 time 3? 3
2 times 3? 3 3
3 times 3? 3 3 3
4 times 3? 3 3 3 3
5 times 3? 33333
6 times 3? 333333
7 times 3?.... 3333333
8 times 3?... 33333333
9 times 3?. .333333333
10 times 3?. 3333333333
92
PRIMARY ARITHMETIC.
8. How many are 2 times 3? 3 times 3? 4 times
3? 5 times 3? 8 times 3? 10 times 3?
9. How many are 5 times 3? 3 times 5? 7 times
3? 3 times 7? 9 times 3? 3 times 9?
10. How many are 3 times 2? 3 times 3? 5 times
1 ? 5 times 2? 5 times 3? 8 times 1 ? 8 times 2?
8 times 3? 6 times 3?
11. How many time? 3 are 6? 9? 15? 12? 18?
24? 21? 27? 30?
WRITTEN EXERCISES.
(1)
Multiply 3
By . . . 2
Multiply
By . . .
(7) (8) (9)
3 3 3
1 7 5
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
3
2
1
2
3
2
3
1
2
6
9
8
7
5
J
6
5
6
(1)
(2)
(3)
(4)
(5)
m
Multiply 33
32
31
30
13
■23
By ... J
4
8
2
3
_2
(1)
(2)
(3)
(4)
(5)
(6)
Multiply 33
33
83
22
22
22
By . .\ 4
5
6
7
8
_9
To Teachers.— Teach the pupil how to proceed when the
product of the two unit figures exceeds 9.
ORAL EXERCISES.
1. Each finger has 3 joints: how many joints have
2 fingers? 3 fingers?
2. If each stool has 3 legs, how many legs have 3
stools ? 4 stools ? 5 stools ?
PRIMARY ARITHMETIC.
93
3. At 3 cents apiece, what will 8 lemons cost?
4. If a barrel will hold 3 bushels of apples, how
many bushels will 7 barrels hold?
5. A drover bought 9 sheep at 3 dollars a head:
how many dollars did he pay for them ?
6. Harry caught 3 fishes in his net, and John
caught 6 times as many as Harry : how many did
John catch ?
[er killed 3 squirrels, and saw 5 times as
lany squirrels did he see?
quarts of chestnuts cost, at 3 cents
^ thread cost, at 3 cents a
yard : how many feet
■
■
PfflEN EXERCISES.
■
B
te these tables :
H
H
(3)
(4)
(5)
3X3
2X4
6 + 2
^Hj^l
IP
5X3
3X4
7 + 3
Ws^
^X7
7X3
1X4
8 + 1
3X4
3X9
9X3
2X5
9 + 2
3X5
3X8
8X3
2X3
9 + 3
3X6
3X6
6X3
3X5
8 + 3
3X7
3X4
4X3
2X4
9 + 1
3X8
3X2
2X3
1X6
7 + 2
3X9
3X5
3X3
2X7
5 + 3
To Teachers. — Explain the sign of addition ( + ) used in
the 5th table, and teach the pupil to read it j^ltis, as 6 pins 2;
7 j>/us 3, etc.
94
PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. How many rabbits are 2 times 4 rabbits? 3
times 4 rabbits? 4 times 4 rabbits?
2. Once 4 sheep are how many sheep? Twice 4
sheep ? 3 times 4 sheep ? 4 times 4 sheep ?
How many are 2 times 3? 3 times 3? 4 times 3?
3. Here are how many groups of arrows ? Five
times 4 arrows are how many arrows? 6 times 4
arrows? 3 times 4 arrows?
4. How many girls are 5 times 4 girls? 6 times
4 girls? 4 times 4 girls?
How many are 5 times 4? 6 times 4? 4 times 4?
^^ ^^ mm
5. How many hoofs has each of these horses ?
How many hoofs have 7 horses? 8 horses?
6. Seven times 4 shoes are how many shoes? 8
times 4 shoes? 6 times 4 shoes?
How many are 7 times 4? 8 times 4? 6 times 4?
7. How many are 9 times 4 fingers? 10 times 4
fingers? 9 times 4 arrows? 10 times 4 arrows?
How man V are 9 times 4 ? 10 times 4 ? 4 times 10 ?
PRIMARY ARITHMETIC. 95
8. How many are 2 times 4 hats? ■ 4 times 4 hats?
5 times 4 hats? 3 times 4 hats? 7 times 4 hats?
9 times 4 hats? 8 times 4 hats? 6 times 4 hats?
How mnnif are
1 time 4? 4
2 times 4? 4 4
3 times 4? 4 4 4
4 times 4? 4 4 4 4
5 times 4? 44444
6 times 4? 4 4 4 4 4 4
7 times 4? 4444444
8 times 4?. ..44444444
9 times 4?. .444444444
10 times 4?. 4444444444
9. How many are 2 times 4? 3 times 4? 5 times
4? 6 times 4?. 4 times 4? 8 times 4? 7 times 4?
9 times 4? 3 times 4? 10 times 4?
10. Five times 4 are how many? 7 times 4? 4
times 7? 6 times 4? 4 times 6? 8 times 4? 4
times 8? 9 times 4? 4 times 9?
(1)
Multiply 4
By . . . 3
Multiply
By . . .
WRITTEN EXERCISES.
(2) (3) {A) (5)
(6) (7) (S)
4 4 4
6 4 2
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
3
2
3
3
2
3
3
2
4
4
7
9
8
6
5
4
(1)
(2)
(3)
(J)
(0)
{«)
:MultipIy 44
43
42
41
40
41
By . \ . _2
3
4
8
_9
5
(1)
(2)
(3)
(4)
(5)
(6)
Multiply 24
43
34
44
23
34
By . . . 5
4
3
6
7
8
96 PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. There are 4 fingers on one hand : how many
fino^ers are there on 2 hands? 3 hands? 5 hands?
2. There are 4 quarts in a gallon: how many
quarts are tliere in 6 gallons? 7 gallons?
3. An elk has 4 legs : how
many legs have 4 elks? 6
elks? 5 elks?
4. Four girls have 4 roses
each : how many roses have
they all?
5. A wagon- has 4 wheels :
how many wheels have 7 wagons? 5 wagons?
6. What will 8 loads of wood cost, at 4 dollars
a load? At 3 dollars a load?
7. What will 7 pairs of shoes cost, at 4 dollars a
pair? At 3 dollars a pair?
8. What will 10 oranges cost, at 4 cents apiece?
9. If a sheet of paper make 4 pages, how many
pages will 9 sheets make?
10. If a man walk 4 miles in an hour, how far
will he walk in 8 hours?
11. How many are 3 times 2? 3 times 3? 3
times 4? 5 times 3? 5 times 4? 7 times 2? 7
times 3? 7 times 4?
12. How many times 4 are 8? 12? 20? 16?
24? 32? 28? 36?
PRIMARY ARITHMETIC.
97
WRITTEN EXERCISES.
Copy and complete these tables :
(1)
4X1 =
4X2-
4X3 =
4X4 =
4X5 =
4X6 =
4X7 =
4X8 =
4X9 =
(2)
4X3
4X1
4X5
4X7
4X2
4X4
4X0
4X0
4X8
3X4
1X4
5X4
7X4
2X4
4X4
CX4
0X4
8X4
(4)
4X4
0X3
6X2
5X4
5X3
5X2
7X4
8X3
9X2
(5)
4 + 4
6 + 3
6 + 4
5 + 4
5 + 2
7 + 4
8 + 3
9 + 4
9 + 3
— T.>»te.-^
ORAL EXl'RCISES.
1. How many bunches of grapes in each of these
groups? In 2 groups? In 3 groups?
2. How many are 2 times 5 doves? 3 times 5
doves? 4 times 5 doves?
How many are 2 times 5 ? 3 times 5 ? 4 times 5 ?
3. The leaves of a flower are called petals. How
many petals has each of these pretty violets ?
4. Jane has picked 5 violets, and Mary 5 times as
many as Jane : how many violets has Mary picked ?
5. How many petals are 4 times 5 petals ? 5 times
5 petals? 6 times 5 petals?
How many are 4 times 5 ? 5 times 5 ? 6 times 5 ?
P. A. 7.
98 PRIMARY ARITHMETIC.
6. Edward has 5 marbles, and Albert 7 times as
many as Edward : how many marbles has Albert ?
J£) J^ jQ S> .^JQ .^JQ ^jQ ^ JJ ^ JO
-d ^ ja _© _© jd j&
...M^ .^o^ ,^o^ .^o^ ^^ jD ~-o ^ ^JijQ
7. Seven times 5 marbles are how many marbles?
8 times 5 marbles?
How many are 7 times 5? 8 times 5? 5 times 8?
#########
8. Mary kejit the account in a spelling match be-
tween two classes. The first class misspelled 9 times
5 Avords; the second 10 times 5 words: how many
words did each class misspell?
How many are 9 times 5 ? 10 times 5 ? 5 times 10?
9. How many are 3 times 5 cents? 5 times 5
cents? 4 times 5 cents? 7 times 5 cents? 6 times
5 cents? 9 times 5 cents? 10 times 5 cents? 8
times 5 cents?
How many are
1 time 5? 5
2 times 5? 5 5
3 times 5? 5 5 5
4 times 5? 5 5 5 5
5 times 5? 5 5 5 5 5
6 times 5? 5 5 5 5 5 5
7 times 5? . . . . 5 5 5 5 5 5 5
8 times 5?... 555 5 5555
9 times' 5?. .555555555
10 times 5? . 5 5 5 5 5 5 5 5 5 5
10. How many are 3 times 5? 6 times 5? 0
times 5? 10 times 5? 8 times 5? 7 times 5? 5
times 5? 4 times 5? 2 times 5?
PRIMARY ARITHMETIC.
99
11. Four times 5 are how many?
times 5? 5 times 5? 7 times t>?
times 3? 9 times 5?
12. How many are 7 times 3?
times 3? 7 times 4? 8 times 4?
times 5? 8 times 5? 9 times 5?
13. How many times 5 are 10? 15? 20? 30?
5 times 4?
8
3 times 5?
5
8 times 3?
9
9 times 4?
7
3? 50? 25?
35? 45?
(6)
5
8
(T)
5
2
(1)
Multiply 5
By . . . 5
WRITTEX EXERCISES.
(2) (3) (4) (5)
5 5 5 5
4 7 6 9
(8)
5
3
Multiply
Bv . .'.
(1)
(2)
(3)
(^)
(5)
(6)
{■)
(8)
3
4
7
6
9
8
2
5
5
5
5
5
5
5
5
5
(1)
(2)
(3)
(4)
(5)
(6)
Multiply 54
By . .'. J
53
3
52
J
51
_6
50
51
_7
(1)
(2)
(3)
(i)
(5)
(6)
Multiply 25
By . . . 4
35
6
45
8
15
2
55
9
52
5
<^^?^
ORAL EXERCISES.
1. An orchard has 6 rows of trees, and each row
has 5 trees : how many trees in the orchard ?
2. A recitation room contains 4 seats, and there
are 5 pupils sitting on each seat: how many pupils
in the room ?
100
PRIMARY ARITHMETIC.
3. Lucy gave 5 plums to her brother, and 6 times
as many to her mother : how many plums did she
give to her mother?
4. If a horse travel 5 miles
an hour, how many miles will
he travel in 7 hours ?
5. If a boat sail 5 miles an
hour, how far will it sail in
10 hours?
6. Willie is 5 years old, and
his father is 8 times as old as he : how old is Willie's
father? How many are 8 times 5?
7. If a ladder have 5 rounds, how many rounds
\vill 3 ladders have?
8. What Avill 7 lead-pencils cost, at 5 cents apiece?
9. What Avill 8 oranges cost, at 5 cents apiece?
10. What will 9 hats cost, at 5 dollars apiece?
11. What will 6 tables cost, at 5 dollars apiece?
WRITTEN EXERCISES.
Copy and complete these tables :
(1)
(2)
(3)
(4)
(5)
5X1 =
5X3
3X5
5X4
5 + 5
5X2-
5X5
5X5
5X6
6 + 5
5X3 =
5X7
7X5
3X7
8 + 5
5X4 =
5X2
2X5
4X8
9 + 4
5X5 =
5X4
4X5
5X8
7 + 5
5X6 =
5X3
3X5
4X9
7 + 4
5X7 =
5X6
6X5
3X9
4 + 5
5X8 =
5X8
8X5
5X6
8 + 4
5X9 =
5X9
9X5
5X9
6 + 4
PRIMARY ARITHMETIC. 101
ORAL EXERCISES.
1. How many girls are once 6 girls? 2 times 6
girls? 3 times 6 girls? 4 times 6 girls?
How many are 2 times 6 ? 3 times 6 ? 4 times 6 ?
2. How many books in each of these rows ? Twice
6 books are how many books? 3 times 6 books?
4 times 6 books? 5 times 6 books?
3. William's little book-case has 5 shelves, and on
each shelf are 6 books : how many books are there
in the case?
4. How many pencils are 3 times 6 x^encils? 4
times 6 pencils? 5 times 6 pencils?
How many are 4 times 6 ? 5 times 6 ? 3 times 6 ?
5. Willie arranged his mother's spools of thread in
6 piles, by placing 6 spools in each pile : how many
spools were there?
6. How many are 6 times 6 spools? 7 times 6
spools? 8 times 6 spools?
7. Six times 6 hats are how many hats? 7 times
6 hats? 8 times 6 hats?
How many are 6 times 6 ? 7 times 6 ? 8 times 6 ?
8. How many legs has a bird? How many has a
mouse? How many has a fly?
102
PRIMARY ARITHMETIC.
9. If a fly has 6 legs, how many legs do 9 flies
have? 10 flies?
10. How many stars are 9 times 6 stars? 10
times 6 stars?
How many arc 9 times 6 ? 10 times 6 ? 8 times 6 ?
11. How many are 2 times 6 slates? 3 times 6
slates ? 5 times 6 slates ? 7 times 6 slates ? 6 times
6 slates? 9 times 6 slates? 8 times 6 slates? 10
times 6 slates?
oo:«::cK.
JIoiv many are
1 time 6? 6
2 times 6? 6 6
3 times 6? 6 6 6
4 times 6? 6 6 6 6
5 times 6? 66666
6 times 6? 666666
7 times 6?.... 6666666
8 times 6?... 66666666
9 times Q1..&QQ%Q^&(S^
10 times 6?. 6666666666
12. How many are 2 times 6? 5 times 6? 7
times 6? 4 times 6? 3 times 6? 8 times 6? 9
times 6? 10 times 6?
13. How many are 4 times 6? 6 times 4? 7
times 6? 6 times 3? 5 times 6? 6 times 5? 8
times 6? 6 times 6?
14. Seven times 5 are how many? 6 times 4? 5
times 3? 8 times 5? 7 times 6? 9 times 3? 8
times 6? 8 times 4?
PRIMARY ARITHMETIC.
103
15. How many 6's in 12? 24? 18? 30? 42?
36? 54? 48? 60?
(1)
Multiply 6
By . '
Multiply
Bv . . .
WRITTEX EXERCISES.
(7) (8)
6 6
3 9
(1)
(2)
(3)
H)
(5)
(6)
(7)
(8)
4
5
7
6
3
8
2
9
6
6
6
6
6
6
6
6
(1)
(2)
(3)
(4)
(5)
(6)
Multiply
64
63
65
62
61
60
By . /.
3
4
6
5
8
_9
(1)
(2)
(3)
(4)
(5)
(6)
Multiply
63
64
55
65
.62
41
By . .'.
6
5
8
4
7
9
ORAL EXERCISES.
1. Charles found 3 bird's
nests, and each nest had 6
eggs in it: how many eggs
did he find?
2. Mary's spelling lesson
consists of 3 columns, and
each column contains 6 words:
how many words in her lesson?
3. How many letters in 6 words, if each word con-
tain 6 letters?
104
PRIMARY ARITHMETIC.
4. A drover bought 10 sheep, at 6 dollars a head :
how many dollars did he pay for them?
5. A house has 8 windows, and eaeh window con-
tains 6 panes of glass : how many panes of glass in
all the windows?
6. If a boat sail 6 miles an hour, how far will it
sail in 9 hours? In 10 hours?
7. What will 5 sheep cost, at 6 dollars apiece?
8. What will 7 lead-pencils cost, at 6 cents apiece?
WRITTEN EXERCISES.
Copy and complete these tables:
(1)
(2)
(3)
(^)
(5)
6X1 =
6X3
3X6
4 + 5
9 — 3
6X2-
6X2
2X6
G + 5
8 — 5
6X3 =
6X4
4X6
7 + 5
9 — 6
6X4 =
6X6
6X6
3 + 4
7 — 4
6X5 =
6X5
5X6
8 + 4
6-3
6X6 =
6X8
8X6
7 + 4
7 — 6
6X7 =
6X7
7X6
2 + 6
8 — 4
6X8 =
6X9
9X6
5 + 6
6 — 6
6X9==
6X1
1X6
4 + 6
9 — 5
ORAL EXERCISES.
1. How many pretty nests do you see? How many
eggs in eaeh nest ? How many eggs in two nests ?
PRIMARY ARITHMETIC.
105
2. How many are 2 times 7 eggs? 3 times 7 eggs?
4 times 7 eggs? 5 times 7 eggs?
3. Three times 7 birds are how many birds? 4
times 7 birds? 5 times 7 birds?
How many are 2 times 7 ?
4. How many bunches of cherries are here ? How
many cherries in each bunch? How many cherries
are there in 4 bunches? How many cherries in all
the bunches?
5. How many cherries are 5 times 7 cherries? 7
times 7 cherries? 6 times 7 cherries?
6. Six times 7 peanuts are how many ? 7 times 7
peanuts are how many ?
How many are 5 times 7 ? 6 times 7 ? 7 times 7 ?
7. This beautiful leaf will fold up like a fan. How
many blades has it?
8. If a leaf has 7 blades, how many blades do 8
leaves have? 9 leaves? 10 leaves?
9. How many are 8 times 7 trees?
trees? 10 times 7 trees?
How many are 8 times 7? 9 times 7 ?
10. How many are 3 times 7 men?
9 times 7
10 times 7?
4 times 7
men ? G times 7 men ? 8 times 7 men ? 5 times 7
men? 7 times 7 men? 9 times 7 men? 10 times
7 men?
106 PRIMARY ARITHMETIC.
Uotv tnnuy are
1 time 7? 7
2 times 7? 7 7
3 times 7? 7 7 7
4 times 7? ......... 7 7 7 7
5 times 7? 77777
6 times 7? 777777
7 times 7?.... 7777777
8 times 7?... 77777777
9 times 7?. .777777777
10 times 7?. 7777777777
11. How many are 5 times 7? 3 times 7?
times 7? 8 times 7? 9 times 7? 10 times 7?
times 7? 4 times 7?
12. How many are 3 times 7? 7 times 3?
times 6? 6 times 5? 7 times 6? 6 times 7?
times 6? 6 times 4?
13. Four times 5 are liow many? 4 times 4?
times 6? 9 times 4? 9 times 5? 9 times 7?
times 5? 5 times 7? 5 times 6?
14. How many 7's in 14? 21? 35? 42?
56? 63? 70?
5
4
4
5
28?
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (6) (7) (8)
Multiply 77 7 77777
By... J _6 _3 _5 J _2 _9 _7
(1) (2) (3) (4) (5) (G) (7) (8)
Multiply 73 75 72 76 74 71 77 70
By... J ^ _5 _6 _8 J_ _7 _7
(1) (2) (3) (4) (5) (6) (7) (8)
Multiply 33 44 55 66 22 77 77 37
By... 8 7 6 4 9 3 5 6
PRIMARY ARITHMETIC. 107
ORAL EXERCISES.
1. There are 7 days in a week : how many days
are there in 4 weeks?
2. Kate found 3 bird's nests one morn-
ing, and each nest had 7 eggs in it : how-
many eggs did she find?
3. There are 5 boys in a grammar class, and each
boy has written 7 sentences : how many sentences
have they all written?
4. If a horse trot 7 miles an hour, how far will
he trot in 8 hours?
5. Kate picked 7 quarts of cherries, and sold them
at 7 cents a quart : how many cents did she receive ?
6. Jane is 7 years old, and her grandfather is 10
times as old as she is : how old is her grandfather ?
WRITTEN EXERCISES.
Copy and
complete
these tables
:
(1)
(2)
(3)
(4)
(5)
7X1 =
7X3
3X7
3 + 7
10 — 7
7X2 =
7X5
5X7
5 + 7
12 — 7
7X3 =
7X4
4X7
4 + 7
11 — 7
7X4 =
7X6
6X7
6 + 7
13 — 7
7X5 =
7X8
8X7
8 + 7
15 — 7
7X6 =
7X7
1X7
1 + 7
8 — 7
7X7 =
7X9
9X7
9 + 7
16 — 7
7X8 =
7X2
2X7
2 + 7
9 — 7
7X9 =
7X1
7X7
7 + 7
14 — 7
To Teacher.s. — Explain the sign of subtraction used in the
5th example, and teach the pupil to read it minus, as 10 minus 7.
108
PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. How many clusters of grapes are 2 times 8 clus-
ters? 3 times 8 clusters? 4 times 8 clusters?
2. How many forks are 2 times 8 forks ? 3 times
8 forks? 4 times 8 forks?
How many are 2 times 8? 3 times 8? 4 times 8?
3. How many fingers has one boy? 2 boys? 4
boys? 5 boys? 6 boys?
4. Five times 8 nuts are how many nuts ? 6 times
8 nuts? 7 times 8 nuts?
How many are 5 times 8? 6 times 8? 7 times 8?
5. Her3 is a plate with 8 apples on it. How many
apples are 7 times 8 apples? 8 times 8 apples?
6. How many are 7 times 8 stars? 7 times 8
men? 8 times 8 stars? 8 times 8 men?
7. How many are 9 times 8 apples? 9 times 8
pears? 10 times 8 apples? 10 times 8 pears?
8. How many are 6 times 8? 7 times 8? 8 times
8? 9 times 8? 10 times 8?
9. Five times 8 stars are how many stars ? 4 times
8 stars ? 6 times 8 stars ? 7 times 8 stars ? 10 times
8 stars? 3 times 8 stars? 9 times 8 stars?
PRIMARY ARITHMETIC. 109
H.OW inauy arc
1 time 8? 8
2 times 8? 8 8
3 times 8? 8 8 8
4 times 8? 8 8 8 8
5 times 8? 88888
6 times 8? 888888
7 tjmes 8?.... 8888888
8 times 8?,.. 88888888
9 times 8?. .888888888
10 times 8?. 8888888888
10. How many are 3 times 8? 5 times 8? 6
times 8? 7 times 8? 10 times 8? 9 times 8? 4
times 8? 2 times 8?
11. How many are 4 times 8? 8 times 4? 6
times 8? 8 times 6? 7 times 8? 8 times 7?
12. Five times 8 are how many? 8 times 5? 7
times 8? 8 times 7? 5 times 9? 9 times 5? 6
times 8? 8 times 6?
13. How many 8's in 16? 24? 40? 64? 48?
32? 72? 80?
WRITTEN EXERCISES.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Multiply
By . . .
8
4
8
_3
8
8
2
8
7
8
8
8
9
8
6
(1)
(2)
(3)
(4)
(5)
(6)
(T)
(S)
Multiply
By . . .
4
_8
3
8
5
8
2
_8
7
_8
8
8
9
8
6
8
(1)
(2)
(3)
(4)
(5)
(6)
Multiply
By . . \
82
_5
81
j6
83
_4
84
3
86
1
87
2
(1)
(2)
(3)
(4)
(5)
(6)
Multiply
By . . ".
24
11
26
12
43
13
36
15
33
14
25
16
110
PRIMARY ARITHMKTIG.
ORAL EXERCISES.
1. A railroad car has 8 wheels : how many wheels
has a train of 5 cars ?
2. There are 8 furlongs in a mile : how many fur-
longs are there in 6 miles?
3. There are 4 rows of desks in a school-room, and
8 desks in each row : how many desks in all ?
4. If a cow give 8 quarts
of milk in one day, how
many quarts wdll she give in
6 days ?
5. There are 8 quarts in a
peck : how many quarts are
there in 9 pecks? 10 pecks?
6. What will 9 vests cost, at 8 dollars apiece?
7. "What will 7 clusters of grapes cost, at 8 cents
a cluster?
WRITTEN EXERCISES.
Copy and complete these tables :
(1)
(2)
(3)
(4)
(5)
8X1-
8X6
6X8
6-{-8
14 — 8
8X2 =
8X4
4X8
4 + 8
10 — 8
8X3 =
8X2
2X8
2 + 8
12 — 8
8X4 =
8X1
1X8
3 + 8
13 — G
8X5 =
8X3
3X8
5 + 8
15 — 9
8X6 =
8X5
5X8
7 + 8
IG — 8
8X7 =
8X7
7X8
9 + 8
17 — 9
8X8 =
8X9
9X-8
8^ 8
18 — 9
8X9 =
8X8
8X8
1+8
14 — 7
PRIMARY ARITHMETIC.
Ill
ORAL EXERCISES.
1. How many pine-apples are once 9 pine-apples?
Twice 9 pine-apples? 3 times 9 pine-apples?
2. Jane picked 9 pinks, and Kate 2 times as many:
how many pinks did Kate pick?
How many are 2 times 9? 3 times 9?
3. Samuel has 3 book-shelves, and 9 books on each
shelf: how many books has he?
4. How many books are 3 times 9 books? 4 times
9 books? 5 times 9 books? 6 times 9 books?
5. Four times 9 cents are how many cents? 5
times 9 cents? 6 times 9 cents?
How many are 4 times 9 ? 5 times 9 ? 6 times 9 ?
,^ -^ "^ '^ ^h J^ '■^is^ -^
6. Here are 8 banana trees. What long leaves
they have! How many leaves are on each tree?
7. How many leaves are 7 times 9 leaves? 8
times 9 leaves? 9 times 9 leaves?
8. A fruit dealer bouglit 10 bunches of bananas,
with 9 bananas in each bunch: how many bananas
did he buy?
112 PRIMARY ARITHMETIC.
9. How many are 6 times 9? 7 times 9? 8 times
9? 9 times 9? 10 times 9?
10. Three times 9 caps are how many caps? 5
times 9 caps? 7 times 9 caps? 9 times 9 caps? 8
times 9 caps? 6 times 9 caps? 4 times 9 caps?
Mow niany are
1 time 9? 9
2 times 9? 9 9
3 times 9? 9 9 9
4 times 9? 9 9 9 9
5 times 9? 99999
6 times 9? 999999
7 times 9? 9999999
8 times 9?... 99999999
9 times 9?. .999999999
10 times 9?. 9999999999
11. How many are 3 times 9? 5 times 9? 2 times
9? 8 times 9? 6 times 9? 4 times 9? 10 times
9? 7 times 9? 9 times 9?
12. How many are 4 times 9? 9 times 4? 6 times
9? 9 times 6? 5 times 9? 9 times 5? 7 times 9?
9 times 7? 8 times 9? 9 times 8?
13. Six times 7 are how many? 6 times 8? 7
times 8? 8 times 9? 8 times 4? 6 times 6? 6
times 9? 9 times 9?
14. How many 9's in 18? 27? 45? 54? 36?
63? 72? 90? 81?
(1)
Multiply 9
By . . . 8
(2)
EX
EXERCISES.
(3)
9
4
(■») (5)
9 9
1 2
(6)
9
7
(7)
9
. 6
(8)
9
8
(9)
9
0
PRIMARY ARITHMETIC. 113
(1)
(2)
(3)
(^)
(5)
(6)
(7)
(8)
(9)
Multiply
5
4
3
G
r
2
8
9
G
By . . .
9
_9
9
_9
9
9
9
9
9
(1)
(2)
(3)
(-1)
(o)
(6)
Multiply
92
93
95
91
96
97
By . .-.
7
8
6
5
3
4
(1)
(2)
(3)
(^)
(5)
(6)
Multiply
91
93
92
91
96
95
By . /.
17
IG
15
14
13
12
ORAL EXERCISES.
1. Heniy has copied 3 columns of figures on his
slate, and each cohmni contains 9 figures : how many
figures has he copied in all?
2. A hunter shot 9 quails, and
saw 4 times as many as he shot:
how many quails did he see ?
3. How many melons in 6 baskets,
if each basket contain 9 melons ?
4. If a w^indow has 9 panes of glass, how many
panes are there in 7 windows?
5. If one copy-bcx)k contain 9 sheets of paper, how
many sheets will it take to make 10 copy-books?
6. A cow gives 9 quarts of milk a day : how many
quarts of milk will she give in 8 days ?
7. What will 5 hogs cost, at 9 dollars apiece?
8. What will 9 combs cost, at 9 cents apiece?
9. "What will be tlie cost of 8 yards of muslin, at
9 cents a yard?
P. A. 8.
114
PRIMARY ARITHMETIC.
WRITTEN EXERCISES.
Copy and complete these tables;
(1)
(2)
(3)
(4)
(5)
9X1 =
9X3
3X9
3 + 9
12 — 9
9X2 =
9X5
5X9
5 + 9
14 — 9
9X3 =
9X7
7X9
7 + 9
16 — 9
9X4 =
9X9
9X9
9 + 9
18 — 9
9X5 =
9X1
1X9
1 + 9
17 — 9
9X6 =
9X2
2X9
2 + 9
16 — 9
9X7 =
9X6
4X9
4 + 9
13 — 9
9X8 =
9X8
6X9
6 + 9
15 — 9
9X9 =
9X4
8X9 ,
8 + 9
11 — 9
ORAL EXERCISES.
1. How many pears are 2 times 10 pears? 3 times
10 pears? 4 times 10 pears? 5 times 10 pears?
2. How many cents are 3 times 10 cents ? 5 times
10 cents? 4 times 10 cents? 2 times 10 cents?
3. How many are 2 times 10? 3 times 10? 4
times 10? 5 times 10?
4. How many are 6 times 10 shells? 7 times 10
shells? 8 times 10 shells? 9 times 10 shells? 10
times 10 shells? 5 times 10 shells?
5. Six times 10 nuts are how many nuts ? 8 times
PRIMARY ARITHMKTIC.
lU
10 nuts? 7 times 10 nuts? 9 times 10 nuts? 10
times 10 nuts? 5 times 10 nuts?
6. How many are 6 times 10? 8 times 10? 9
times 10? 10 times 10?
Sow many are
1 time 10?
2 times 10?
3 times 10?
4 times 10?
5 times 10?
6 times 10?
7 times 10?
8 times 10?
9 times 10?
10 times 10?
7. How many are 3 times 10? 6 times 10? 5
times 10? 8 times 10? 7 times 10? 4 times 10?
9 times 10? 10 times 10?
Tow many
are
10 times
1?
10 times
2?
10 times
3?
10 times
4?
10 times
5?
10 times
0?
10 times
7?
10 times
8?
10 times
9?
10 times
10?
WRITTEN EXERCISES.
Multiply
By . . .
(1)
25
22
(2)
33
22
(3)
14
22
(4)
17
33
(5)
20
34
(6)
15
25
Multiply
By . .
(1)
22
23
(2)
25
33
(3)
34
15
(4)
44
13
(5)
18
18
(6)
17
17
REVIEW.
1. How many are 2 times 5? 3 times 2? 3 times
4? 2 times 7? 4 times 5?
2. How many are 3 times 8? 6 times 5? 3 times
10? 7 times 4? 6 times 4? 7 times 5?
116 PRIMARY ARITHMETIC.
3. How many are 5 times 6? 4 times 7? 7 times
6? 5 times 4? 8 times 6? 8 times 7? 7 times 2?
6 times 9 ? 9 times 6 ?
4. How many are 5 times 7? 6 times 8? 10 times
6 ? 7 times 9 ? 5 times 8 ? 6 times 7 ? 10 times 7 ?
5 times 9? 8 times 9?
5. How many are 3 times 7? 7 times 4? 9 times
3? 6 times 5? 8 times 2? 7 times 5? 6 times 7?
7 times 8? 8 times 7? 5 times 7?
6. How many are 4 times 6? 6 times 9? 9 times
7? 8 times 5? 7 times 3? 9 times 8?
7. How many are 2 times 6 ? 8 times 7 ? 7 times
6 ? 9 times 9 ? 7 times 9 ? 10 times 5 ? 8 times 8 ?
7 times 10? 8 times 9?
8. How many are 2 times 2? 3 times 2? 4 times
2? 3 times 3? 5 times 2? 4 times 3? 7 times 2?
6 times 3? 4 times 4? 9 times 2?
9. How many are 8 times 4? 3 times 7? 8 times
3 ? 5 times 3 ? 9 times 3 ? 7 times 4 ? 10 times 4 ?
8 times 4? 6 times 4?
10. How many are 5 times 5? 9 times 4? 4 times
10? 7 times 6? 9 times 5? 8 times 6?
11. How many are 7 times 7? 10 times 5? 9
times 6? 4 times 5? 8 times 7? 5 times 9? 9
times 7? 8 times 8?
12. How many are 4 times 7? 9 times 8? 8
times 9? 9 times 7? 7 times 9? 9 times 10?
10 times 9? 10 times 10?
13. How many are 5 times 8? 7 times 8? 9
times 8? 8 times 8? 6 times 8?
PRIMARY ARITHMETIC. 117
REVIEW.
I. An ox has 2 horns; how many horns have 5
en? How many have 3 oxen? 6 oxen?
2. A bird has 2 wings : how
many wings have 6 birds?
8 birds? 10 birds?
3. There are 3 seats in a
stage-coach, and 3 men are
sitting on each seat : how
many men in the coach?
4. There are 3 feet in a yard : how many feet are
there in 10 yards?
5. How many cherries in 8 bunches, if each bunch
has 3 cherries?
G. If John read 4 chapters a day, how many chap-
ters will he read in 7 days?
7. If you give 4 marbles to each of 8 boys, how
many marbles will you give to all ?
8. An orchard contains 4 rows of trees, and each
row has 8 trees : how many trees in the orchard ?
9. Edward attends school 5 days each week: how
many days will he attend school in 6 weeks?
10. A stranger gave 7 boys 5 cents each: how
many cents did he give to all?
II. A house has 7 windows, and each window has
8 panes of glass : how many panes of glass in the
house ?
118 PRIMARY ARITHMETIC.
12. Frank has 6 rows of blocks, and each row con-
tains 7 blocks: how many blocks has he?
13. What will 2 bunches of grapes
cost, at 8 cents a bunch ? 4 bunches?
6 bunches ? 3 bunches ?
14. Joseph writes 10 lines each
day: how many lines will he write
in 6 days? In 5 days? In 7 days?
15. What will 10 slates cost, at 8 cents apiece?
16. If a man work 8 hours a day, how many houi*3
will he work in 6 days?
17. There are 10 lines on a page of Ellen's primer,
and each line contains 9 words : how many words on
the page?
18. If it take 9 steps to cross a room once, how
many steps will it take to cross the room 9 times?
19. A railway train runs 10 miles an hour: how
many miles will it run in 9 hours?
20. An orchard contains 10 rows of trees, and each
row contains 7 trees: how many trees in the orchard?
21. What will 8 loads of wood cost, at 5 dollars a
load? At 3 dollars a load?
22. If a man earn 9 dollars a week, how many
dollars will he earn in 7 weeks?
Mtiltiplication is the process of taking a number
one or more times.
The result obtained by multiplying one number by
another is called the Product.
PRIMARY ARITHMETIC. 119
3uiBSSOM
£.x:kix.
REVIEW,
(1)
8
7
(2)
18
7
(3)
7
6
(4)
17
_6
(5)
24
3
(6)
16
5
(7)
16
6
(8)
18
9
(9)
27
_4
(10)
36
_5
(11)
47
3
(12)
38
6
(13)
45
8
(14)
34
9
(15)
56
_7
(16)
27
8
(17)
24
12
(18)
33
13
(19)
43
15
(20)
50
16
(21)
60
14
(22)
30
28
(23)
70
17
(24)
50
18
(25)
23
23
<2G)
36
27
(27)
44
21
(28)
27
27
(29)
36
25
(30)
44
23
(31)
55
17
(32)
28
33
(33)
1 205
' 1 3
(34)
304
2
(.35)
107
6
(36)
109
8
(37)
106
5
(38)
108
4
(39)
103
7
(40)
108
9
;
' (41)
21
30
(42)
24
40
(43)
15
50
(44)
27
20
(45)
16
60
(46)
17
40
(47)
24
30
(48)
30
30
(49)
40
20
(50)
50
10
(51)
17
50
(52)
14
70
(53)
19
50
(54)
18
40
(55)
25
20
(56)
33
30
(57)
44
20
(58)
28
30
(59)
17
50
(60)
16
60
(61)
13
70
120
PRIMARY ARITHMETIC.
DIVISION.
ORAL EXERCISES.
1. Here is »a gay winter scene. How many sleighs
are in sight? How many times 1 sleigh are 2 sleighs?
2. How many boys are putting on their skates? How
many times 1 boy are 4 boys?
3. How many boys are coasting? How many times
1 boy are 7 boys?
4. How many times is 1 sled contained in 4 sleds?
1 sled in 6 sleds? 1 sled in 7 sleds?
PRIMARY ARITHMETIC.
121
5. How many times is 1 skate contained in 8 skates?
1 skate in 9 skates?
6. How many times is 1 contained in 2? 1 in 4?
1 in 6 ? 1 in 8 ? 1 in 7 ? 1 in 9 ? 1 in 10 ?
ooXXc
} inaii
1/ times
1 are
1?
1 are
2?
1 are
3?
1 are
4?
1 are
5?
1 are
6?
1 are
7?
1 are
8?
1 are
9?
1 are 10?
Bow
1
1
1
1
1
1
1
1
1
ninny times
in 1?
2?
3?
4?
5?
6?
7?
8?
9?
1 in 10?
To Teachers. — These two tables should be recited together,
thus : Once 1 isl: 1 in 1 once. Tiro times 1 are 2 : 1 m 2 hco times.
Three times 1 are 3: 1 in 3 three times, etc. The subsequent tables
should be recited in the same manner.
Division is here treated as the inverse of multiplication, but
it may also be derived from subtraction, 4 is contained in 12
as many times as 4 can be taken from 12.
At this point pupils may be taught the division of a material
unit into halves, thirds, fourths, etc. They may also be taught
to add and subtract halves, thirds, fourths, etc., and to find the
fractional part of small numbers.
ORAL EXERCISES.
1. How many times 2 horses are 4 horses? How
many times 2 sleds are 4 sleds ?
2. How many persons in each sleigh? (See picture.)
How many times 2 persons are 6 persons?
How many times is 2 contained in 2? 2in4? 2iii
6? 2 in 8?
122
PRIMARY ARITHMETIC.
3. Howmany times 2 blocks make 10 blocks? How
manv times are 2 blocks contained in 10 blocks?
4. How many times are 2 marbles contained in 10
marbles? 2 marbles in 12 marbles?
How many times is 2 contained in 10? 2 in 12?
5. How many times 2 grape-clusters make 14
grape-clusters? 16 grape-clusters?
6. How many times are 2 clusters contained in 14
clusters? 2 clusters in 16 clusters?
How many times is 2 contained in 14? 2 in 16?
7. How many times 2 boys make 18 boys? How
many times are 2 boys contained in 18 boys?
8, How many times are 2 men contained in 18
men? 2 men in 20 men?
How many times is 2 contained in 18? 2 in 20?
3>«<C
w man
1/ times
2 are
2?
2 are
4?
2 are
6?
2 are
8?
2 are
10?
2 are
12?
2 are
14?
2 are
16?
2 are
18?
2 arc
20?
Jlotv tnnny times
2 in 2?
2 in 4?
2 in 6?
2 in 8?
2 in 10?
2 in 12?
2 in 14?
2 in 16?
2 in 18?
2 in 20?
PRIMARY ARITHMETIC.
123
9. How many times 2 make 4? 6? 10? 14?
12? 16? 20? 18?
10. How many times is 2 contained in 4? 2 in 6?
2 in 10? 2 in 8? 2 in 14? 2 in 20?
11. How many times is 2 contained in 12? 2 in
16? 2 in 14? 2 in 18?
12. How many times is 1 contained in 8? 2 in 8?
1 in 12? 2 in 12? 1 in 14? 2 in 14?
WRITTEN ]
EXERCISES.
I.Divide 12 by 2, thus: 2)12
Copy and
complete :
QAns.
(1)
(2)
(2)
(3) (4)
(5) (C)
2-
-2 =
o • 2
6^2
10^2
2)8
2)6 2)10
2)14 2)16
4-
6-
_ 9
8-
-2 =
14-2
(7)
(8) (9)
(10) (11)
10-
-2 =
18-^2
2)12
2)18 2)20
2j22 2i24
12-
-2 =
8^2
—
— —
— —
14-
-2 =
4-^2
16-
- 2 ^=
12 --2
(12)
(13) (14)
(15) (16)
18-
-2t==
16-^2
2)28
2)42 2j82
2)62 2)44
20-
r-2 =
20-^2
ORAL EXERCISES.
% 666 M6
1. How many times 3 pears make 6 pears? 9
pears? 12 pears?
2. How many times are 3 pears contained in 6
pears? 3 pears in 9 pears? 3 pears in 12 pears?
How many times is 3 contained in 6? 3 in 9?
124
PRIMARY ARITHMETIC.
3. How many times 3 oak leaves make 15 oak
leaves? 18 oak leaves?
4. How many times are 3 acorns contained in 15
acorns? 3 acorns in 18 acorns?
How many times is 3 contained in 15? 3 in 18?
5. How many times 3 nuts make 21 nuts? 24
nuts? 27 nuts? 30 nuts?
6. How many times are 3 balls contained in 21
balls? 3 balls in 15 balls? 3 balls in 27 balls?
3 balls in 24 balls?
7. How many times are 3 cents contained in 24
cents? 3 cents in 30 cents? 3 cents in 27 cents?
3 cents in 21 cents?
Motv ninny times
3 are 3?
3 are 6?
3 are 9?
3 are 12?
3 are 15?
3 are 18?
3 are 21?
3 are 24?
3 are 27?
3 are 30?
Hoiv many times
3 in 8?
3 in 6?
3 in 9?
3 in 12?
3 in 15?
3 in 18?
3 in 21?
3 in 24?
3 in 27?
3 in 30?
8. How many 3's in 6? 12? 18? 24? 30?
9. How many times is 3 contained in 9? 3 in 15?
3 in 6? 3 in 12? 3 in 18? 3 in 24? 3 in 27?
3 in 21? 3 in 30?
10. How many times is 2 contained in 12? 3 in
12? 2 in 18? 3 in 18? 2 in 16?
PRIMARY ARITHMETIC.
125
ORAL EXERCISES.
1. It takes 2 boots to make a pair : how manj
pair of boots will 6 boots make?
2. Two clucks make a pair :
how many pair will 10 ducks
make ?
3. How many peaches at 2
cents each can you buy for
20 cents?
4. If John step 2 feet at a
time, how many steps must he take to go 16 feet?
5. There are 3 feet in a yard: how many yards
are there in 18 feet?
6. If a man walk 3 miles an hour, how many
hours will it take him to walk 27 miles?
7. How many sheep at 3 dollars a head can be
boui^h
t for 24 dolla]
WI
^S?
^
IITTEX
EXERCISES.
0)
(2)
3)15
(3)
3)21
(4)
3)18
Copy and
(1)
complete :
(2)
(0)
8)G
(6)
3)12
(T)
3)21
(8)
3)30
3-^3 =
6-!-3 =
9-4-3 =
12-3 =
6-3
12-4-3
18-3
9^3
(9)
3)15
(10)
3)27
(11)
3)33
(12)
3)36
15-^^3 =
18^3 =
21 --3 =
15 -V- 3
21-3
30-^3
(13)
3)G6
(14)
3)99
(15)
3)63
(16)
3)69
24-^-3 =
27 --3 =
30-^3 =
24 -f- 3
27^3
3-^3
126
PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. Here are 8 rabbits in 2 groups. 8 rabbits are
how many times 4 rabbits?
2. How many times are 4 ducks contained in 4
ducks? 4 ducks in 8 ducks?
How many times is 4 contained in 4? 4 in 8?
3. How many times 4 quails make 12 quails? 16
quails? 20 quails?
4. How many times are 4 pigeons contained in 12
pigeons? 4 pigeons in 16 pigeons?
How many times is 4 contained in 12? 4 in 16?
5. How many times 4 keys are there in 20 keys?
In 24 keys? In 28 keys?
How many times is 4 contained in 20? 4 in 24?
4 in 28?
6. How many times 4 boys make 28 boys? 32
boys? 3Gboys? 40 boys?
7. How many times is 4 contained in 28? 4 in
32? 4 in 30? 4 in 40?
8. How many times are J^^^^^^Kiined in 8
pages? 4 pages in 2^^^]^^^^^^^^^ in 16 pages?
PRIMARY ARITHMETIC.
127
4 pages in 28 pages'
in 24 pages?
Jlott: inatiy times
4 are 4?
4 are 8 ?
4 are 12?
4 are 16?
4 are 20?
4 are 24?
4 are 28?
4 are 32?
4 are 36?
4 are 40 ?
4 pages in 12 pages ? 4 pages
<x:.'i^oo
ITotv iiinnij times
4 in 4?
in
8?
12?
16?
in 20?
in 24?
in 28?
in 32?
in 36?
4 in 40?
9. How many times is 4 contained in 12? 4 in
16? 4 in 24? 4 in 8? 4 in 20? 4 in 28? 4 in
36? 4 in 32?
10. How many times 2 in 18? 3 in 21? 4 in 40?
2 in 20? 2 in 14? 3 in 27? 3 in 18? 4 in 16?
4 in 28? 3 in 24? 3 in 30?
ORAL EXERCISi:S.
1. If 4 girls can sit on one settee, how many settees
will be required to seat 12 girls?
jffl:qgq^^ 2. A wagon has 4 wheels : how
aa^^^-^^W^-. many Avagons will 16 wheels furnish?
3. Four quarts make a gallon: how many gallons
are there in 32 quarts?
4. At 4 cents apiece, how many lemons can you
buy for 40 cents? 32 cents?
5. If a load of wood cost 4 dollars, how many
loads can be bouirht for 12 dollars?
128
PRIMARY ARITHMETIC.
6. If there be 4 trees in a row, how many rows
will 36 trees make?
7. If a man can build 4 rods offence in a day, how
long will it take him to build 40 rods of fence ?
8. There are 4 pecks in a bushel : how many bush-
els are there in 20 pecks ?
(I)
4)12
(5)
4)8_
(9)
2)44
(13)
3)36
(2)
4)20
(6)
4)28
(10)
2)66
(14)
3)66
WRITTEN EXERCISES.
(3)
4)16
4)35
(11)
2:88
(15)
3)99
(4)
4)24
Copy
(1)
4-f
(8)
8--
4)32
12 -f
16^
(12)
20 -^
2,22
24-
28^
32-
(IG)
36-^
3)39
40-4
Copy and complete
(2)
4
8 -
-4
4
12-
-3
4
18 •
-2
4
20-
-4
4
24-
-3
4
28-
-4
4
86-
-4
4
21 -
_ 3
4
40-
-4
4
20-
-2
ORAL EXERCISES.
1. How many groups of 5 tops each will 10 tops
make? 15 tops?
^^ -3^ J9^ ^^^ ^Sk .e^ ^K ^-. A^ .^
^rt fssm fe^ fsscS p=^ ^^ ^sa ^^ ^^ ^sm
2. Harry has 1 5 blocks : how many rows of 5
blocks in each will they make?
How many times is 5 contained in 5? 5 in 10?
5 in 15?
PRIMARY ARITHMETIC.
129
3. Cliarles has 25 marbles : how many groups of
6 marbles each will they make?
^ j9
^ -0
^ S}
J£i JO
jSi
Jd
.^
^©
.^^
^^
,-e-Q
^^
^ Si
4. How many times are 5 marbles contained in 25
marbles? 5 marbles in 30 marbles?
How many times is 5 contained in 25? 5 in 30?
5. A violet has 5 leaves or petals : how many vio-
lets will together have 35 petals ? 40 petals ?
G. How many times are 5 pinks contained in 35
pinks? 5 pinks in 40 pinks? 5 pinks in 45 pinks?
5 pinks in 50 pinks?
How many times i;:. 5 contained in 35? 5 in 40?
7. How many times are 5 cents contained in 20
cents? 5 cents in 30 cents? 5 cents in 25 cents?
5 ijents in 35 cents? 5 cents in 45 cents'?
o many thtics
How rnnnij limes
5 are 5?
5
in 5?
5 are 10?
5
in 10?
6 are 15?
5
in 15?
6 are 20?
/ 5
in 20?
5 are 25?
5
in 25?
5 are 30?
5
in 30?
5 are 35?
5
in 35?
5 are 40?
5
in 40?
5 are 45?
5
in 45?
5 are 50?
5
in 50?
8. How many 5's in 20? 30? 50? 45? 35? 25?
9. How many times is 5 contained in 15? 5 in 25?
5 in 35? 5 in 40? 5 in 50? 5 in 45? 5 in 20?
P. A. 9.
130
PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. Charles has 30 blocks: how many groups of 5
blocks each can he make from them?
2. If a squirrel eat 5 chestnuts a clay, how many
days will 40 chestnuts last it?
3. If a boat sail 5 miles an hour, how many hours
will it take to sail 50 miles?
4. Edward goes to school 5 days each week : in
how many weeks will he attend school 35 days?
5. How many oranges at 5 cents apiece can be
bought for 45 cents?
6. How many hours will it take a horse to travel
25 miles, if he travel 5 miles an hour?
7. At 5 cents apiece, how many pencils can l)e
bought for 35 cents?
8. How many times can you take 5 from 20? 4
from 32? 3 from 18? 4 fl^om 28? 5 from 35?
WRITTEN
EXERCISES.
(1)
(2)
(3)
(4)
Copy and
comp
let
5)15
5)25
5)30
5)45
1
—
—
—
— ■
(1)
(2
5-
-5
50^
-5
(o)
(«)
(7)
(8)
10-
-5
35 -^
-5
5)10
5)85
5)40
5)50
15-
-5
25-
-5
20-
-5
40-
-5
(9)
(10)
(11)
(12)
25-
- 5
36-
-4
4)44
4)88
3)63
3)69
30-
-5
27^
-3
— ■
—
— ■
35 -
-5
32^
-4
40-
-5
21 -r
-3
(13)
(14)
(15)
(16)
45-
-5
24-
-4
5)55
5)50
4)48
3)96
50-
-5
20 -f
-5
PRIMARY ARITHMETIC.
131
ORAL EXERCISES.
1. How many times 6 bunches of cherries make
12 bunches? 18 bunches?
2. How many times are 6 plums contained in 12
phuns ? 6 plums in 18 plums ? 6 plums in 24 plums ?
How many times 6 in 12? 6 in 18? 6 in 24?
3. Here are 30 books : how many shelves holding
6 books each, will they fill ?
4. How many times 6 books make 30 books ? 36
books? 42 books?
5. How many times 6 sheets of paper in 30 sheets ?
6 sheets in 36 sheets? 6 sheets in 42 sheets?
How many times 6 in 30? 6 in 36? 6 in 42?
6. Lucy has 48 spools : how many piles will they
make if she put 6 spools in each pile ?
7. How many times 6 spools in 48 spools? 6
spools in 54 spools? 6 spools in 60 spools?
How many times 6 in 48? 6 in 54? 6 in 60?
8. How many times are 6 dimes contained in 18
dimes? 6 dimes in 30 dimes? 6 dimes in 42 dimes?
6 dimes in 54 dimes? 6 dimes in 48 dimes?
132
PRIMARY ARITHMETIC.
Hotv inauy times
6 are 6?
6 are 12?
6 are 18?
C are 24?
6 are 30?
6 are 36?
6 are 42?
6 are 48?
6 are 54?
6 are 60?
JIow many times
6 in 6?
6 in 12?
6 in 18?
6 in 24?
6 in 30?
6 in 36?
6 in 42?
6 in 48?
6 in 54?
6 in 60?
9. How many times 6 are 12? 30? 42? 54? 36?
10. How many times is 6 contained in 30? 6 in
24? 6 in 42? 6 in 54? 6 in 60? 6 in 48?
11. How many times is 4 contained in 24? 3 in
24? 6 in 24? 5 in 30? 6 in 30? 4 in 36?
ORAL EXERCISES.
1. If a column contain 6 words^ how many col-
umns will contain 12 words?
2. If a cart have 6 stakes,
how many carts will 18 stakes
supply ?
3. If a window contain 6
panes of glass, how many win-
dows will contain 30 panes
of glass ?
4. An orchard contains 48 trees, and has 6 trees In
each row : how many rows of trees in the orchard ?
5. At 6 cents apiece, how many lead-pencils can
be boudit for 42 cents?
PRIMARY ARITHMETIC.
1 oo
loo
6. Joseph writes 6 lines a day : how many days
will it take him to write 60 lines ?
7. A farmer bought 48 young j3each trees: how
many rows will they make if he set 6 trees in a row?
8. How many sheep, at 6 dollars a head, can be
bought for 54 dollars?
9. How many times can you take 5 from 25? 4
from 24? 3 from 18? 6 from 18?
WRITTEN
EXERCISES.
(1)
(2)
(3)
(4)
Copy and
complet
6)12
6)24
6)36
6)48
X
(1)
6--6
(2)
54 --6
(5)
(6)
(■)
(8)
12^6
42^6
6)54
6)66
6)90
6)60
18^6
45-5
24-4-6
36 --4
(9)
(10)
(11)
(12)
30 --6
50 --5
4)48
4)84
4)88
3)69
36 -:- 6
35 --5
42 --6
48^6
27 --3
24-4-4
(13)
(14)
(13)
(16)
54^6
32 -H 4
6)72
6,84
6;96
6)78
60-^6
30-4-5
ORAL EXERCISES.
1. If each nest contain 7 eggs, how many nests
will contain 14 eggs? 21 eggs?
2. How many times are 7 nuts contained in 14
nuts? 7 nuts in 21 nuts? 7 nuts in 28 nuts?
How many times 7 in 14? 7 in 21? 7 in 28?
134
PRIMARY ARITHMETIC.
3. This pretty leaf has 7 points. How many times
7 points malve 35 points? 42 points?
^ m
4. How many times are 7 leaves contained in 35
leaves? 7 leaves in 42 leaves?
How many times is 7 contained in 35? 7 in 42?
5. Charles has 49 cherries, and he wishes to put
them up in bunches of 7 cherries each to sell : how
many bunches will they make?
6. How many times are 7 cherries contained in 49
cherries? 7 cherries in 56 cherries? 7 cherries in
63 cherries? 7 cherries in 70 cherries?
7. How many times is 7 contained in 49? 7 in
56? 7 in 63? 7 in 70?
How many times
Hoiv many times
7 are
7?
7
in 7?
7 are
14?
7
in 14?
7 are
21?
7
in 21?
7 are
28?
7
in 28?
7 are
35?
7
in 35?
7 are
42?
7
in 42?
7 are
49?
7
in 49?
7 are
56?
7
in 56?
7 are
63?
7
in 63?
7 are
70?
7
in 70?
8. How many times 7 are 14? 28? 42? 56?
49? 70?
9. How many times is 7 contained in 21? 7 in
35? 7 in 56? 7 in 28? 7 in 63? 7 in 14?
PRIMARY ARITHMETIC.
135
ORAL EXERCISES.
1. How many bunches of 7 cherries each will 14
cherries make?
2. How many quarts of milk, at 7 cents a quart, can
be bought far 21 cents?
3. There are 7 days in one week : how many weeks
are there in 28 clays?
4. A horse travels 7 miles an hour: how many
hours will it take him to travel 42 miles?
5. Frank has 35 blocks : how many rows will they
make if he place 7 blocks in each row ?
6. At 7 cents apiece, how many melons can be
bought for 42 cents ?
7. If 7 words make a line, how many lines will 70
words make? 77 words?
8. IIow many settees will seat 49 boys, if each
settee seat 7 boys?
WRITTEN EXERCISES.
(1)
7)28
(5)
7)84
(9)
7)147
(2)
7)42
(6)
7)77
(3)
7)56
(7)
7)91
(10) (U)
7)217 7)357
(4)
7)63
(8)
7)98
(12)
7)497
(13) (14) (15) (16)
7)154 7)161 7)175 7)182
Copy and complete
7 -^ 7
36 --6
14 -f- 7
48-^8
35-^7
42-6
42 -f- 7
45 -^ 5
28-^7
28-4
21-7
30-6
49-^7
40 — 5
63^7
27 — 3
56-^7
36-^4
70^7
54-6
136
PRIMARY ARITHMETIC.
ORAL EXERCISES.
1. How many times 8 fingers make 16 fingers?
24 fingers?
32 finders?
40 fingers?
2. How many times are 8 trees contained in 16
trees? 8 trees in 24 trees? 8 trees in 32 trees?
3. How many times is 8 contained in 16? 8 in
24? 8 in 32? ' 8 in 40?
4. Here are 48 apples : bow many plates will they
fill if each plate hold 8 apples?
5. How many times 8 apples in 48 apples? In 56
apples? 64 apples? 72 apples? 80 apples?
<x,>«Koo
V many times
Jloiv many times
8 are
8?
8 in 8?
8 are
16?
8 in 16?
8 are
24?
8 in 24?
8 are
32?
8 in 32?
8 are
40?
8 in 40?
8 are
48?
8 in 48?
8 are
50?
8 in 56?
8 arc
64?
8 in "64?
8 are
72?
8 in 72?
8 are
80?
8 in 80?
6. How many times 8 are 16? 32? 48? 56?
40? 64? 80? 72?
7. How many times 8 in 24? 8 in 16? 8 in 32?
8 in 40? 8 in 56? 8 in 72? 8 in 64?
PRIMARY ARITHMETIC. 137
ORAL EXERCISES.
1. If 8 panes of glass will fill one window, how
many windows will 24 panes fill?
2. If a railroad car has 8 wheels, how many cars
will 40 wheels supply?
3. If a horse travel 8 miles an hour, in how many
hours will it travel oQ miles?
4. How many days will it take a man to work 48
hours, if he work 8 hours a day?
5. At 8 cents apiece, how many slates can be
bought :
for 80 c(
-nts ?
WRITTEN EXERCISES.
(1)
8)24
(2)
8)40
(3) (4) (5)
8)64 8)72 8)88
(6)
8)96
(7)
8)192
(8)
8)120
(9)
8)168
(10) (11)
8)248 8)208
(12)
8)272
(13)
8)264
(14)
7)147
(15)
7)154
(16) (17)
7)112 7)301
(18)
7)245
(19)
7)252
■-'»-T«o^;<'ito<v>£-« — -
ORAL EXERCISES.
1. How many times 9 crovv'ns make 18 crowns?
J crowiis? 36 crowns? 45 crowns?
How many times is 9 contained in 27? 9 in 45?
138
PRIMARY ARITHMETIC.
2. Harry has gathered 54 acorns : how many piles
of 9 acorns each will they make ?
3.
each
4.
nuts
^s^ -^^ '•^m ^^ -^^ -^^
How many palm trees will bear 72 leaves, if
tree bear 9 leaves?
How many times are 9 nuts contained in 63
? 9 nuts in 72 nuts? 9 nuts in 81 nuts?
JIoiv inatiy times
9 are 9?
9 are 18?
9 are 27?
9 are 36?
9 are 45?
9 are 54?
9 are 63?
9 are 72?
9 are 81?
9 are 90?
5. How many times 9 are 18? 36? 27? 72?
63? 54? 45? 81?
6. How many times is 9 contained in 27?
45? 9 in 81? 9 in 36? 9 in 54? 9 in 63?
Sow mnny tltnes
9
in
9?
9
in
18?
9
in
27?
9
in
36?
9
in
45?
9
in
54?
9
in
63?
9
in
72?
9
in
81?
9
in
90?
Hoic man
y times
Sow niai
y times
10 are
10?
10 in
10?
10 are
20?
10 in
20?
10 are
30?
10 in
30?
10 are
40?
10 in
40?
10 are
50?
10 in
50?
10 are
60?
10 in
60?
10 are
70?
10 in
70?
10 are
80?
10 in
80?
10 are
90?
10 in
90?
10 are
100?
10 in
100?
in
7. How many times is 10 contained in 70? 10 in
50? 10 in 80? 10 in 60? 10 in 90?
PRIMARY ARITHMETIC. 139
ORAL EXERCISES.
1. If a copy-book contain 9 sheets of paper, how
many copy-books will 27 sheets of paper make?
2. If 9 words fill a line, how many lines will 45
words fill? 36 words?
3. If a train of cars run 9 miles an hour, in how
many hours will it run 90 miles?
4. If 9 melons fill a basket, how many baskets will
63 melons fill ?
5. If a pupil write 9 lines a day, how many days
will it take him to write 54 lines?
WRITTEN EXERCISES.
(1) (2) (3) (4) (5) (6) (7)
9)54 9)72 9)81 9)45 9)90 9)108 9)117
(8) (9) (10) (11) (12)
9)180 9)288 9)225 9)396 9)-549
(13) (14) (15) (16) (17) (18)
10)70 10)90 10)60 10)200 10)500 10)400
(19) (20) (21) (22) (23) (24)
10)250 10)360 10)480 10)570 10)430 10)270
3L.BSSOM i^:k:k5Cxx.
REVIEW.
1. There are 3 feet in a yard: how many yards are
there in 30 feet?
2. If Mary read 4 chapters a day, in how many
days will she read 32 chapters?
140 PRIMARY ARITHMETIC.
3. There are 7 clays in a week : how many weeks
are there in 70 days?
4. Willis picked 72 cherries, and tied them up in
bunches of 8 cherries each : how many bunches did
they make?
5. There are 8 quarts in a peck : how many pecks
are there in 56 quarts?
6. At 9 cents a bushel, how many bushels of coal
can be bought lor 90 cents ?
7. If a steamer sail 9 miles an hour, how long
will it be in sailing 63 miles?
8. At 10 dollars a barrel, how many barrels of
flour can be bought for 70 dollars?
Division is the process of finding how many times
one number is contained in another.
The result obtained by dividing one number by
another is called the Quotient.
WRITTEN
EXERCISES.
(1)
2)118
(2)
2)676
(3)
3)588
(^)
3)231
(5)
4)872
(6)
4)804
(7)
5)450
(8)
5)665
(9)
5)725
(10)
6)174
(11)
6)906
(12)
6)474
(13)
7)231
(14)
7)266
(15)
7)476
(16)
7)189
(17)
7)329
(18)
7)840
(19)
8)272
(20)
8)408
(21)
8)512
(22)
8)328
(23)
8)504
(24)
8)960
(25)
9)279
(26)
9)396
(27)
9)477-
(28)
9)648
(29)
9)864
(30)
9)387
PRIMARY ARITHMETIC. 141
GE^fERAL REVIEW.
ORAL EXERCISES.
Study and recite these examples across the page, thus : 2 and
7 are 9; 2 from 9 leaves 7; 2 times 7 are 14 ; 2 in 14, 7 times.
1.
2 and 7?
2 from 9? 2 times 7?
2 in 14?
2.
3 and 9?
3 from 12? 3 times 9?
3 in 27?
3.
4 and 8?
4 from 12? 4 times 8?
4 in 32?
4.
5 and 7?
5 from 12? 5 times 7?
5 in 35?
5.
6 and 9?
6 from 15? 6 times 9?
6 in 54?
6.
7 and 8?
7 from 15? 7 times 8?
7 in 56?
7.
7 and 4?
7 from 11? 7 times 4?
7 in 28?
8.
8 and 6?
8 from 14? 8 times 6?
8 in 48?
9.
8 and 7?
8 from 15? 8 times 7?
8 in 56?
10.
9 and 5?
9 from 14? 9 times 5?
9 in 45?
11.
9 and 7?
9 from 16? 9 times 7?
9 in 63?
WRITTEN EXERCISES.
(1) (2)
(3) (4) (5) (6)
(7) (S)
2 24
48 64 121 135
233 450
3 35
64 43 132 144
246 108
4 46
77 57 140 155
328 200
5 55
39 46 135 166
344 306
-6 24
48 68 124 177
422 437
7 43
56 39 155 188
346 330
8 66
66 47 166 199
166 149
Add 9 27 44 84 143 145 222 128
(9)
(10)
(11)
(12)
(13)
(H)
(15)
I 407
564
640
702
506
547
603
289
347
518
486
389
388
486
142 PRIMARY ARITHMETIC.
(16)
(17)
(18)
(19)
(20)
(21)
ultiply 270
345
383
209
460
244
y . . . 3
6
4
6
5
7
(22) (23) (24) (25) (26) (27)
Divide: 3)408 4)760 5)565 6)876 7)945 8)904
]bBSSaM
XCI.
ORAL EXERCISES.
1.
2 and 9?
2 from 11?
2 times 9?
2
m 18?
2.
Sand 8?
3 from 11?
3 times 8?
3
m 24?
3.
4 and 7?
4 from 11?
4 times 7?
4
m 28?
4.
5 and 9?
5 from 14?
5 times 9?
5
m 45?
5.
6 and 8?
6 from 14?
6 times 8?
6
m 48?
6.
6 and 7?
6 from 13?
6 times 7 ?
6
m42?
7.
7 and 9?
7 from 16?
7 times 9?
7
m 63?
8.
8 and 6?
8 from 14?
8 times 6?
8
m48?
9.
9 and 8?
9 from 17?
9 times 8?
9
m 72?
10.
9 and 9?
9 from 18?
9 times 9?
9]
m 81?
WRITTEN EXERCISES.
1. Add 234, 275, 366, and 484.
2. Add 244, 412, 561, 308, and 445.
3. Add 327, 303, 482, 206, 409, and 292.
4. From 865 subtract 336.
5. From 642 subtract 516.
6. From 736 subtract 345.
7. Multiply 241 by 4, and 5.
8. Multiply 165 by 3, 4, and 6.
9. Multiply 250 by 4, 5, and 6.
10. Divide 248 by 2, 4, and 8.
PRIMARY ARITHMETIC. 143
11. Divide 512 by 4, 8, and 2.
12. Divide 864 by 3, 6, and 9.
13. Divide 492 by 3, 4, and 6.
14. What is the sum of 486 and 237?
15. What is the difference between 486 and 237?
16. What is the product of 348 multiplied by 6?
17. What is the quotient of 348 divided by 6?
ORAL EXERCISES.
1. William bought 8 marbles^ and Edward gave
him 6: how many marbles had he then?
2. A cooper made 15 barrels, and sold 7 of them:
how many had he left?
3. Sarah found 12 eggs, and Kate found 9: how
many eggs did both find?
4. Albert has 21 plums : if he give 8 of them to
Alice, how many plums will he have left?
5. There are 7 days in a week : how many days
are there in 9 weeks?
6. There are 8 quarts in one peck: how many
quarts in 10 pecks? In 8 pecks?
7. If a man earn 8 dollars a week, in how many
weeks will he earn 64 dollars?
8. If a cord of wood cost 5 dollars, how many
cords can you buy for 35 dollars?
9. How long will it take a steamer to run 90 miles
at the rate of 9 miles an hour ?
144 PRIMARY ARITHMETIC.
WRITTEN EXERCISES.
1. There are 267 boys, and 289 girls in a school :
how many pupils in the school?
2. A drover bought 564 sheep, and sold 288 of
them: how many had he left?
3. A merchant had 408 yards of cloth, and sold
184 yards: how many yards had he left?
4. There are 338 apples on one tree, 467 apples
on another, and 169 apples on another: how many
apples on all the trees?
5. A miller made 467 barrels of flour, and sold
237 of them : how many barrels remain unsold ?
6. There are 320 rods in a mile : how many rods
are there in 3 miles ?
7. If a steamship can sail 290 miles in a day, how
far can it sail in 6 days?
8. There are 7 days in a week : how many weeks
are there in 427 days ?
9. If 3 bushels of apples will fill a barrel, how
many barrels will 468 bushels fill ?
10. A farmer bought 26 cows at 18 dollars a head:
how much did they cost?
11. If a man build 8 rods of fence in a day, in
how many days will he Uuikl 464 rods?
12. If a man can walk 28 miles a day, how far
can he walk in 24 days?
NEW GEOGRAPHIES,
IPTJBILISIIEID BY
wim '
.4)^ILS0N, HiNKLE &ir.O.
If ■
Oiiiciimati, O.
The Eclectic Series of (icograpliies, consistm- .1
: r'nree books, by A. ^"ON Steinwehr and D. G. Brinton;
i No. K T'/ie Primary Seograpl^y, is adapted to the -ise i
j of pupils ( omni'iiK-mg the study. The language is sim le ;
i and rlea, ; tlie dehnitii .is and descriptions art exact; tlve j
! ^,lan of r' .' book is natural and the copper- plate, maps are I '
\v«*nderfiiilv rlear and definite
No. 'I. rne iJUeraiediate Geograpliy, is intended or
lie use e, ..1' hi'^bcr classes in Graded Schools, and cGn:-iuiri;*
i th^ leading iv.j^ ':'l.s of the science, so arranged as to ^n've
• rorrect id;: ro piij)!!;, and, at the same time, recpii. less
' aid from ih.. teacher than any other book extant. T'^ '■ ' •^^'
contains full instructions in map-drawing.
No. 3, TilC SellOOl GeOj^rapliy, embraces a ful^ V[ th-
ji ematical, P.litical, and Physical description of the i^rth,
jl and is intended ,^' -^ the high^ t classes in this br.iiicb '>f
l study. The n\rps. which are li-e basis of al^ geogrp[>i i a!
|j sludy, ar^ n.odelr of clearness, '^he physical f^a'tui . l(
i'*'t^ch cr- ntrv^ a.re fully brought chU,. and it is thus mu-^e ' - ...-
sil^^e |.o 1 -cT^! Geograph\ objcctivel;
'^1'
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