i

\r

D BY M. GIBSON.

WHICH- 15 ANNKXKD AN APPENDIX, CONTAINING

.oKAXlON Ox^' SURFACES, TABLES OF FOREIGN MONEY, AND BOOK-KEEMNG.

I

SXI:i£tJt]OT^Sri»B EX>ITI01Sr.

rJCnMONl):

WEST & JOHNSTON, 145 MAIN STREET. 18G4.

iiJ

\.

THE

WILLIAM R. PERKINS LIBRARY

OF DUKE UNIVERSITY

Rare Books

A

A

THE ^-— «

\

SOUTHEllN SCHOOL ARITHMETIC;

YOUTH'S ASSISTANT.

CONTAINING

THE MOST CONCISE AND ACCURATE RULES FOR PERFORMING OPERATIONS IN

A.R I T H M E T I C,

ADAPTED TO THE EASY AND REGULAR INSTRUCTION OF YOUTH,

FOR THE USE OF SCHOOLS, Sec. By a. & J. FOWLEK,

TEACHERS OP AIIITHMETIO.

REVISED BY M. GIBSON,

TO uuicH lo A^^'^;xKD an appendix, confaining

MEWSUKA'LION On' SURFACES, TABLES OF FOREIGN MONEY, AND BOOK-KEEMNG.

E5X£l£tJBOT"YI»B EX>ITI03Sr-

PJCHMONl):

WEST & JOHNSTON, 145 MAIN STREET. 1864.

wmmamad

E.niKRKD Hccordinp lo act of Congress, in the ycm hy AitiJAH h .luBlAil FoWLKK, in tlie Clerk's C>iricc for llic Kubtcra Ditflritt of Tcnuet^soi-, ui KuoxvilK;.

J\K KSTKniD acrordiiig lo act oC Coniirosi^, in the year ]Sr;'>, by L. GiKKoRD, in the Clerk's OHict? '"ur tho E:is!riii Di.sirii't of Tennessee, of Knoxville

Ke-extbred according to act of Congress, in tlic year ISlV}, 1»y Wk»T ik. .TojiMSTON. in the Cleik's OlHcc, for llie KasJera

l>i-.iii,' (.( Vrr"iiii;i ;it Uii'lnimiiil.

KECOMMENDATIONS.

MESSRS. FOWLERS' ARITHMETIC.

This work, which was handed me some time since, for ex- amination, exhibits a degree of industry and ability highly creditable to the authors. The order of arrang^ement appears to be judicious, and the iHustrations clear and plain. The cir- cumstance that it is primarily adapted to our national currency, is, to me, one of its chief recommendations; and were no works of an opposite character introduced into our common schools, we should soon have a currency or mode of reckoning, simple, uniform, and intelligible to every one. I trust the gen- tlemen will meet with such encouragement from the public, as will more than compensate for the trouble and expense of publication. Joseph Estabrook,

President of the East Tennessee College.

Knoxville, April 29th, 1834.

MESSRS. FOWLERS' ARITHMETIC.

From a hasty examination of this work, I would say, its judi- cious arrangement, the perspicuity and conciseness of its rules, the clearness and simplicity of its illustrations, and its adaptation to our national currency, render it a desirable companion for the beginning in this important branch of education. I trust the industry and ability exhibited by its youthful authors, will meet with liberal encouragement.

Allen II. Mathes, Late Principal of the Male Acadeiny.

Madisonville, June 14th, 1834.

THE FEDERAL INSTRUCTOR ; OR. YOUTHS' ASSISTANT.

The above work, in my opinion, has considerable merit The rules appear to me, to be made plain to tlie understanding of beginners, and unadvanccd learners, in the very useful branch of knowledge on which it treats. Hope is entertained that Messrs. Fowlers', the authors of it, will be liberally rewarded for their undertaking, by the patronage of a gencrotis public.

Henry C. Saffkll, Principal of the Holston Seminary. New-Market, June 26th, 1835.

ip.-^- -. . ■ ']■'''■■ I 1 1 I

iv RECOMMENDATIONS.

Having- carefuHy examined " Fowlers' Arithmetic," I make no hesitation in saying that I fully concur with the foregoing gentlemen in opinion, with respect to the merits of the work, and cordially unite with them in recommending its introduction into our schools and academies, as well as particularly into the Tyro's Library.

JosiAH P. SniTHf Philom. Kingston, Oct, 1836.

_____ j

Messrs. Fowlers :

1 have carefully examined your Arithmetic, and must say, after twenty-five years experience as a teacher, that I have not seen a work of the kind that I would prefer before it, especially for young beginners. The shortness, simplicity, and plainness of the rules, as you have very justly remarked in your preface, must I think greatly accelerate the progress of*^ learners. I trust you will meet with the patronage of our fellow-citizens generally.

Landon Duncj^n.

Giles County, Virginia, March 15th, 1836.

Messrs. Fowlers : " ?^

Gentlemen — I have carefully examined your treatise on Arithmetic, and I think it superior to any other now in use to facilitate the progress of the young learner, and is fully ade- quate for all the common business of our country. It well merits a place in our schools and Academies, as well as in our houses. *

Michael Morris, Teacher of the EstillviUe Academy,. Estillville, Va., 13th July, 1836.

.

EXPLANATION OF CHARACTEKS, SIGNS AND SIGNIFICATIONS.

= Equal, as 100 cts. = $1.

+ More, as 4 + 2 = 6.

— Less, as 6 — 2 = 4.

X Into, with, or multiplied by, as 4 X 2 = 8.

rr By, i. c. di\'ided by, as 6 ~ 2 = 8. or 2)6(3.

: : : Proportion, as 2 ; 4 : : 6 : 12.

i/ Squai'c Root, a,s V 64 := 8.

^ Cube Root, as ^ 64 = 4.

y Fourtli Root, as V 16 = 2, &c.

JL

(V)

^

P 11 1^: FACE.

The design of the authors in brinpfinfr this work before the public is, to teach the science <»f .Auithmetic in a different and ; ! easier manner than has been customary. To attain this object, J wo have simplified the necessary rule's, thus leading the student :out of the darkness uf ignorance by a plain path, into the light iof knowledge. Tl»e shortness, simplicity and plainness of the I rules, will enable the student to advance with greater ease and I speed than those hitherto promulged.

As calculating in English money is measurably obsolete, the authors have, with but iew exceptions, employed, in this work, the legal currency of our country. Dollars and Cents, Two things among us have been but too well fitted to retard the progress of Arithmetical knowledge; calculations in pounds, shillings, pence and far tilings, a currency unknown among us, and unsuited to the transactions of our common country con- cerns; and long, complex rules, difficult to be remembered, and still more diflicult to comprehend. But, make your rules short, familiar, and easy to be understood, and the student is encouraged to pursue tiie shining path of science, thus plainly pointed out to him with alacrity and delight.

Tiiough this work may appear short, yet there are in it 1300 questions, or upwards — a sufficiency, we should think, in point of number; selected so as to be useful, and adapted to the cii-| cumstances of our country. !

Many persons wlio have ciphered for months, and some who' have gone through the Arithmetic, are at a loss because tiiey ■ do not understand, or have not paid attention to the rules, i This evil will be the more easily remedied on our system, as ; our rules are plain and short, and may, with but little labour, bel committed to memory. j

When our Saviour came into the v.orld, he was condemned,' by the Jews by asking a simple question — ocm any thing goodl come out. of ISazareth ? If any are disposed, in a similar way, ; to denounce our work, we would beg of them to examine care-j fully and candidly before they decide, and to remember, that, I as the Messiah did come out of N*^zareth, so, it is possible for a good Arithmetic to be made in Tennessee. We are, indeed, devotedly attached to this study, and as we think we have made improvements in the mode of teaching it, we have risked our all to give publicity to the book, to enable others to judge of it ^nd to profit by it.

(vi)

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CONTENTS.

P.IOK.

Numeration 9

Addition 10

Multiplication 12

Subtraction 16

Short Division 18

Long Division 20

Tables of Money, Weights and Measures 23

Compound Addition 25

Compound Multiplication , 32

Compound Subtraction ^ 38

Compound Division 43

Reduction Descending iCi

Reduction Ascending 49

Rule of Two 5^

Rule of Three 56

Double Rule of Three " 61

Practice 64

Interest 68

Brokerage 77

Discount 78

Tare ^md Tret 80

Equation ,> 83

Barter 85

Loss and Gain 87

Partnership 89

Exchange 91

Vulgar Fractions ' 97

Decimal Fractions 107

Involutions or Raising of Powers 113

Square Root ^ . . , 114

Cube Root , 117

Single Position 118

Double Position 120

AUegaticn s 121

ArithmetiEal Bx)gression 122

(7)

■ttfSSVMasszaeBai

8 CONTENTS.

Tage.

Geometrical Progression 125

Compound Interest by Decimals 127

Permutation 131

Combination • • • v 131

Duodecimals .^ 132

Promiscuous Eiamples 134

Appendix 141

Mensui-ation of Surfaces 141

Parallelogi'am, &c 141

Triangle 142

Circle .142

Elipsis , 143

Mensm-ation of Solids 144

Hewn Timber, Box, &c 144

To G-auge a Com House or Box 144

To make a Box of a given length or width to contain

a given nun^ber of bushels, &c 145

The Cylinder 146

A Vessel in the shape of a Frustrum of a Cone 147

Gauging of Casks 147

Tonnage of Flat Boats 148

Tables of Foreign Money 150

A Short Method of Counting Interest 166

lleduction of Coins 166

A Table of Interest 171

Book-Keeping 172

Form of Notes, Receipts, &c 181

AEITHMETIC.

Arithmetic is that part of the Mathematics which

teaches the art of computation by numbers. All operations

in Arithmetic are performed by means of the following

figures, viz: One 1, two 2, three 3, four 4, five 5, six 6;

I seven 7, eight 8, nine 9, cipher 0.

NUMERATION.

Numeration teaches the different value of figures by their different places, and to express any proposed numbers cither by words or charactei's ; or to read and write any sum or number.

NUMERATION TABLE.

PL,

t-i

P-. o

o

1-5

P O

ts'

0 0

P-.

CD

o

a.

I

o

One.

Twenty-one.

Three hundred 21.

Four thousand 321.

54 thousand 321.

654 thousand 321.

7 million 054 thousand 321.

87 million 654 thousand 321.

987 million 654 thousand 321.

10

ADDITION.

The preceding contains only nine digits, wliich render it sufl&cie»tly large for young students or common business, although it may be extended much farther, thus :

Quintillions. Quatrillions. TrlUions, Billions. Millions. Units.

987,654; 327,241; 278,325; 256,148; 212,563; 652,324.

addition:

The use of Addition is to ascertain the amount of two or more numbers when put together.

RULE.

1st. Set down any one of the numbers and place under j it all the rest in such a manner that units may stand under ! units, tens under tens, hundreds under hundreds, and so on^ 'and draw a line under the last.

2d. Begin at the right hand column and add together all the figures contained in that column. If it amounts to ten ' or more, set down the right hand figure and carry the left hand figure or figui-es, which add to the next line, and so ! proceed till adding the last line. Then set down the whole amount. ,

EXAMPLES.

(No. 1.) (2.) S3- m ja-

(3.)

t-' ti ^

(4.)

I-

""^

w

4 4 2 2

5 8 4 1

6 9 2 5

2 3 4

1 2 1 4 6 8

2 2 4

13 4 6

7 2 12 10 3 2

8 10 3

(5.)

2 4 6 8

17 5 5

10 2 0

12 8 0

Ans. 12 188 1047 17693 65 2i^

"*g*jgt>?.y?

ADDITION.

m

(6.) (7.) (8.) (9.)

123 2408 87561 42146

422 6273 10420 23323

631 2103 32619 13357

246 4 3 12 31427 24557

323 3102 61422 12787

1645 18258 2 2 3449 116170

(10.) (11.) (12.)

2? 256312 4621

410 80191 2300

11224 4307 96131

24795 779 1200 12

36135 2 402 12

87282 124800 900

159868 418791 223976

13. Add the following numbers, viz : 14, 16,,23, 29, 80, 31, and 100, and tell their amount. Ans. 293.

14. What is the amount of 36, 97, 125, 384, 1176 ?

Ans. 1818. *

15. Add 640, 79, 80, 100, 210, 450, 787, 21fand 2. j

Ans. 2869. '

16. John gave Joseph 33 apples; James gave him 91; Peter gave him 56 ; Joel gave him 107 ; and David gave him 95 ; how many had he ? Ans. 382. '

17. A person went to collect money, and received of one, man $542 ; of another 654; of another 550; of another 787, and of another 3405. I demand the sum collected. Ans. 5938. '

18. John owes to one man $302; to another 540; to: another 70 ; to another 2356, and to another 999. How ' much does he owe in all ? Ans. $4267. !

19. John and Charles went to collect nuts; when they^ i^d collected a quantity, sat down to count them ; when one '■ had collected 276 and the other 196, what number did both '' of them collect ? Ans. 471. '

20. Desired to purchase a suit of clothes which cost as 1 follows, viz : a coat $25, a pair of pantaloons 10^ a waiaicoati 6, a shirt 2, and a paii* of socks 1. What is the cost of the wholo? Ans. $44.

21. A butcher bottght of one man 25 hoad of cattle ; of

-au

12

MULTirLIOATION.

another 16 ; of anotber 40, aud of anotlier 9. How many did lie buy in all ? Ans. 89 head.

22. A man in buying cider received of one man 90 gal- lons; of another 200 j of another 300; of another 400, aud of another 500. How many gallons did he buy in all ?

Ans. 1490.

23. A gentleman went to purchase brandy, and bought of one man 125 gallons; of another 160; of another 190, and of another 210. ^ IIcfw much did he buy in all ?

Ans. 685 gallons.

24. A man in buying corn, received of one person 400 bushels; of another 500; of another 600, and of another 700. How many bushels did he buy in all ? Ans. 2200 bushels.

MULTIPLICATION.

When the multiplier does not exceed 12, work by

RULE I.

Set the multiplier under the right hand figure or figures of the multiplicand : then beginning with the units, multiply aU the figures of the multiplicand in succession, and set down the several products ; but if either of the products be more than §. set down its right hand figure only, and add its left hand figure or figures to the next product. The whole of the last product must be set down.

pROor. Divide the answer by the nmltiplier, and the quotient will equal the given sum.

MULTIPLICATION TABLE. The learner should commit the following tabic to memory before he proceeds further :

Twice

1 make 2

2 4

6

4

5

0

7

H

0

10

11

12

8 10 12 14

10

18 20 22 24

3 times

1 make 3

2 6

3 4 5 6 7 8 0 10 11

9 12 15 18 21 24 27 30 33 36

4 times

1 make 4

2 8

8

4

5

6

7

8

9

10

11

12

12

16 20 24 28 32 86 40 44 48

5 times

1 make 5

2 10

3

4

5

6

7

8

9

10

11

12

15

20 25 30 35 40 45 50 55 60

6 times

1 make 6

2 12

3 4 6

6

7

R

9

10

11

12

18 24 30 36 42 48 54 60 66 72

7 times

1 make 7

2 14

3

4

5

6

7

8

9

10

11

12

21

28 35 42 40 56 63 70 77- 84

JX

MULTITlitCATION.

13

8 times

1 make 8

2 16

3 34

4 32

5 40

6 48

7 56

8 64

9 72

10 80

11 88

12 96

9 times

1 make 9

2 18

3 27

4 36 5- 45

6 54

7 63

8 72

9 81

10 90

11 99

12 108

10 times

1 make 10

2 20

3 30

4 40

5 50

6 60

7 70

8 80

9 90

10 100

11 110

12 120

11 times

1 make 11

2 ^22

3 S3

4 44

5 55

6 66

7 77

8 88

9 99

10 110

11 121

12 132

12 times

1 make 12

2 24

3 36

4 48

5 60

6 72

7 84

8 . 1)6

9 108

10 120

11 132

12 144

( i.) 412 multiplicand. 2 multiplier.

^ 824 product.

(2.) Ans. 1

5498 3

(3.) 12347 4

Ans. 49388

6494

(4.) 12^49172 (

5

5.) 5

98754 6

(6.)

12345678910

7

. ., 61745860

92524

86419752370

(7.) 64115928 ( 8

8.) 21938 (9.) 9

197442

98765432144 10

■ 512927424

987654321440

(10.)

5324786 11

(11.

Ans.

) 84532911 12

Ans.

58672646

1014394932

' (12.)

148100076

3 3

9

(13.). 1 Ans. 3

50000000000

2

} Ans.

444800228

00000000000

'1 <^''-)

110008191 4

(15.) Ans.

987554321 2

J Ans.

440032764

1975108642

!i (16)

17853440 5

(17.)

1888880000 5

Anp.

89267200

Ans.

9444400000

^

2

14 MULTIPLICATION.

(18.) 1280721 (19.) 9922446688 3 4

Abb. 8692163 Ans. 39689786752

(20.) 6001150084S211

7

Ana. 420080505902477

21. Multiply 21141 by 2 Auawcr 42282

22 73211 3 219633

23 87092 4 350768

24 95698 5 478490

25 91144 6 546864

26 83456 7 584192

27 21110 8 ........ 168880 •

28 34000 9 806000

29 10056 10 100560

30 -. . 20000 11 220000

31 800510 12 9606120

When the multiplier excjeeds 12, work by

RULE n.

l^Iultiply by each figure separately. First by the one at the right hand, then by the next, and so on, placing their rebpective productH one under another, with the right hand figure of car-h produot directly under that figure of the muUipKcT by which it in produced. Add these product* together, and their amount will bo the answer.

SXAMFLKS.

(32.) 120 multiplicand. (33.) 1461

14 multiplier. 16

480 8706

120 1461

Am 1680 Ana. 23216

ir

MULTIPLICATION. 15

(34.) 124680 (35.) 468

^ 142 72

^

249360 9^»6

498720 3276

124680 ^5^

17704560

86. Multiply 4875 by 29 Answer 141375

37 11271 36 394485

38 19004 305 5796220

39 . :. :. . ; 76976 ...... .489 37641264

40. 84769 976 82734544

41 1978987 4809 9516948483

JVoie, When there are ciphers at the right of either tho multiplicand or multiplier, multiply as in the preceding case, only omitting the ciphers. Then add together the several products, and place to the right of the amount as many ciphers aa are to the right of both fiactors. -

EXAMPLES.

(42.) Multiply 400 by 200 Answer 80000 200

80000

43 8000 400 3200000

44 3700 200 740000

45 4870 2500 12175000

46 876956 990000. . . .868186440000

JSTote. When the multiplier exceeds 12, and is the exact product of any 2 factors in the multiplication table, the op^ ration may be performed thus : — Multiply the given sum by one of eaid factors, and that product by the other factor.

EXAMPLES.

(47.) MuUiply 2851 by 15 3 times 5 are 15 3

8558

Ans. 42765

SUBTRACTION.

48. Multiply 476 hy 25 Answer 11.900

49 769G 81 623376

50 8976 48 .430848

51 87698 72 6814256

52 20784 108 2244672

53 81207 182 10719324

54 47696 144 6868224

55 75687 56. ..... .. 4238472

56 ..... . .'. ; ...34075 36 1226700

PRACTICAL EXAMPLES.

57. A man has 25 stables, and in each stable there are five horses, how many has he in all ? An8. 125.

58. A man has four chests, and in each chest there are four dollars, how many dollars are there in all? Ans. 16.

59. Josiah has 30 apples, and James has six times tliat number, how many has James ? Ans. 180.

60. A man has three tracts of land, each containing 52 acres, how many acres has he in all ? Ans. 156.

61. A laborer hired himself for six years, at ^75 per year, '' how much did he receive for the six years' labor ? Ans. $450.

62. A certain potato field is 90 hills in length, and breadth 100, how many hills are there in the field? Ans. 9000.

63. A certain cornfield is 98 hills in length, aiid 10 in breaxlth, how many hills are there in the field ? * Ans. 980.

64. A man ha\'ing built a house, found he had used 18,175 bricks, how many bricks will be necessary to build 14 houses of the same size ? Ans. 254450.

SUBTRACTION.

^ Subtraction is used to- know the difference between a larger and smaller number.

RULE.

Set down the larger number first, and under it with units under units, tens under tens, the smaller. Then begin at the right hand or unit's place, and take the lower figure from the one above it, if the upper figure be more than the lower, and set down the remainder. But if the upper figure be less than the lower, add 10 to the upper figure, take the lower figure from the amount^ set down the remainder, and carry one to the next lower figure.

rnc

SUBTRACTION.

17

!|

PiiooF. Add the lower number and tte answer together, and their amount will equal the upper.

(1)

From Take

EXAMPLES.

964

, 3. 4. 5.

6; / .

8.

9. 10. 11.

Ans

From 487

875

967

1001

9705

87696

455692

1000000

10000

333 631

(2.)

841 579

Take 96

302

351

4J87

1307

10091

300120

1

9

Ans. 262

Ans. 391 573

616 514

8458

77605

155572

999999

9991

How Kany more

Ans. 20.

IIow mnny

Ans. 17.

He has now

Ans. $<)2.

had §1000, but has lent 105. How

Ans. !i?895. After I pay $69, how much will I still

Ans. $491.

12. JaiiiCR ha,s 44 apples, and John 24. has James than John ?

13. Henry has 25 marbles, and Charles 8 more has Henry than Charles ?

14. William holds Jesse's note for paid $37. How much does he still owe?

' 15. A merch;iiit much has he left?

16. I owe $560. owe?

17. A merchant had 180 yards of cloth, but sold 75. How many had he left ? Ans. 105 yds.

18. A farmer had 999 acres of land, but has given his son 500. How much has he left? Ans. 499 acres.

19. There are two piles of bricks. In tl^e greater pile there are 7896, and in tlie less 4389. How many more arc there in the greater pile than in the 'less? Ans. 3507.

20. A merchant bought 4875 bushels of wheat, out of which he sold 2976 bushels. How many bushels had he left? Ans. 1899 bushels.

21. I deposited in bank $1240. I have since taken out S1082. How much remains? Ans. $158.

22. A farmer had 5487 acres of land. He sold to A 325, to B 750, and to G 1000 acres. How many had he left?

Ans. 3412 acres.

18 8II0RT DIVISION.

23. I had 1200 pounds of pork, and sold to one ma?i 400, to another 350, and to another 125. How much was left ?

Ans. 325.

24. In a certain milk house there were 44 crocks of milk, but it so happened an unruly cat broke in and destroyed 19. How many were left? Ans. 25.

25. In a certain baiTcl are 04 gallons of wine. If 20 be di-awn out, how many will be left ? Ans. 74.

26. A ship's crew consisted of 75 men, 21 of whom died at sea. How many arrived safe in port ? Ans. 54.

27. A tree had 647 apples on it, but 158 of them fell off. How many were there then remaining on the tree ?

Ans. 489.

28. I saw 15 ladies; 8 returned back. How many passed on? Ans. 7.

29. A general had an army of 43^50 men ; 15342 of them deserted. How many remained ? Ans. 27908.

30. A man starting a journey of 950 miles. When he may have gone 348 miles, how far has he still to go?

Ans. 602 miles.

31. A trader had 655 bogs; 99 of them were stolen; 24 died of sickness; he then sold 400. How many had he left? Ans. 132.

SHORT DIVISION.

By Division we ascertain how often one number is con- tained in another. The number to be divided is called the dividend. The number to divide by is called the divisor. The number of times the dividend contains the divisor is called the quotient. If on dividing there be a remainder it is called the overplus.

RULE.

Place the divisor to 'the left of the number you wish to divide. Consider how many times the number by which you wish to divide is contained in the first figure or figures of the number to be di^'ided, and set down the result, noting whether there be any remainder. If there be no remainder, consider how often the divisor is contained in the next figure or figures; but if there be a remainder, con- ceive it to be placed to the left of the next figure; into which divide as before, and set down the result.

SHORT DIVISION.

19

Proof. Multiply the quotient by the divisor ; add in the remainder, if any. The product will equal the dividend.

EXAMPLES.

(1.) Divide 836 by 3 3)386

(3.)

(5.)

(7.)

0. 10. 11. 12. 13. 14. 15. 16.

Ans. 112 2)4681278

2340639 4)1896481

474107 -f 3 6)9654630

1609105

Divide 8767

— 9698

— 97899

— 80409

— 981021

— . 897697

— 9876978

— 4967844

(2.) Divide 448 by 2 2)448

Ans.; 224 (4.) 3)63912964

(6.)

21304321 5)863200

by

5 '6

— 7

— 8

— 9

— 10

— 11 -- 12

172640 (8.) 7)1269503450

181357635 -f 5 Answer

1753 + 2

1616 + 2

13985 + 4

10051 + 1

109002 + 3

89769 + 7

897907 + 1

413987

17. Di\T[de 336 pounds of sugar equally among 3 boys?

Ans. 112.

18. Divide 1284 pounds of cotton equally among 4 girls ?

Ans. 321.

19. Divide 8655 acres of land equally between 2 heirs ?

Ans. 4327:

20 Bought 6 horses for 318 dollars. How much did

each cost ? Aus. 53 dollars.

21. John would divide 120 ears of corn among 10 horses. What was the share of each ? Ans. 12.

22. Divide 1200 pounds of coffee among 12 womcu?

Ans. 105.

23. I would divide 8880 apples among 8 boys. What was the share of each? Ans. 1110.

^

20 LONG DIVISION.

LONG DIVIsiON.

Long Division is used when the divisor exceeds 12.

RULE.

Place the diviboi* to the left of the dividend, as in short division. Consider how often the divisor is contained in j the least number of figures into which it can be divided, and i set down the result to the right of the dividend. Multiply ;| the figures set at the right of the dividend by the divisor, and set the pi-oduct under the figure in which you con- sidered how often the divisor was contained. Subtract the product from the line above it, and set down vs^hat remains, which must always be less than the divisor. Bring down the next figure to the right of the remainder, and proceed as before, till all the figures of the dividend are brought down. When there are ciphers at the right of both factors, the operation may be shortened by cutting off an equal number of ciphers from each.

EXAMPLES.

(1.) Divisor 24)480 di^ddend. Ans. 20.

- 48

0 (2.) 25)450 Ans. 18. 25

200

,. 200

3. Divide 456 by 21 Ans. 21 Remainder 15

4. 861 19 19

5. 958 18 53 4

6. 12350 15 823 5

7. 1475 28 52 19

8. 4277 31 137 30

9. 25757 37 696 5

10. 256976 41 6267 29

11. 997816 59 16912 8

12. 4697680424 125 37581443 49

13. 9924000 54000 183 42

14. 74000000 3700 20000

LONG

15 Divide 80906000 by 180 Ans. 449477 Remainder 14

16. 555555555 55555 10000 5555

17 3875642 7898 490 5622

18 98765432 1234 80036 1008 19* • 12486240 87654 142 39372 20 57289761 7569 7569 2l' 99007765 27000 3689 4765- 22! 15463420 1600 9664 1020

PRACTICAL EXAMPLES.

23. If 18G0 pounds of beef be divided equally among 60 men, what will be the share of each? Ans. 31 pounds.

24. 4556 pounds of salt are to be equally divided among an army of 44 men. AVhat will be the share of eacli man ?

^ Ans. 103 + 24.

25. 4006 pounds of malt are to be divided equally among an 'ivmv of 84 men. What will be the share of each man y

^ Ans. 47 -1- 58.

26. 1600 bushels of corn are to be divided equally among 40 men, how much is that a piece ? Ans. 40.

• 27. A regiment consisting of 500 men are allowed 1000 pounds of pork per day. How much is each man's part ?

Ans. 2 lb.

28. If a field of 32 acres produce 1920 bushels of corn, how much is that per acre? ^ Ans. 60 bushels.

29. A prize of $25526 is to be equally divided among 100 men. What will be each man's part? Ans. 8255 + 26.

30. How many horses, at $30 per head, may be bought for $38040? Ans. 1208.

31. If a field containing 25 acres produces 37o bushels of wheat, how mmk docs one acre produce ?

Ans. 15 bushels. . 32. 96 persons are to have 480 pounds of beef divided equally among them. What is the share of each?

Ans. 5 pounds.

33. 144 men are to pay equal shares of a debt which amounts to $144000. How much must each man advance to make up the sum? Ang. $100.

34. If $2400 be equally divided among 16 persons, what will be the share of each? Ans. $150.

85. A man gave 35 reapers $385, each to have an equal I part. How much did each man receive ? Ans. Sll.

22 LONG DIVISION.

86. A man travelled 560 miles in 40 days. How far was that in one day ? Ans. 14 miles.

37. A boy hired 60 days, for which he was to receive $120. How much was one day's labor worth ? Ans. $2.

38. When I have labored 60 days for' the sum of '$180, how much is one day's labor worth at that rate ? Ans. $3.

EXAMPLES TO TRY THE STUDENT IN ORDER THAT HE MAY UNDERSTAND THE FOREGOIN(J RULES, VIZ : ADDITION, MULTIPLICATION, SUBTRACTION AND DIVISION.

39. John had 40 apples. He gave his brother 10 ; kept 10 ', and divided' the rest equally between his two sisters. How many had each sister ? Ans. 10.

40. John owes James ^50. Peter owes him $80. David owes him $105. Samuel $91. Eli $7. And Joseph $40. After James collects the above debts and pays $99, which he owes, how much will he have? " Ans. $274.

41. A farmer has three tracts of land, ejieh containing 20 acres ; buys an adjoining one of 90 acres. If he sell 40 acres, and divide the rest equally between his two sons, what will be the share of each ? ' Ans. 65.

42. A person has 50 sheep ; buys from his neighbor 50 more J he then sells 25 to the butcher. How'many has he left? ' Ans. 75.

43. A gentleman dying left $2500, to be divided as fol- lows; To his son 1500 dollai'S, and the rest equally between his two daughters. How much did each daughter receive ?

Ans. 500 dollars.

44. A person went to collect money, and received of one man 800 dollars; of another 50; of another 18; of another 440, and of another 25. After which, by gambling, he lost 103 dollars. How much had he left ? Ans. 1230 dollars.

45. Suppose a certain field be 140 hills in length, and 124 in breadth. Admit there be two stalks in every hill, and on each stalk an eai' of corn, how many bushels are there in the field, suppose 100 ears to make a bushel ?

Ans. 347 bushels + 20.

46. Bought 25 yards of fine cloth for 250 dollars. How mnch was it per yard ? Ans. 10 dollars.

47. Bought 16 loads of hay at 4 dollars per load. What did it amount to ? Ans. 64 dollars.

TABLES OF WEIGHTS AND MEASURES. 23

48. How many yards of cloth, at 6 dollars per yard, can I have for 90 dollars ? Ans. 15 yards.

49. How many pair of gloves, at 1 dollar per pair, can I have for 4 dollars ? Ans. 4.

TABLES

0£ MONEY, WEIGHTS, AND MEASURES.

FEDERAL MONEY.

The denominations are,

10 Mills (marked m.) make 1 Cent, ct.

10 Cents 1 Dime, d.

10 Dimes (or 100 cts.) . . 1 Dollar, D. or 0

* 10 Dollars 1 Eagle, E.

AVOIRDUPOIS WEIGHT.

Th*e denominations are,

16 Drams (marked dr.) make 1 Ounce, oz.

16 Ounces 1 Pound, lb.

28 Pounds 1 Quarter, qr.

4 Quarters (or 112 lbs.) . 1 Hundred weight, ewt. 20 Hundred weight ... 1 Ton, T.

TROY WEIGHT.

The denominations are,

24 Grains make 1 Pennyweight, dwt. 20 Ponnywcights ... 1 Ounce, ' oz. 12 Ounces 1 Pound, lb.

«

APOTHECARIES WEIGHT.

The douomiuatiou.s arc,

20 Grains (gr.) make 1 Scruple, 9

3 Scruples 1 Dram, 3

8 Drani.s J. Ounce, 3

12 Ounces 1 Pound, ft

JVote. By Avoirdupois AVeight are weighed all things of a coarse, drossy nature ; and all metals, but gold or silver, by Troy Weight. Jewels, gold, silver, and Tupiors, arc weighed by Apothecaries Weight. Apothecaries mix their medicine byTroy, but buy and sell by Avoirdupois Weight.

ime

24

TABLES OF WEIGHTS AND MEASURES.

LONG MEASURE.

The denominations are,

12 Inches (m.) make 1 Foot, .... ft.

3 Feet i Yard, . . . yd.

5 J Yards (or 16^ feet) . . 1 Rod, pole, or porch, P.

40 Poles (or 220 yds.) . . 1 Furlonr, . . . fur.

8 Furlongs (or 1760 yds,) . 1 Mile, .... M.

3 Miles 1 League, ... L.

60 Geosraphic, or ) ., t t\ /

69jS0,tuli }™'^^ • l»«g^«. • ■ • •^'^-

360 Degrees the circumference of the Earth.

LAND OR SQUARE* MEASURE. "

The denominations are, 144 Square inches (

9 Square feet . 30.1 tScjuare yards .40 Square perches

4 Roods . . f>40 Acres . .

CLOTH MEASURE.

Tlie denominations are, ^

2^^ Inches (in.) make 1 Nail, .... na.

4 Nails 1 Quarter of a yar'd, qr.

4 Quartern 1 Yai-d, .... yd.

8 Quarters 1 Ell Flemish, \ E. Fl.

T) Quarters 1 Ell Enjili^h, . . E. E.

6 Quarters ....". 1 Ell French, . . E. F.

in.) make

1 S<|uare foot, . . //. 1 Square yard, . . yd. 1 Rod, pole, or perch,"* P. 1 Rood, .... R.

1 Acre, .... ,3.

1 Square Mile, . . M.

LIQUID MEASURE.

The denominations arc,

4 Gills (gL) makfe 1 Pint, .

2 Piiit.s 1 Quart, .

I (Jallon, .

is;

4 C^udi'lrf

31^ Gallons 1 l^arrel,

63 Gallons

2 Hogsheads 1 Pipe or butt,

2 Pipes (252 gal. or i hhds,) 1 Ton, . .

2>L

ql.

bar. hhdl P. or B. T

COMPOUND ADDITION. 26!

I DRY MBASLRE.

The denominations are,

2 Pints (pt.) make 1 Quart, qt.

8 Quarts 1 Peck, pe.

4 Pecks 1 Bushel, bu.

J\rote. Long Measure is used for measuring lengths, dis- tances, etc. Land or Square Measure is used for measuring lands, &c. Cloth IMcasure is used for measuring cloth, tape, &c. Liquid Measm-e is used for measuring vinegar, rum, brandy, wine, cider, perry, oil, &c. And Dry Measure is used for measuring grain, fruit, salt, &c.

TIME.

The denominations are, 60 Seconds (sec.) make 1 Minute, min.

60 Minutes 1 Hour, hr.

24 Hours 1 Day, da.

7 Days 1 Week, w.

52 Weeks, 1 day and 6 hours, or ) , v-

365 Days and 6 hours, J ^ ^®^' V'

12 Calender months .... 1 Year, y,

^ 13 Lunar months 1 Year, y.

The following is a statement of the number of days in each of the twelve calender months:

Thirty days hath September, April, June and November; All the rest have thirty-one, Exoept ihe second month alone, Which has but twenty-oight in fine, Till leap year gives it twenty-nine.

COMPOUND ADDITION.

Compound Addition consists of several denominations.

RUTiE.

Set the numbers of like denomination under each other, leaving a space between. Then begin at the right hand column, and add, as in Simple Addition. Divide the amount by as many as will make one of thj next greater. If there be any remainder, set it down under the column aaded. K no remaindei*, set down a cipher. Carry the quotient pro-

26 COMPOUND ADDITION.

duced by dividing, to the next higher denomination^ and bo Iproceed.

Proof. Ah in Simple Addition.

J^oie, In adding fractions, count i one, ^ two,-f three, because four fourths niaJke a Ts^holc one. Or if thirds, count ^ one, •§ two; because three thii-ds make ^ whole one. ',

EXAMPLES. ^., ,, :

(1.) '$ cis. (2.) $ cts. '(3.) ^.$ ">«/«-i3

5 XT 10 80 110 '50-

1 JO 5 14 • 12 25

^ 50 .2 62 9 20

8 44 1' ' 75 112 18

Ans. 17' -16 Ans. 19 81 Ans; 244 13

(4.) % 'Cts. (5.) $ els. (6.) $ cts.

125 50 120 18| 910 31i

812 30 56 25 16 18

560 12 130 12 J 122 12 J

12. 10 25 25 90 09

i> 00 72 56 J 999 99

,,80 01 1 09 125 06^

(5.) $

Cts.

120

18|

56

25

130

12^

25

25

72

56J

1

09

Ans. 4Q5

m

.(?•) .^-.

/cU-

24

-m

19

37i

50

Ans. 1816 03 Ans. 4Q5 \rq Ang. 2263 76

(7.) -t^ rtf^ (?.) S- Ms. (9.) S cts

500 00 24 "68f 40 00

200 00 19 37 i 6 00

150 00 22 50 2 00

140 00 • 17 55 2 00

130 00 10 37 i 2 00

120 ^t] 1 06i -8 75

— ~ , o i2| 1 12^

Ad-*.1240 621 ••■•■■---- ■^' ''"W^7i

Ans.- 97. 67^ ™

Ans. 58 25

10. Laid out in market for cloth 12 dollars 50 cents; for tobacco 20 dollars 75 cents ; for salt 13 dollars 50 cents ; for calico 40 doikrs; for cinnamon 18 dollars 29 f cents; and for sugar 90 dollars 22 cents. How much did the whole asaoimt to? Aub. 195 dollars 26f cents.

COMPOUND ADDITION. 27

11. I have bought 4 yards of lace for 5 dollars; a veil for 8 dollars 50 cents ; 9 yards of silk for 18 f^oljajcs 87 \ cents; 12 y^rds of ribbon for 1 dollar 18 J cents; 19 yards of linen for 14 dollars 50 cents ; 2 pair of gloves for 87h cents ; 3 pieces of domestic for 5 ddiars 37J cen|s ; 9 yards of lace for 7 dollars 87^ -cents, and 6 yards of cambrick for 20 dollars. What did the whole amount to ? '

Ans. 82 dollars 18| cents.

12. Bought of Buckner Wiilingham, cloth for a coat, for 25 dollars ; a pair of pantaloons for 12 dollars 50 cents • a vest for G dollars 12 J cents ; a hat for 8 dollars 60 cents ; a shirt for 2 dollars; a cravat for 1 dollar; a pair of socks for 1 dollar 50 cents; a p:^ of boots for 7 dollars 56 J cents; a pair of slips for 1 dollar 25 cents; a pair of suspenders for 75 cents; a pair of gloves for 1 dollar; a handkerchief for 1 dollar ; and a great coat for 35 dollars. What did the whole suit cost .? An4. 103 dollars 10 J cents.

13. A gentleman in building a fine house, finds his plank costs 950 dollars; his workmen will have 1000 dollars; the stone will cost J60 dollars; the window glass 40 dol- lars, boarding his hands 600 dollars. What is the cost of the whole ? Ans. 2850 dollars.

14. My agent has bouglit in market a turkey for 1 dollar 87J cents ; a pair of shoes for 1 dollar 68| cont^^ ; a liam of pork for 43J cents; a quarter of venison for,! dollar 37| cents; a piece of beef for y3| cents; a.hog-for 56^ cents ; a quart of strawberries for 37j cents ; some lard for 31 J cents; and a peck of potatoes for 12 J cents. What did the whole amount lo ? Ans. 7 dollars Q8^ cents, j

16. A man desirous lo set up a store, laid out monies as I follows, viz : for cloth 650 dollars 91 cents/ for iron 220 ' dollars; for calicoes, &c., 1200 dollars 5 cents; sugar 90 dollars 4Qi cents; coiiee 559 dollars 99J cents; nails 80 dollars; books 1000 dollars >ink-s;ands 40 dollars; slates GO dollars; leather 100 dollars; tobacco 96'|:]ollars; blankets 205 dollars 1 cent; cinnamon 13 dollarsJst cents; oil 29 dollars 19 cents; steel 30 dollars 33^ cefits; molasses 16 dollars; hats 109 dollars 4h cents; castings 400 dollars 55 cents; thread 75 dollars 71 i cents; and for rum 227 dollars 37^ cents. What is the cost of the whole ?

4i)S. 5204 dollars 8| cente. I

»t<r<wrMw*— II

28 COMPt UND ADDITION.

AVOIRDUPOIS WEIGHT.

(16.) T. cwL qr. l?. (17.) T. cwi. qr. lb. oz.

2 14 1 .') 3 2 1. 5 6

4 11 3" 4 12 378

5 6 2 li> 5 6 2 0 2 1 3 1 (3 4 19 0 27 15

Ans. 13 16 0 {^ Ans. 18 0 3 12 15

18. Add 12t. 16cwt. Iqr. 191b. 15oz. 114t. lOcwt. 2qr. 271b. 4oz. 13dr. 72t. 4cw . 2qr. 241b. 14oz. 3di-. 176t. 15cwt. 3qr. 41b. 15qz. lldr. Ans. 376L 7cwt. 2qr. 211b. loz. lldr

19. Add 139t. 19cwt. 3qr. 181b. 13oz. lOdi-. 1754t. lOcwt. 2qr. lUb. 2oz. 14dr.27t. 3cwt. l^^b. lloz. 13cwt. 13oz.

Ails. 1922t. 6cwt.. 2qr. 171b. 8oz. 8dr.

20. Add 20t. 2cwt. 2qr. 12t. 15t. 2qr. arwi 2t.

Ans. 49t. 3cwt.

TROY WEIGHT. Ih. oz. dwt, IK oz. cwL gr.

(21.) 4 5 6 (22.) 185 2 19 20

8 9 13 56 9 15 6

14 7 ife 11 2 17

5 8 11 385 0 8 5

13 2 10 8 7 12

21 6 19 2110 8 13 12

23. Add 71b. 9oz. lldwt. 22gr. 161b. 4oz. 18dwt. 6gr, 1631b. 7oz. 12dwt. 18gr. 171b. 13dwt.

Ans. 2041b. lOoz. ISdwt. 22gr. 34. Add 101b. 5oz. 2dwt. lOgr. 51b. lOoz. lOdwt. 2gr. 221b. 9oz. 15dwt. Igr. 8,;z. lOgr. 31b. 4oz. 2dwt. Igr.

Ans. 431b. loz. lOdwt.

25. Add 121b. lOoz. 2dwt. 3gr. 41b. 5oz. 8dwt. 19gr.

131b. 7oz. lldwt. Ans. 301b. lloz. Idwt. 22gr.

APOTHECARIES' WEIGHT.

(26.) fe 3 3 a (27.) fe 3 3 9 (28.) % ^ Z ^ gr.

6 321 3213 10 9426

12 817 6432 19 1644

112 635 10 024 75232

40 4 1 0 108 6 1 0 126 8 1 1 3

2621 19 432 1122 2 3 8 1

174 4 5 2 147 5 5 2 1286 3 6 0 16

COMPOUND ADDITION. , ■ 29

' 29. Add 161b. loz. Idr. 2sc. 12gr. 1751b. lOoz. 5dr. lOgr. 3201b. 3oz. Idi-. logr. lloz. 2dr. 3sc.

Ans. 5131b. 2oz. 3dr. Osc. 17gr. 30. Add 181b. lloz. 7dr. Isc. 19gr. 1261b. 7oz. 5dr. 2sc. 15gr. 961b. Idr. 3gi-.

Ans. 2411b. 7oz. 6dr. Isc. 17gr.

LONG MEASURE.

(31.) L, M. fur. P. (32.) yd. ft. in.

- -' 2 14

5 2 7

6 0 11 9 3 5 1 1 1

2

4

7

10

4

6

5

1

1

3

2

20

75

9

8

25

256

0

1

16

Ans. 3 46 1 0 32 26 0 4

33. Add 500L. IM. 2fur. 20P. 1yd. 2ft. 4m. UP. 1yd. 3in. IjM. 2fur. 29P. lOin. 4fur. 2fur. lOin. 1yd. 2ft. 3m.

Ans. 501L. OM. 3fLir. 23R 5yd. Oft. 6in.

34. Add 462L. IM. 7fur. 29P. 1yd. 1ft. lOin. IIP. 1ft. lO:^. IL. IM. 2fur. 28P. 1yd. 2ffc. 9in. 13P.

Ans. 467L. 3fur. IP. 4yd. 5in.

CLOTH MEASURE.

( 35.) yd. qr. na. (36.) yd. qr. na. (37.) E.E. qr. na.

234 111 19 32

5 15 222 423

76 2 1" 3 3 .3 27 3 1

21 1 2 5 4 2 14 1 4

. • 106 1 2 14 0 0 66 1 2

88. Add 19yd. 2qr. 3na. 14yd. 2qr. 32yd. 2na. 3qr. Ina. 142Yd. 3qr. 2ua. Ans. 210vd3.

39, Add 20E.F. 2qr. 3na. 401KF. 3qr. 2na. 126E.F. 5qr. Ina. 782E.F. Ans. 1330E.F. 5qr. 2na.

40. Add 2E.F1. Iqr. 3na. lE.Fl. Iqr. Ina. 3qr.

Ans. 5E.F1.

30 COMPOUND ADDITION.

LAND OK SQUAKE MEA^UBE. (41.) A;.^i2, P. (42.) ^. 'J2/'jp! (43.)^. 11.

21

P.

.m

10

o

12

SO

')

18

110

I

2<)

l>2;i

ij

10

39

,87

51

e

02

1

17

17

«8

(1

ns

1P>

3

120

12

21

1

582

1

}S

1

1

Aus. 40G 2 11 ^TI2' 2 2 105 0

I .44 Add 021iA. 211. 20?. 908A. IH.iSOP. 173A. 3R. U:7f inOUA-iR. ITP. ' Ana. 2703A. IE. 28P.

i 45. Add i)90A. 8K. 88r.lS21A. 14P. 25A. SR. 19P. ! 150 A. 211. IIP. aud 2000A. Acs. 4997A. 111. 87P.

I ■ LIQUID MEASURE. - .

! ( :G.) T. hhd. gal (47.) hhd. gal. qt. pt. gi, ! 4 18 2 19 0 0 1

j 45 ;; 40 0 Olio

I 75 1 2 8 17 2 0 2

I 91 2 58 ' ' 0 21 0 1 0

\ ■ ^!7 :> .r, 0 0 0 0 1

804, 8 54 5 58 0 1 0

48.' Add kB'jHr. l,oal. Iqt. Ipt. Igi. 13gal. 2qt. Opt. 8gi. ilUir. 2gal. 3qi. '2pt. Ogi. Igal. '2{&. Ipt. Ogi. 6bar.

... . „ ^Ana. 81]=^ar. 19gal. 2qt. Ipt. Ogi. 49. Add 3851ilid. 42gal. Sqt.'lpt. 27hhd. S6gal. 2qt. !Pi;i}Jid. 17^. leSlihd. 47gal. 2qt. Ipt. 2gi.. 1 - Ar.s. 7091ihd. ISgal. Oot. Opt. 2gi.

-|i DRV MEASURE.

1 . . , ,.,,. J,.,,. <;/. ( 51.) h(. fp, qt. jiL (52.) hu. pc. qt. pt.

^ 87 2 1 . 50 2 7 1 85 1 .5 1

rs2 8 2 G5 8 5 2 • 9G 3 40

428 1 0. 1S5 I 2 0 191 2 3 1

'af52-'S 1- 178 2 1 1 201 17 0

■^857 0 2 90 8 4 0 909 3 5 1

TiesT!'^ ieo"" i 5 o i485 1 i~i

53. Add 144bu. 3pe. 2qilpt. Ipe. 2qt. 8qt. Ipt. 462bu.. ' J8pt\' Ipt. 72bu. 5qt. Ipt. Ans. 680bii. Ope. Gqt. Opt.

COMPOUND ADDITION. 83

54. Add eObn. Ipe. Iqt. Ipt. 41bii. 3pe. 4qt. Opt 500bu. 2pe. 7qt. Ipt. 183bu. Ope. 5qt. Opt.

Alls. 786bu. Ope. 2qt. Opt.

TIME. .

(55.) F. M. (b(y.}w. da. hr.min.(b1.')da, lir. mrn.sec.

80 5 3 2 9 20 4 23 45 30

12 3 15 10 30 1 12 14 16

15 7 2 1 9 25 3 19 17 22

20 8 3 3 15 57 2 00 00 10

Ans.128 11 10 5 21 12 12 7 17 18

§8. Add 25y 7«>. 12y. 3m. 96y. 10m. 26j. 9ra. lly. 7m. and 9y. Ans. lS2y. Om.

APPLICATION.

59. Bonglit potatoes to the amount of $37 50 ct^?. ; corn to the amount of 119 21 J ct^.; wheat to the amount of ^Sl 37*^ ct-s. Wllat is the cost of the whole?

Ans. S138 08f cents.

60. Bou-ght pcppei' to the ani|jiunt of $358 75 cents; oil to the amount of $105 OOJ cents; molasses to the amount of $4 43 1 CoS. What did the whole amount to ?

Ans. S468 25 cents.

61. Bouo'lft 6 pieces of linen; the fh'st contains 57yds. 2qr. ; the second 20yds. oqr. 2na. ; the thii'd 45yds. ] qr. ; the fourth 32yds. 3qr. Ina. ; and the other two each 38yds. 2qr. What number of yards are there in the whole ?

Ans. 242yd.^. Iqr. 3na. Qr^: There are 4 bags of com ; the first contains 2bu. 2pe. ; the second 3bu, 3pe. 5qt; the third 3bu. Ipe. 3qt. ; the fourth 2bu. and 4qt. IIosv mucli_ is in tlie four bag.s ?

' --^ • Ans. llbu. 3p«. 2qt

63. A man l^as three 'fehns j't^ev- first contains. 142a. 2r. ; the second 32a. 3r. 12]^! • the third 108a. 3r. 18p. How many acres are there in ;rll ? Ans. ■284a. Or. 30p.

64. There are 3 pieces of lape; the first yiea^urcs 15yds. 3qr. ; the r.econd iSyds. Iqr. 2na. ; the third 25yds. 3qr. 2na. How many yards are there in the three pieces ? Ans. 60yds.

65. If a man on a journey, travel the first day 43m. ofur., the second 29ra. 34p., the tliird 57m. 2fur. 32p., and the fourth 12m. 3fui'. 18p., how many miles did lie traTcl in the four days ?• Ans. 142m. 2fnr. 4p.

32 COMPOUND MULTIPLICATION.

66. Suppose a man to have, in one barrel 40bii. 3pe. Iqt. of wheat, in another 50bu. 6qt. Ipt., in another 41bu. 2pe., in another 64bu. 5qt., in another 6bu. Ipe., in another 19bu. Ipe. 2qt. Ipt., and in another 65bu. 6qt. 2pt., how many bushels are there in the whole ? *

Ans. 287bu. Ipe. 6qt. Opt.

67. Suppose a man has in one trunk 4871b. lOoz. ISdwt. 22gr., in another 5001b. 8oz. lldwt. lOgr., in another 2341b. lloz. lOdwt. 16gr., how much has he in all ?

Ans. 12231b. 7oz. Idwt. Ogr.

68. A physician received from Baltimore three boxes of medicine, which cost him as follows, viz. ; the first box $21 321^ cts. ; the second 819 37^ cts. ; the third $40 17| cts. What did the whole cost? Ans. $80 87^ cts.

COMPOUND MULTIPLICATION.

When the multiplier does not exceed 12, work by

BiJLE I.

Set down the number to be multiplied, and place the mul- tiplier under its right hand denomination ; and in multiply- ing observe the same rules for caj-rying from one denomi- nation to another, as in Compound Addition.

JVo/e. If there be i in the sum, divide the multiplier by 4 ; a ^ by 2 ; f by 2 and 4 ; a ^ by 3 ; or if there be a frac- tion in the multiplier, divide the sum in like manner, and add ctieir amount to the sum produced by the whole number.

EXAMPLES.

FEDERAL MONEY.

(1.) $ cts, (2.) $ cts. (S.) $ cts.

2 50 12 66i 22 12J

2 4 6

Ans. 5 00 Ane. 50 25 Ans. 132 75

(4.) $ cts. (6.) $ cts, (6.) 8 cts

26 18f 58 78| 125 06

3 5 7

Ans. 78 56i Ans. 293 93f Ans. 875 43f

COMPOUND MULTIPLICATION. 33

3 cts. $ els.

7. Multiply 58 06^ by 4 Answer 232 2G

8. 25 87J^ 8 203 00

9. 565 62J 12 6787 50

10. 112 lOi 10 1121 05

11. • 222 22J 11 2444 47J

AVOIRDUPOIS WEIGHT.

(U.^T.ctoLqrJb. (lS.yT.cwt.qr.lb.oz.dr. fU.) qr.lb.oz.dr. 861 16 * 6 14 2752 •3 14 64

3 4 8

Ans. 24 19 0 20 26 18 1 1 4 8 - 28 3 2 0

15. Bought eight bags of sugar, each weighing 2cwt. Iq. 41b# What is the weight of the whole ?

Ans. 18cwt. Iqr. 41b.

16. Multiply 4cwt. 3qr. 171b. by 11.

Ans. 53cwt. Sar. 191b.

TROY WEIGHT.

j ( 17.) lb. oz. dwt. ( 18.) lb. oz. dwt. gr. ( 19.) lb. oz. dwL gr. 56 4 14 47 2 0 8 112 8 2 20

2 3 5

*i

112 9 8 141 6 1 0 563 4 14 4

20. Multiply 961b, 9oz. lldwt. lOgr. by 8.

Ans. 7741b. 4oz. lldwt. 8gr.

APOTHECARIES' AVEIGHT.

(21.) ft 3 3 9 (22.) ft 3 3 9 gr. (23.) ft 3 3 9 gr.

4 8 2 1 47 2 1 2 12 12 3 4 2 0

5 7 12

•

Ans. 23 5 3 2 330 3 5 0 4 147 7 0 0 0

24. Multiply 671b. 6oz. 3dr. 2sc. by 7.

Ans. 4721b. 9oz. Idr. 2sc.

25. There are 9 parcels, each weighio^ 1091b. 7oz. 6dr. 2sc. 2gr. what is their weight ?

Ans. 9861b. lOoz. 4dr. Osc. 18gr

34 COMPOUND MULTtPLIOATIO*\.

LONG MEASURE.

(26.) Jyj. Pur. P. (27.) L. M. Pur. P.

1 3 86 3 2 1 28

12 7

17 6 32 26 0 -3 SC

28. Multiply 14M. 6Fur. 39P. by 11.

Adb. 162M. 1 Fur. 29P

29. Multiply IL. 2M. 3Fiir. IP. 1yd. 1ft. 2in. by 2.

Ans. 3L. IM. 6Fur. 2P. 2yd. 2ft. 4in.

CLOTH MEASURE.

(SO.)yd.qr.na. (dl.) E.E.qr.na, (32.)*E.F. jr.na. 12 3 2 22 2 3 16 2 1

4 6 8

Ans. 51 2 e 135 1 2 131 0 0

33. If 20yd. 2qr. 3na. be multiplied by 7, what number of yards will there be? Ans. 144yd. 3qr. Ina.

LAND OR SQUARE MJ]ASURE.

(34.)j3. iJ. P. (35.)^. /J. P. (30.)^. ii. P.

38 3 13 47 2 10 20 3 30

2 % 5 9

77 2 26 237 3 10 188 1 30

37. Multiply 40A.1R.19P. by 12. Ans. 484 A. IR. 28P.

38. How many acres will 7 teams plough in one day, allowing them lA. 3R. 39P. each? Ans. 18A. 3R. 33P.

LIQUID ilEASURE.

( 39.) hhds.galqt. (40.) T. hhd.galqt.pt. ( 41 .) hJid.galqt.pi. 2 13 3 2 1 12 2 1 6 43 2 1

4 *8 7

8 55 0 18 1 38 0 0 46 53 1 1

42. Multiply 2T. Ip. 40gal. 3qt. Ipt. by 6. .

Ans. 15T. Ip. Ihhd. 56gal. Iqt.

43. Multiply 4T. Ihhd. lOgal. Ipt. by 10.

[ ' Ans. 42T. 3hhd. 38g;il. Iqt.jj

COMPOUND MULTIPLICATION.

ai5

DRY MEASURE. (4'f.) hu. pe. qt. pL

180 5 2 1 8

(45.) iv. pc. at. pi li: 2 7 1

145a 2 4 0 38 0 6 1

46. Multiply 120bu, :3po. Oqt. 2pt. by 4.

Aus. 483bu. 0i>c. Iqt. Opt.

47. MuHiply 189bu. 3pe. 7qt. by 7.

Ans. 1329bu. 3pc. Iqt.

48. Multiply 98bu. O])©. 5qt. Ipfc. by 0. . .

Ans. 883bu. 2pe. Iqt. Ipt.

TIME.

(49.) Y. M. (50.) F. M (51.) F. W: D, 3 11 8 4 12 19 5

3 6 2

11 9 50 0

52. Multiply 49Y. 9M. by 7.

53. i\Iultiply 19Y. 29Da. by 9.

24 39 3 Ans. 348Y. 3M. Ans. 171Y. 261Da. When the multiplier is more than twelve, and is the ex- act product of two factors in the multiplication tabic, -s^ork oy rule 2. Multiply the given sum by one of the facte vs; then multiply that product by the other fact-or. '

( 51.) Multiply 66

EXAMPLES,

cts. m. 37 5 by 36 6

S (55.) 5

cfs.

09 by M

398 25 0 6

An;3. 2389 50 0

57. 58. 59. 60. 61. 62.

06

44

12

• 22

Cl-<. 7)1.

2:. 3

18J

12 5

18 7

24 9

by 86 56 96 42 48 81

10 18 8

81 M

S ctfi. ' n

Ans. 2389 50 U

2478 16 8

1170 00 0

929 25 0

1256 97 6

C095 16 9

36

COMPOUND

MULTIPLICATION.

'

63. 20

64. 10

cts. 08 J 12.}

by 108 144

Ans. 2169 1458

cts. jn. 00 0 00 0

A.

65. 47

66. 25

R. P.

3 20

2 8

by 54 30

.9.

2585 766

R. P.

1 I

2 00

67. 48

F. 1\

7 25

by 88

Jtf.

4307

F. P.

7 0

ft

68. .56

3 3 9 6

by 84

ft

4772

:5 o (

3 0

Wlien the multiplier is not the exact product of any two factors in the multiplication table, work by rule 3. Use the two factors whose product coraes nearest the multiplier; then multiply the given sum by the number which supplies ! the deficiency, and add its product to the sum produced by the two factors.

EXAMPLES.

69, Multi

$ cts. ply 2 25

m. '

4x2 10

* by 52

1

22 54

6 5

112 70 4 50

0

8

117 20

8

*Tcn times 5 ma.Vc 50,

and 2 su

pplies the deficiency.

70. Multi

71.

72.

73.

74.

75.

76. 7cwt.

77. 121b.

$ cts. m. ply 4 75 8 by 29 7 87* 47 28 683 r,8 49 75 87 94 181 31 42 31i , 58 3qr. 221b. by 51. 5oz. 8dwt by 39.

Ans. 137

370

1950

4328 2919 2454 Ans. 405cwt Ans. 4851b. 6

cts. m. 98 2 12* 75 25 81i 12^ . Ifjr. 21b.

oz. 12dwt.

_, . ..1

COMPOUND MULTIPLICATION.

78. 4m. 6f\ir. 21p. by 87 An^. 418m. 7fur. 27p.

79.50a. 2r. 5p. 34 1718a. Or. l(fe.

80. 60bu. 2pe. 5qt. 43 2608bu. Ope. 7qt

81. 2hlid. 41gal.2q.lpt. 17 46blid. 14gal.2qt.lpt.

When ihe multiplier is ^eater than the product of any two factors in the multiplication table, work by rule 4.

Multiply continually by as many tens, less one, as there are figures in the multiplier. Thou multiply the product of the last ten by the left hand figure of the multiplier. If greater than 1, again multiply the given sum by the units figure of the multiplier j the product of the first tcu by the tens figure; the product of the second ten, if any, by the hundreds figure, &c. Then add ike producte of these several figures together for the answer.

9 cts. $ cts. m.

(83.) Multiply 2 02ix2by222. (83.)1 11 2xlby511. 10 10

20 25X2 . il 12 0x1

10 10

202 50 111 20 0

2 left hand figure. 5

406 00 556 00 0

4 05 1 11 2

40 50 11 12 0

449 55 568 23 2

$ cts, $ cts,

84. Multiply 5 18f by 326 Answer 1685 93}

85. 1 56J 466 713 64

86. 2 87J 576 1656 00

87. 4 81i 679 2928 ISf

88. 18 931 457 8654 43f

89. 25 48i 879 22359 56i

yd, ft, in. yd. ft. in.

90. 5 12 604 2716 0 0

M.Fur.P. J^. Fur.P

91. 25 3 18 1265 32170 4 10

=SmE

38 COMPOUND SUBTRACTION.

vd. qr. na. yd. qr. na.

02. Multiply 2li 2 1 by 3204. Am. 72290 1 0.

APrLlCATlON. \

98. Sold 125 bunbels of wheat at 22 centa per bushol \ "What did it amount to 'i Ans. §27 50 cents, i

94. Sold 60 bushels of applea at 15 cents i>er bushel, i What did th(,'y amount to '{ Ans. $^. f

95. If I buy 18 yards of cloth at 10 cents per yard, what I must I pay ? Ant. 91 30 cents, j

96. When one eord of wood coyt 92 10 ccntc<, what will- be the prii'C of nine cords at the same rate ?

Ans. $18 00 centa.

97. Sold 5cwt of tobac<To at $12 50 eentii per cwt., what did the whole ambunt to ? Ans. $62 50 cents.

EXAMPLES.

% cts. % cts.

(98.) Multiply 10 62Jby4 (99.) Multiply 5 12iby8 4 8

42 48 40 96

2 2

Ans. 42 50 40 98

100. Bought 24 bushels of wheat at SI 12* cents per buiihel. What did the whole amount to ? Ans. §27.

101. Bought 44 bu. of ecru at 37 J centa per bushel. What did the whole eosti' Ans. n516 50 cents.

102. A merchant bought tn o pit^:3 of linen, the one con- tained 38 }ardB and the other 26 yardd. What did the two pieces cobt at ??8 87A cents per yard 't Ans. 1^48.

103. What cost a box of sugar wwighing 106 lbs., at 15i cents, per pound? ' Ans. 16 16 i cts.

104. What ^vill 13 ^ gallons of molasses come to at 40 I cents per gallon 'f Ans. ^ 40.

105. How muih will 25 bushels of oats come to at, 15 'cents per bushel? Ans. $3 75 cente.

COMPOUxND SUBTKACTION.

EULE.

Place the numbers under each other which are of the same denomination : the less always being under the greater.

Ilwn MIIMIB

^

COMPOUND SUBTRACTION. 39

Begin at the right hand figure, and if it be larger than the one above it, consider the upper one as having as many ad- ded to it as make one of the next greater denomination. Subtract the lower from the upper figure thus increased, and fiet down the remainder, observing to carry one to b<.^ added to the next higher denomination, and ho proceed. Proof as in Simple Subtraction.

♦ EXAMPLES.

FEDERAL MONEY.

$ cts. m. $ cts. m, $ cts. m.

(l.)5 54 7 (2.)1 50 2 (8.) 19 84 4

2 10 5 28 4 10 18 9

i)

Ads. 3 44 2 1 21 8 § 65

$ cts. ^ cts. $ cts.

(4.) 64 87i (5.) 10 37i (O.)IOO 00

25 12J 5 06J 55 62^ [

89 75 5 811 44 37^

$ cts. $ cts. ^ cts.

(7.) 45 64| (8.) 30 30 (9.) 150 93|

5 99J 1 12^ 90 10

39 65J 29 17^ 60 83f

10. I owed 8559 22^ cents, but have paid $148 50 ct« How much remains unpaid? • Ans. $410 72 J- cent<».

11. .Lent a man $400; he now returns $211 12 J centR. How much does he still owe ? Ans. $188 87^ coi\ta.

12. A merchant had in his desk $500 87 J ce*its, but drew out $120 93 cts. to pay a debt. How much had he le^ in the desk ? Aiis. 379 dollars 94 J cents.

13. I had 303 dollars 6^ cents, but lent 9 dollars 91i cent^^. How much had I left? Ans. 293 dollars 15 cents.

14. From $1000 take 1 mill. Ans. $999 99 cts. 9m.

AVOIRDUPOIS WEIGHT.

cwt. qr. lb, T. cwt. qr. lb.

(15.) 6 3 25 (16.) 28 3 I 27

4 2 12 13 1 0 19

Abb, a 1 18 15 2 1 08 ,

40 COMPOUND SUBTftACTIQN.

17. From 14t. lOcwfc. 2qr. lOlb. take lUb.

Ans. 14t. lOcwt. 2qr. 51b.

18. Bcught 400cwt. of sugar, but have since sold 2cwt. 3qr. 141b, What quantity remaina ?

Ans. S97cwt. Oqr. 141b.

TROY WETGIHT.

lb. ox. dwt. g-^. IbT oz. dwt. gr.

(19.) 24 6 19 18 (20.) 13 9 5 22

19 5 18 23 8 11 16 10

Am. 5 1 0 14 4 9 9 12

21. ProM 271b. 9oz. 16dwt. take 19dwt.

Ans. 271b. 8oz. 17dwt.

22. Subtract lib. Ooz. 17dwt. 15gr. from 151b. 9oz. 18dwt. 8gr. Ads. 141b. 9oz. Odwt. 17irr.

APOTHECAEIES' WEIGHT.

f. 33 ft539 fe339

(28.) 186 7 5 (24.) 96 4 02 (25.) 1009 82

67 8 4 75 4 2 1 99 8 3 2

Ans. 118 11 1 20 11 6 1 115 0

CLOTH MEASURE.

yds. qr. na. . yds. qr. na. yds. qr, na.

(26.) 160 3 3 (27.) 969 2 1 (28.)'l4 0 3.

37 12 786 1 2 9 3 2

.1.1.1. fti—

A»s. 123 2 1 183 0 8 4 11

'•A t >'•'■■

29. Bought 27 yards of domestic, but have since sold

9yds. 3qr. How much remains? Ans. 17yds. Iqr.

E.E. qr. na. E.Fr.qr. no. E.Fr.qr. na.

(80.) 44 3 2 (81.) 62 2 3 (32.) 27 5 2

1^3 3 1 43 3 2 19 3 3

Ans. 21 0 1 18 5 1 8 13

COMPOUND SUBTRACTION. 41 1

LONG MEASURE.

L. M.fur.p, yd in, ft. L. M.fur. p. yd, ft in-

(33.) (5^ 5 9 4 2 6 (34.) 9 1 7 18 5 1 11

4 3 2 8 13 7 7 2 .5 19 1 2 9

Aus. 123121 11 121 39 322

35. Two men travelling the same road; one tnivels at the rate of 27m. 2fur. 39p. ; the otlicr at the rate of 19m. Ifur. 17p. At night how fai- are they distant ?

Ans. 8m. Ifur. 22p.

LAND OR SQUARE MEASURE. Ji.R.P, ^JR.P, Jl.R,P. ^.R.P,

(3G.)9G 2 16 (37.) 640 S 12 (38.) 96 0 18 (39.) 50 3 19 87 3 18 114 4 3 74 2 4 13 1 5

Ans. 8 2 38 525 3 9 21 2 14 37 2 14

40. A father dying left his son Joseph 200a. 2r. 20p and to James 180a, 3r. 39p. What is the diiference il then- shares? Ans. 19a. 2r. 2 If

LIQUID MEASURE.

^al. qt. pt,

i2 2 1 (42.) 1.. _ . ^.

3 2 14 ,3 0 96 2 8 2

r. Jilid.gal qt. pt, T. hJid. gal at.

(41.) 8 2 42 2 1 (42.) 186 3 9 1

Ans. 5 0 27 3 1 90 1 0

^ 4o. A person bought 4hhd. 25gal. of cider: — he has smce sold 2hhd. 15gal. Sqt. Ipt. How much has he re "^'^;;^"^«- Ans. 2hhd. 9gal. Oqt. Ipt.

44 If 5hhd. Igal. Iqt. Ipt. of oil be drawn fiW6hhd. 2giil 2qt. Ipt. how much will remain ?

Ans. Ihhd. Igal. Iqt. Ojd,

DRY MEASURE.

(450 44 2 1 1 (4C.)80 3 7 1,(47.) 789^0 5, 0 32 3 2 1 ^ -^15 1 11 ■

I Ans. 11 2 7 0 {;5 2 6 0

! 4'-^ ~" —

•42 COMPOUND SUBTIIAOTIO.V.

48. From TlOLu. Ope. 5qt. take 583bu. 2pc. Gqt.

Ans. ISGbu. Ope. Tqt.

49. Kaieed ISQbu. Ipc. Tqt. Ipt. of corn; have siuce sold 167bu. 2pe. Iqt, ; whut quantity have I remaining ?

■AuH. 21bii. 8pc. Gqt. Ipt.

, TIME.

K M. Y. M. hr. min. sec.

(50.) 12 11 (51.) 7 1 (52.) 18 45 59

7 5 8 10 2 51 28

Ans. 5 G 8 3 15 54 31

53. .Subtract 1^5y. 9m. from 450y. llui.

Ans. 325y. 2m.

54. Take o6da. 141ir. 30min. and 25,sec. from 44da. Ihr. 48ni}n. and 58sec. Ans. 7da. lliir. 18min. 33scc.

•Vo/c. The intcn\Tl or «pace of lime between two given i dates is thus found: Set down the greater date, and under it the less : Begin with tlie days. If the upper number of days be greater than the lower, subtract the lower from it, and set down the remainder. But if the lower number be gi*eater, add as many days to the upper as make a moiith of the lower, and subti'act the lower therefrom; then carry one to I the months of the less date, and subtract as before, and so proceed. ■'*^-- ■^*'

EXAMPLES.

55. Abijah was born on the 15th of November, 1807, and Josiah on the IGth'of July, 1811. What is the differ-

'. ence in their asies ?

Y.

M.

de.

1811

T"

IG

1807

11

15

An^. 3 8 1

*NoTE. — July is the seventh month, and November the eleventh.

56. Charles was born on the 18th day of June, 1821. How old will he be on the 13th day of August, 1840 ?

Ans. 19y. Im. 25da.

»-»»i»MMw«iMiiMi»«M»MM«w»iiM«i»»»e»iMM»»^»ii«— — — Mi»»i»— «i»» II I il ii j»««— ——«—»— JMS lirllriTii T

COMPOUND DIVISION. 43

57. William was born on the llth day of August., 1813, and John on the 5th day of July, 1827. How much older is William than John ? Ans. 13y. 10m. 25da.

58. A man gave his note on the 10th day of May, 1824, and lifted it on the 8th day of December, 1829. For what time did he pay interest ? Ana. 5y. 6m. 29da.

API'LIOATION.

59. Bought 2 pair of stockings, at 75 cts. per pair; lOyds. of linen, at 87^ cts. per yard; 28yds. of domestic, at 22 cts. jxjr yard; and 5 pair of gloves, at olj cts. per pair; and to him from whom I bought those articles, I deliver $50 00, out of which he is to t<akc the sum due him. How much change will there be coming to me? Ans. $26 771 cts.

60^ If I buy 660yds. of muslin for $90 60 cts., and sell the same again for $100 04 cts., how much do I gain l)y the sale ? Ans. $9 44 cts.

00. Bought 50yds. of superfine cloth at $8 75 cents per yard; 30 pounds of coifee, at 22 1 cts. per pound; and 44 bushels of salt, at $2 per bushel. What sum must I pay for the whole ? Ans. $532 25 cts.

62. I have several tracts of land ; one of them contains 69Qa. 2r. 16p. ; another 400a. ; and two others, each 63a. 3r. 24p. If I sell 200 acres, what number remains ?

Ans. 1018a. Ir. 24p.

63. Bought 400bu. 8pe. of wheat; 160bu. of rye; 150bu. 2pe. of oats. I have since sold 225bu. Ipe. of wheat; 37bu. 2pe. of rye; 78bu. 3pe. of oats. How many bushels of each have I remaining);' C 175bu. 2pe. wheat,

Ans. -j r22bu. 2pe. rye, (^ 71bu. Pj])e. oats.

COMPOUND DIVISION.

Compound Divi^ion teaches to divide any sum or quantity which consists of several, denominations.

RULE.

Begin at the highest denomination, and divide the several denominations of the given sum or quantity one after ano-

44 COMPOUND DIVISION.

tlier, and set their respective quotients underneath. \Vlien a remainder occuig, reduce it to the next lower denomina- tion by multiplying it by as many of the next denomination as make one of that denomination from which the remainder is derived, and the next denomination to. the product; then divide as before, and so proceed.

JS'ote. If the dividend be not large enough to contain the divisor reduce it till it ttjJI be, and proceed dfi before.

EXAMPLES.

(1.) % cts. (2.) % cts,m. (3.) % ct^. 2;12 61 3;187 91 4 4)168 99

Ans. 6 30 J Ans. 62 63 8 Ans. 42 24|

6 cts. 8 cts.

4. Divide 366 18f by 3 Ans. 122 06^

5. 496 75 8 62 09^ 4-

6. 384 87^ ' 6 64 14j +

7. 587 681 9 65 29f +

8. 976 43f 11 88 76^ +

9. 1979 BH 12 164 94i +

yd. qp. na. yd, qr, na.

10. Divide 44 1 2 by 7 Ana. 6 11 +

11. 56 3 3 11 5 0 2 +

M. fur. P. M.fur. P.

12. Divide 105 5 22 by 12 Ans. 8 6 18 +

13. 45 7 18 6 7 5 9 +

hu. pe. qt Jm* pe. qt. pt.

14. Divide 48 2 0 by 4 Ans. 12 0 4 0

15. ■ 86 3 7 3 28 3 7 1 +

JYote. "When the divisor is more than 12, work by Long Division. Divide the highest denomination of the given sum by the divisor, and reduce the remainder, if any, to the next lower denomination, adding to it when reduced the

COMPOUND DIVISION. 45

number there is of that denomintition in the given sum or quantity. Then divide as before, and so proceed.

EXAMPLES. ,

$ cts.m. $ cis.

^16.) Divide 88 45 6 by 19. ( 17.) Divide 250 50 by 25. 'ii'OT- $ cts.m. $ cis,

19)88 45 6. (Ans.4 65 5. '25)250 50. (Ans. 10 02.

7G 25

.124 0 50

114 50

105 00

95

100 95

11 Kcmainder.

$ els. m. $ ets.

m.

18. Divide 98 77 8 by 44 Anj?. 2 24 4 +

19. 45 66 5 .36 1 26 8-f

20. 77 87 5 96 0 81 1-f

21. 288 68f 0 108 2 67j +

22. 496 37| 0 132 3 76 0-f

23. 47 68 7 45 1 05 9 +

24. 196 75 0 78 2 62 2 +

25. 496 87^ 0 97 6 12 2-f

26. 376 81 J 0 123 3 06 3 +

27. A laborer received for thirty days $900. How much did he receive per day ? "Ans. $30.

28. If a boy receive $60 for twelve months work, how much is that for cue month ? Ans. $5.

29. How many bushels of com may be bought for ^00, at $2 per bushel ? Ans. 200 bushels.

30. When 72 bushels of com cost $56 25 cents, what is the price of one bushel ? Ans. 78cts. Im. -f-

31. Suppose S1875 81 i cents to be equally divided among 125 men, what will be the share of each man ?

Ans. S15 OOi cent, -f

46 llEDUCTION DESCENDING

32. 89 men agree to equally divide ISOgals. 2qts. Ipt. of brandy among them, how much will be the share of each ?

Ans. Igal. 2qt. Ipt. + 48.

REDUCTION DESCENDING.

if

Reduction Descending teaches to change any sum or quan- tity to a lower denomination, but retaining the same value.

RULE,

Multiply the highest denomination of the given sum o^ quantity by as many of the next lower denomination as make one of the higher, adding to the product the number there is of that denomination in the given sum or quantity.

J^ote, To reduce dollars to cents, annex two ciphers to the dollars.

EXAMPLES.

FEDERAL MONEY.

( 1.) Reduce $18 50 cts. to cts. ( 2.) Bring $75 to ets. 100 100

Ans. 1850 7500

3. Bring $100 to cents. Ans. 10000 cents.

4. Reduce 20 dollars to cents. Ans. 2000 cents. 6. Bring 25 dollars to cents. Ans. 2500 cents. 6. Reduce 45 dollars to cents. Ans. 4500 cents. J^ote. To reduce dollars to halves, quarters or thirds of

a cent, bring them first into cents, and then bring the cents into halves, quarters or thirds, as required. (7.) Bring $50 into half cts. ( 8.) Bring $40 into thirds of a ct. 100 100

5000 4000

2 3

Ans. 10000 halves. Ans. 12000 thirds.

(9.) Reduce 25 cts. to fourtha. ( 10.) Reduce 12 cts. to thh-ds. 4 3

Ans. 100 fourths. Ans. 36 thirds.

11. Reduce 10 dollars to dimes. Ans. 100 dimes.

REDUCTION DESCE:<DINa. 47

12. Reduce 220 dollars to mills. Ans. 220^000 mills.

13. Reduce $426 88 J cts. to halves of a cent.

Ans. 85377 halves.

14. Bring §487 44| cents to fourths of a cent.

A^s, 194979 fourths.

15. Bring $17 18 1 cents to fourths of a cent.

Ans. 6875 fourths.

AVOIRDUPOIS WEIGHT.

10. Bring 2 tons to cwt. ( 17.) Reduce 260 cwt to quarters. 20 4

Ans. 40 cwt. Ans. 1040 quarters.

18. Reduce 36qr. to pounds. Ans. 10081b.

19. Bring 17 pounds to ounces. Ans. 272oz.

20. Bi-iug 2qr. 251b. lOoz. to drams. Ans. 20896dr.

TROY WEIGHT.

21. Reduce 20 penuyweidits to trains. . 24

80 40

Ans. 480 grains.

22. Reduce 5 ounces to grains. Ans. 2400gr.

23. Bring 40 pounds to peimyweights. Ana. 9600dwt.

24. IIow many grains are there in 191b. lloz. 14dwt. -Igr- Ans. 115077gr.

ArOTHECARlES^ WEIGHT.

25. Reduce 40 pounds to ounces. Ans. 480oz.

12

480

26. Bring 72oz. to drains. Ans. 576dr.

27. Reduce 151b. 9oz. 4dr. 2sc. 17gr. to grains.

Ans. 91017gr. LONG MEASURE.

28. Reduce 10ft. to inches. Ans. 120in.

]2

120

148 REDUCTION BESOENDIKG.

29. Bring 40yd. to feet. Ans. 120ft.

30. Reduce 120yd. 1ft. 4in. to mctcfl. Ans. 4336m.

81. Reduce 20 miles to yards. Ans. 85200yd.

82. Reduce 450m. 6fur. 32p. to poles. Ans. 144272p.

83. In 2L. Im. 3fur. 16p. 3yd. 2ft. lOin. Kow many inches? Ans. 470590in.

CLOTH MEASURE.

34. Reduce 22 quarters to xiails. Ans. 88na.

4

88

35. Bring 86yd. to qr. Ans. l'44qr«

36. Bring 20 English Ells to qHarters. Ans. lOOqr

37. Bring 20 French Ells to quarters. Ans. 120qr.

38. Bring 8yd. Iqr. to qr. Ans. 83qr.

39. In iSyd. 2qr. Ina. how many nails? Ans. S13na.

LAND OR SQUARE MEASURE.

40. Bring 2 roods to perches. ♦ Ans. 80 pei'ches.

40

80

41. Reduce 140 acres to perches. Ans. 22400 perches.

42. Bring 54 acres, 3 roods, 23 polcvS, to poles.

Ans. 8783p.

43. Bring 6 squ/ire feet to square inches. Ana. 864iu.

44. Bring 120 square yards to square inches.

Y' ^ Ans. 165520in.

45. Bring 29 square yards, 2 square feet, 102 square inches to square inches. Ans. 37974 square inches.

LIQUID MEASURE.

46. Reduce 31 quarts to pints. Ans. 62p4.

2

.62

47. Bring 28 gjil. to quarts. Ans. 112qt.

48. Reduce 5bhd. to gallons. Ans. 315gal.

49. In 6 tons, how many pints ? Ans. 12096pt.

50. Reduce 4hhd. 3qt. to pints. Ans. 2022pt.

51. Bring 5 tons. Ihhd. 15gal. Iqt. Ipt. to pints.

Ans. 10707j)t. |

ff

HHWHU«W—»W»— lt«<MI—

REDUCTION ASCENDING.

DRY MEASURE. 52. Reduce IGqt. to pints.

82

53 ]?ring 32pe. to quarts. *

54. Reduce 7bu tc pecks.

55. Reduce 12bu. to pints.

56. Bring 24bu. Ipe. 2qt. Ipt. k> pints.

TIME.

57. Bring 40 minutes to seconds.

60

49

Ans. 32pts.

Ans. 256qt.

Afts. 28pe. Ans. 768pts. Ans. 1557pt.

Ans. 2400860.

58. 59. 60.

2400

Bring 20 hours to seconds. Ans. 72000sec

Reduce 12 years to months. Ans. 144m.

Bring 45 years to days. Ans. 16425da.

61. Reduce 3 days, 5hr. 29nnn. to minutes.

Ang. 4649min

62. Reduce 7y. 3w. 4da. 20hv. 20min. and 20sec. to seconds. ^ Ans. 222380420sec

t REDUCTION ASCENDING.

Reduction Ascending teaches to change any sum or quan- tity to a higher denomination.

EULE.

Divide the given sum or quantity in the lowest denomi- nation, by as many of that denomination as make one of the next highor, and so on, until you have brought it into that denomination which your question requires.

jyote. Mills may be brought to dollars, cents and mills, by cutting off one figure on the right for mills, two more for cents; the rest will be dollars. Or to bring cents to dollai*s and cent,s, cut off two figures on the right for cents.

EXAMPLES.

FEDERAL MONEY.

1. Bring 2800 cents to dollars. 28100

Ans. $28.

^ }dO REDUCTlOiJJ ASCENDINQ.

2. Ering xl'2il2 mills to dollars, cents and mills. 11112-212 Alls, m 2iiets. 2m.

3. Bring 4-144 cents to dollars and CQjits.

Ans. $44 44cts.

4. Bring 864 halves of a cent to whole cents.

Aus. 432cts.

5. In^063 thirds how many cents ? Ans.*321cts.

6. In 501 fourths hnv many cent^? Aus. 147icts.

7. Brh)g 680 thii'ds to cents. xVns; 21-Octs.

AVOIBDUPQIS WEIGHT.

8. Bring IlSib. to quarters. 28)ll«(An9. 4<ir. 61b.

112 .;

6

9. Bring 90qr. to cwt. Ans. 22e^?t. 2qr.

10. Bring 17811b. to.cM^t. Aus. i5cwt. 3qr. 171b.

11. In I872dr. how many pounds? Ans. 71b. 5oz. •

12. Bring 75cwt. to tons. Ans. 3t. 15cwt.

13. Bring 98561b. to cwt. Aus. 88cwt.

TEOY WEIGHT.

14. Bring 186oz. to pounds. Ans. 15Ib. 6oz: 12)186 ■ :

15Ib. 6oz.

15. In 544dwt. how many pounds ? Ans. 2Ib. 3oz. 4dwt.

16. Bring 960dwt. to pounds. Ans. 41b.

17. Bring 9624gr. to pounds. Ans. lib. 8oz. Idwt.

APOTIIEOABIES^ WKimiT.

18. Bring 2105 to RmiplcP. Ans. 129. 2tO)24IO

12

19. Bring 27209 to ounccfi. Ans. 113 3 23 2 d.

20. Bring 126(p0gi-. to pounds. Ans, 2fe 23 33.

21. In 155520gr. how niany pounds ? A»av27-,|b,

LONG MEASURE. '^ ]

f,

22. Brine; 120 miles to leas^Q9,. Ans. 40^

3)120 '

40

REDUCTION ASCENDING. 51 j

23. Bring 1280 poles to fur. Ans. 32fui'.

24. Bring 2880 poles to leagues. Ans. 31.

25. Bring 5760 poles to leagues. Ans. 61.

CLOTH MEASURE.

26. In 60 quarters how many yards ? Ans. 15yds

4)60

15

27. Bring 4000 nails to yards. Ans. 250yds.

28. Bring 1260 quarters to E. F. Ans. 210 E. F.

29. Bring 1818 nails to yards. Ans. 113yds. 2qr. 2na.

' LAND OR SQUARE MEASURE.

30. In 2400 perches how many Roods ? Aug, 60 R.

410)240|0 — *

60

31. Bring 2040 perches to Acres. Ans. 12A. 311.

32. Bring 1908020 perches to A. Ans.ll925A. OR. 20P.

33. In 1728 square inches how many square feet ?

Ans. 12 feet.

LIQUID MEASURE.

34. In 480 gills how many pints ? Ans. 120 pis 4)480 ^

120

85. Bring 1840 pts. to gals. Ans. 230 gals.

36. Bring 1890 gal. to hhdn. Ans. 30 hhds.

37. In 504 gallons how many bar. ? Ana. 16 bar.

DRY MEASURE.

38. In 800 pint;3 how many qts ? Ana 400 ats 2)800 * ■

400

39. Bring 240 pints to pe. Ans. 15 pe.

40. Bnng 8888 pecks to bn. . Ans. 2222 bu. 41- In 12840 pints how many bu. ? Ans. 2G0bu. 2pe. 4qt!

^62 IIEDUOTION ABCBNDINO.

TIME.

42. Bring 2400 seconds to minutes. Ans. 40 miu r)|0)240j0 |[

40

43. In 7200 seconds how many hours ? Ans. 2 lioiirs.

44. Bring 144 months to years. Ans. T 2 years.

45. In 4649 minutes how many days?

Ans. 3da. 5hr. 29m.

PROMISCUOUS EXAMPLES.

1. In 20 dollars how many cents ? Ans. 20Q0 cents.

2. In 63 roods how many perches? ' "Ans. 2520 per.

3. How many miles are there in 98 fur. ? Ans. 12m. 2fur.

4. In 175 pecks how many bushels? Ans. 4obu. oj^c.

5. How many min. are theje in 720 sec. ? Ans. 12miii.

6. In 103 pints how many quarts ? Aus. 51qts. Ipt.

7. In 1824 cents how many dollars ? Ans. $18 24 cts.

8. In 8t. 15cwt. how many hundred weight ?

Ans. 175 cwt.

9. How many English Ells arc there in one hundred quarters of a yard ? Ans. 20 E. Ells.

10. How many scruples are there in 9 3 ? Ans. 27 9.

11. In 203 days how many weeks? Ans. 29w.

12. In lOSdwt. how many ounces? Ans. 5oz. 8d\Yt.

13. How many cwt. are there in 20 tons ? Ans. 400cwt.

1 4. In 202 cents how many qrs. of a cent ? Ans. 808qrs.

15. How many dollai-s are there in 8762 cents ?

Ans. $87 62cts.

10. How.many fur. are there in 3m. Ifur. ? • Ans. 25fur.

17. In i31b. avoirdupois how many drams ? Ans. 3328dr.

18. In 21 gallons 3qts. Ipt. how many pints?

Ans. 175 pints.

19. How many Ells F. are there in 60 qrs. ? Ans. lOE.F.

20. How many lbs. are there in 2461 dwt.

Ans. 101b. 3oz. Idwt.

21. How many drams are there in 7251b. 6oz. av. ?

Ans. 185696dr.

22. In 12yds. 2qrs. Ina. how many nails ? Ans. 201na.

23. How many cwt. are there in 275521b. ? Ans. 246cwt.

RULE OF TWO. Oo

RULl^: OF TWO.

The Rule 6f Two is that iii wMcli two terms are given to find «i, tliivd, which is the answer.

To Ihul the whole cost of any number of articles at any price per article.

RULE.

Multiply the articles by the given price of one article; the product will I'e the annwer.

EXAMPLES.

1. What will eleven oranges come to at 12 i cente each?

2. How much will 60 bushels of apples come to at 8 i cents per bushel ?

11 00

12^ the given pr. of one article. 8 1

132 * 480

. S^the half of 11 is 5i 15 the fourth of60 is 16

Ans. ^1 37i . Ans. U 95

o. ITow much will 105 pounds of sugar come to at 12 J cts. per pound ? " Ans. $13 12^ cent«.

4. Whi)t will 60 apples come to at 2^ cents each ?

Ans. ^1 35 cents.

5. "What will 87^' pounds of beef come to at tlfree cents per pound? Ans. $2 G2^ cents.

0. IJought 40 pounds of coffee ai; 81} cents per pound; what did it amount to ? Ans. $12 50 cts.

7. IVirchascd ninety gallons of molasses at 55 J cents per g;i1km ; what did it amount to? Ans. $50 02 1 cts.

8.. What will nineteen pounds of biwion come to at 8J cents per pound ? • Ans. $1 58 J cents.

9> Wliat is tlic -cost of 400 poumls of cheese at 8^ cents jper pound? Ans. -SSo 33} cents.

10. ]>ought 101 buslicls of wheat at ^1 04 cents per bushel; wh;ii did it amount to? Ans. -$105 04 cents.

11. What will 022" gallons of whiskey come to at 02^ • jcentii per gallon? Ans. $39 OG^ cents.

J 2. What \Yill 25 bushels of oats come to at 25 cents per 'Ijushel? Ans. $0 25 cents

fi *

MatWHaniiaMinpi

54 UUXE OF TWO;

13. How mucli will eleven pounds of butter come to ut 8^ cents per pound? Any. 91 j cents.

14v. What will 84 pounel» of "lard come tn) at ten cents per pound ? Ans. $8 40 cents.

15. How inuch will two thousand books come to at 20 cents per book ? Ans. $400. [

16. What cofc^t 789 pound.s of iron at 4 1 cents per pound?

Ans. ^35 50^ cents.

17. What cost 40 bushels of rye, at 20 cts. per bushel ?

Ans. 8«.

18. What will 6 pounds of soap come to at ten cents per •j>ound ? Ans. 60 cents.

■When iti.«> rcquh'ed to know how many articles may be bought with any sum of money.

llUlJfl.

i)i^■ide the sum by the price of one article; have the lividond and divisor of one dfcuumination. The quotient will be the number of articles.

EXAMPLKS.

1. How many, pounds of butter may be bought with ^1 60 ccntS; at 8 cents per pound ?

2. How many pounds of iron can I buy with $7 00 cts. at 3^ cents per pound ?

8)1 60 Aus. 20 lbs.

hiilves.

3^ 7 00

2 2

T) 14 00 halves

Ans. 200 pounds.

3. When one prmnd of sugar costs 12 i cents, how many pounds may be had for 30 dollars? Ans. 240 pounds.

4. A gentleman gavd" his son 60 dollars, which he was to lay out for tea at 37^ cents per pound. How many pounds did he buy? Ans. 160 pounds.

5. How many bushels of corn can I buy for 400 dollars^ if I give 13 cents per bushel ?

Ans. 3076bu. 3pe. 5qt. Ipt. +

6. When I can buy one pound of tobacco for 25 cents, i how many pounds can I buy for $75 ? Ans. 300 pounds.

RULE OF TWO. 00

7. How many pounds of iron may be bought with 37 dollars, at 4 cents per pound ? Aus. 925 pounds.

8. Having ^378 10 cents, a;id wishing to purchase feathers, what quantity can 1 purchase at 83^ cents per pound? Ans. 1134^- pound. +

9. If sixty dollars be the price of an acre of land, how many acres can I have for $192 GO cent^?

Ans. 3^1. Or. 33p.-f

10. Suppose a man lias ^1900 06 J cents, and is desirous to purchase salt. IIow many bushels can he buy, at 1 dol- lar 62} cents ? * Ans. 1160^ bu.+

n . How many pounds of cofl'ec, at 22 cents per })ound,

can I have for 22 dollars ? Ans. 100 pounds.

• 12. How many pounds of pork, at three cents per pound,

can I have for 960 dollars 60. cents? Ans. 32020 pounds.

lo. How many yards of cloth, at 15 cents per yard, can I have for 450 dollars 45 cts. ? Ans. 3003 yards.

14. How, many fowls, at 6} cents each, can I buy for ninety dollars ? * Ans. 1440 foTvls.

When a number of articles cost any sum of money, o.nd the price of one article is required at the same rate.

RULE.

Divjde the w'hole cost by the number of articles ; tlio quotient will be price of one article.

Note. If the dividend be not large enough to contain the divisor, reduce it till it will be.

EXAMPLES.

1. If 100 bushels of corn cost 12 dollars 50 cents, wh?.t| is the price of one bushel at the same rate ? |

2. If 4.} pounds of pepper cost $2 00 cents, what cost' one pound at the same rate ?

The axtidt^. lOia 12 510 4^ 2 00

~ 2* 2

^ng. 12 J cts. 1

9) 4 00 • Ans. 44 cts. 4.m. -f

56 RULE OF THREE.

3. If S fish cofit 50 ote., what will one cost?

Ans. 84- cents.

4. If I buy 40 bushels of flaxseed for 40 dollars 40 cents, how much do I give per bushelj Ans. ^1 01 cent.

5. A man travelled 420 miles in twelve days. How far did he travel each day ? Ans. 85 mi^es.

0. Bought 120 pair of shoes for 400 dollars 60 cents. What was the cost of one pair? . Ans. 83 33 1 qU.

7. Bought 6000 gallons of whiskey for nine hundred dollai-s. What was the price of one gallon ?

Ans. 15 cents.

8. If I buy 1517^ acres of land for 7500 dollars 37j cents, how much does it cost me per acre ?

Ans. U 94 J cts. +

9. A merchant bought 1950 penknives for 960 dollars 44^ cents. What did one cost? Ans. 49 i- cts. -f

10. If I buy 22 ^ yards of cloth with 7 dollars 50 cents, what cost one yard? Ans. 33 J cents.

11. I was offered 2000 books for $500 00 cent.^. Tell me what one book would cost at that rate ? Ans. 25 cents.

12. I was offered 2000 books for ^380 50 cents. How much was that for one book ? Ans. 19 cents. -|-

13. When a man's yearly income is $474 50 cents, how much is it per day ? Ans. $1 30 cents.

14. If seven months^ work bring $25 00 cents, how much will one month bring ? Ans. $3 57 cents. +

15. Suppose tlie President of the United States receive $25000 00 cents a year, how much is that per day ?

Ans. $68 49 cts. 3m. -f

PROPORTION; OR, RULE OF THREE.

The Rule of Three is that in which three terms are given to find a fourth or answer.

RULE.

Set that term in the third place which is the same kind of the answer. Consider from the nature of the question whether the answer ought to be greater or less than this third term. If it is to be greater, set the greater of the two remaining terms in the middle for the second, and the less for the first ; but if it is to be less, set the le«s of those two

RULE OP THREE. 57

teriiis ill the middle for the second term, and the otlier for the first. Then have the first and second terms of one de- nomination. If the third term consist of several denomi- nations, reduce it to the lowest deubmination in it; then multiply the second and third terms together, and divide the product hy the fir>t term. The answer will ]>e of the same dcQominatiou as the third ternj.

A'^oie. The operation may frequently be performed, thus: If the first term will divide the second by the quotient, mul- tiply the third; or if the second will divide the first by the quotient^ divide the third term.

EXAMPLES.

1 . If four bushels of cora cost 80 cent*'; how much will S bush(!lrf cost ?

2. If three yards of cloth costi fifty cents, how much will

ten yards cost y

hu. lu. cts. yd. yd. cts.

4 : 8 : : 80 3 : 10 :' : 50

o

10

Aus. $1 GO 3 1 500

Ans. ^1 66f

3. If four yards of muslin cost six cents, what will eight cost? ^ Ans. 12 cents.

4. If six yards of cloth cost IT cents, what Avill seven yards come to at the same rate'/ Ans. 19 cents 8m. +

5. If five bushels of potatoes cost 80 cents; what cost 14 bushels at the same rate? Ans. ?>2.24 cents.

6. If four bushels of corn cost $2 00 cents, how much wU 12 bushels cost at the same rate? Ans. ^6 00 cents.

7. If eight yai-ds of silk cost 40 cents, how nmch will 16 1 yards cost ? Ans. 80 cents. I

8. If three pounds of cheese cost 10 cents, what will 80 pounds come to at the same rate? Ans. ^2 66 f cents.

9. If six pounds of coftee cost 55 cents, what will 75 •pounds come to at the same rate ? * Ajis. $6 87j cts.

10. If 2^ bushels of salt cost U 08 cents, how much will 15 i busbals come to at the same rate ?

Ans. $24 88 J cents.

58 RULE OF THREE.

11. Boiiglit 24 po-nnds of beef for $1 62^ cents, how much is 90^ pounds worth at that rate ?

Ans. 16 12| cents. -^

12. "What arc 60 bushels of apples worth, when 13 bushels cost 45 cents 'f Ans. 2 dollars 07^ cents. 4-

lo. If 8 bushels of potatoes cost 3 dollars 94 cents, what will 105 bushels cost? Ans. 51 dollars 71i cents.

14. If 45 cents buy 11 pounds of tobacco, how much will 91 1 cents buy at that rate ? Ans. 22ilb. +

15. What will 22 books come to, if 60 cost 20 dollars 51 cents? • Ans. 7 dollars 52 cents. +

16. If 1 yard 2 quarters of cloth cost 56^ cents, what will 17 yards 1 quarter cost? Ans. 6 dollars 46f cts.-+

17. If 4 dollars will pay for 16 days' work, how many days work may be had for 98 dollars ? Ans. 392 days.

18. If 2 J bushels of salt cost 2 dollars 62 fr cents, how many bushels may be had for 556 dollars 18|- cents ?

Ans. 529 f bushels. +

19. If 7 pounds of coffee cost 87* cents, what must I pay for 244 pounds ? " Ans. 30 dollars 50 ct>\

20. If 450 barrels of flour cost 1350 dollars, what will 8 barrels cost ? Ans. 24 dollars .

21. If 750 men require 2250D rations of bread for .a month, what will a garrison of 1200 require ?

Ans. 36000 rations.

22. If 12 men can do a piece of work in 20 days, in what time will 18 men do it? Ans. 13 J days.

23. Wliat will be the cost of 17 tons of lead, if 5 tons cost 500 dollars? Ans. 1700 dollars.

24. If a pasture be sufficient for 3000 horses 18 days, how long will it be sufficient for 2000 ? Ans. 27 days.

25. ]f 8 men can build a tower in 12 days, in what time can 12 do it ? Ans. 8 day*.

26. IIow much carpeting that is 1^ yards in breadth, will cover a lioor that is 7^ yards in length, and 5 yards in breadth ? Ans. 25 yards.

27. How many yards of matting, 2^ feet ])road, will cover a floor that is 27'feet long and 20 tbet broad? Ans. 72yds.

28. What must %e the length of a board that is 9 inches in width, to make a surfixce of 144 inches or a square foot ?

Ans. 16 inches.

29. If 5 yard;? of cloth cost 1 dollar 12 J cents, what is

RULE OF TUllEE. 59,

the value of -1 pieces, each containing 8 yards and 1 quar- ter ? Aus. 7 dollars 42^ cents.

30. If IJ ounces of spice cost 13 cents, what cost 16^ ounces? Ans. 1 dollar 40 1 cents. +

31. If 100 "skeins of silk cost 25 dollars 21 cents^ how many may be bought for 1800 dollars 50 cents ?

Ans. 7142 skeins. + 82. If 2 dollars 50 cents pay fgr two weeks' boaiwiing, how long can I board for 40 dollars 40 cents !

Ans. 32 weeks 2 days. +

33. Suppose A hired to B 12 months for 60 dollai-s, after Avorking 7 months B agreed to pay A at that rate, what must he pay '{ Ans. 35 dollars.

34. If 1 cwt. of sugar cost 11 dollars 37^ cents, what will IScwt. 3qv. 191b. cost? Ans, 215 dollars 21 cts. -f 10^

35. How many men will it require to repair a piece of work in 50 days, when 14 men can do it in 100 days ?

Ans. 28 men.

36. Li what time will 600 dollars gain the interest which 80 dollars would gain in 15 years ? _ Ans. 2 3'cars.

37. If 2 yards of tape cost 50 cents, what will 54 j^nglish Ells 3qr. cost at the same rate? Ans. 17 dollars 6f cts.

38. If the price of 1 acre of land be 5 dollars 25 cents, what will 350 acres 1 rood 18 perches come to at that rate?

Ans. 1839 dollars 40 cts. 3ui. 4- \

JWUe. In all cases wherein labor is required to be per- formed, the day must be reckoned at 12 hours.

39. Suppose 20 days be required for 12 men to build a liousc, in what tin:ic can 18 men do the same ?

Aus. loda. 4hr.

40. In what time 'will 48 men make a fence which 12 men can do in 24 days ? Ans. 6da.

41. If G men. can do a piece of work in 18 days, hOw long will it require 12 men to do it ? Ans. 9da.

42. If 8 men can mow a piei-e of meadow in 24 da3'S, how many men can do it in 1 days ? Ant. 48 men.

43. If a traveUcv jx^rform a journey in 5 days, when the days are 11 hours long, how lono; will ho require to do it when tlio days ar« 16 hours long? Ans. 3da. 8hr.

44. How many yaxda of paper 2^ feet wide will be

j60 RULE OF THREE

required to ooTer a wall which is 12 feet long and 9 feet high ? Ans. 14yd. 1ft. 2in. +

45. What quantity of linen that is 3 quarters of a yard wide, will line 7 J yards of cloth that is lA jards wide?

Ans. 15 yards.

46. A ship's crew consisting of 45 men are provided with 4500 pounds of bread, of which each man eats one pound pcr-^ay ; how many weeks will it last them ?

Ans. 14w. 2 da.

PROMISCUOUS EXAMPLES,

IN THE RULE OF TWO AND THREE.

47. If 7 oxen be worth 10 cows, how many cows will 21 oxen be worth ? Ans. 80 cows.

48. If boai-d for one year amount to 182 dollars, what will 39 weeks come to ? Ans. $13(> 50 cts,

49. If 30 bushels of rye be bought for 120 bushels of 1 potatoes, how many bushels of rye can be bought for COO ! bushels of potatoes? Ans. }50bu. rye.

60. A f\irmcr made 14G barrels of eider, which he after- wards sold at 3 dollars 12 1 cents a barrel ; what was the amount of the whole ? Ans. 456 dollars 25 cts.

51. A lady purchased a set of silver weighing 51b. 6oz, 5dwt. at 1 dollar 50 cents an ounce; what was the cost of the whole ? Ans. 809 S7^ cts.

52. A lady intending to make a bed-quilt containing 6 square yards, desired her daughter to inform her how much domestic, o quarters of a yard wide, would be required to line the same. How many did it take? Ans. 8yds,

53. A pijte will drain off a cistern of water in 12 hours. iHow many pipes of the same size wll empty it in 30 ! minutes? • An^^ 24 pipeb'. I 54. A gentleman bought a bag of coffee for his own use, ! weighing 1271b.j for which he gave 15 dollars 25 cents.

What was it a pound? Am. 12 cts. -f-

55. If a man spend 4 dollars 62 J cents each day, how much will that amount to. in a year? Ans. 1688 12^ cts.

56. I lent my friend 350 dollars for five months, be pro- mising to do me the same favor, but when requested, he could spare only 125 dryllar.-. How long ought I io keep jit to balance the favor? Ans. 14 monthi->.

57. If a person's income be 1000 dollars a year, how

DOUBLE RULE OF THREE. 61

much can lie save provided he spend $1 50 cents each day? Ans. 452 dollars 50 cts.

58. If the third of six he. three, what may one-fourth of twenty be? As 2 : 5 : : 3. Ans. 7 J.

59. If 80 days tuition cost 3 dollars 50 cents, how much is one day worth at that rate ? Ans. 11 f cts.

60. How many planks 6 inches wide and 12 leet long will it require to lay a floor that is 18 feet wide and 24 feet long? Ans. 72 planks.

ol. A certain boat is 80 feet long and 18 feet wide. I demand the number of planks re<:j[uired to floor i , 18 feet long and 1 foot 3 inches wide ? Ans. 88 J. -f-

JVote. The diameter of a circle given to find the circum- ference. State, if 7 give 22, what will the diameter give ? Or the circumference given to find the diameter. As 22 is to 7, so is the circumference.

62. K a wheel be 20 feet in diameter, what is its circum- ference? 7: 20:: 22. (ijis. 62f.

63. If a wheel be 60 feet in circumference, what is its diameter ? 22 : 60 : : 7. (Ans. 19. +

DOUBLE RULE OF THREE.

Double Rule of Three i8_that in which five terms ai*e given to find the sixth or answer.

HOLE.

That which is the principal cause of gain, loss, or action, is the first term. Space of time or distance of place the second. The gain, loss, or the action, the third. Then place the other two terms under those of the same name. If ihe blank fall .under the third term, multiply the first and second terms together for a divisor; the other thi^ee for a dividend. But if the blank fall under the first or second terms, multiply the third and fourth terms together for a divisor; the other three for a dividend. The answer will be of the same denomination as the blank term.

J^ote. If the blank fall under the third term, it is direct proportion, If under the fii-st or Eacoud, inverse proportion.

6

i

ni ■ ■ jiiii ij I ^1 t^l ■r ' I II n«iiii I '■ ■. . —^M— i

D(>LBLE RULE OF THREE,

MWiM'.irfn

EXAMPLES.

i 1. If 6 men iu 10 days mow 60 acres of grass, how long! ijwill it take 5 meu to mow 80 acres?

2. If 7 men am' reap 8-1 acree of whe^i In 12 days, bow many men c^n reap 100 acre* iu 6 days ? 1

men

da. A. mtn. da, Ji.

10 : : 60 T : 12 : : 84

80 5 100

60 10 12

300 800 84 1200- ..

6 . 5 7

;-'>j00)48|00 42|0) 840|0 (Am. 20 meu.

84

Ans. 16 daj-g.

0

3. If 4 men in 8 dayy eat 5lb. of bread, how nmeh will ^12 men ecit in 20 days? Ans. 37Mb.

\ 4. Suppose 4 men mow 48 acres in 12 days, how many acres can 8 men mow in 16 days? Ans. 128a.

! 5. If $100 gain 86 in twelve months, what will ^400 ^gain in 9 months? Ans. 18 dollars.

6. If .8 men in 16 days can earn 96' dollars, how much can" 12 men earn in 26 dayn ? Ans. 284 doilari^.

7. If ten men in 18 days can earn 56 dollaxB, how many dollars can 20 meu earn in 35 days?

■ Ans. $217 77ctti. 7m, 4-

8 Suppose 8 men can make i20 pair of shoes in 30 days,

how many can 12 men make in 90 daya ? Ans» 540 pair.

9. If 66 dollars 31.} cents be the wagen of 20 men for 5 days, what will 46 meu earn in 32 days ? Ans, $828 92ct6.

10. If 100 dollars in a year mrc 6 dollars interest, what will 335 dollars give in 3 years ? Ans. 60 dollars 30 cts.

11. "When 10 oxen in 18 days eat 2 acres of grass, how many acres ^vill serve 20 oxen 27 days? Ans. 6 acres.

12. Sup|X!3e the wage?? of 6 person?, for 21 weekM be 288 , dollars, what must 14 persons receive for 46 weeks ? I / Ans. 1472 dollars

13. If STlb. of l^eef be suSicient for 12 persons 4 days, how many pounds will suffice 38 men 16 days ?

hm 4681b. lOfAT.

— ^— ™^"'— — *— *— ^"^ ' . ""■'*" _i. ' -.,^','T'-'J;3-l;^'■i" i

I>OUBLi: RULE or THREE. (58

14. If 30 hoi*ses in 4 days eat 40 bushels of corn, how many bushels will suffice 100 horses 20 days ?

Ans. 666fbu.

15. If the carriage of 9cwt,. 45 miles, cost 54 dollars 54 cents, how far may S6cwt. be carried for 98 dollars 72 cts. ?

Ans. 20m. 2fur. 86p. +

16. K 100 dollars in 12 months gain 6 dollars interest, what will be the interest of 400 dollars for 14 months ?

Ans. 28 dollars.

17. If 100 dollars in 12 months gain 8 dollars interest, what sum will gain 50 dollars in 24 months ?

Ans. 312 dollars 50 cts.

18. If 100 dollars in 365 days gain 6 dollars interest, what will be the interest of 1000 dollars for 27 days?

Ans. 4 dollars 44 cts. nearly.

19. If 100 dollars in 52 weeks gain 10 dollars interest, what will be the interest of 75 dollars for 7 weeks ?

Ans. 1 dollar 00 f ct.

20. If 12 bushels of oats be sufficient for 20 horses 22 days, how many biiBhels will serve 62 horses 86 days ?

Ans. 60bu. 3pe. 3qt. Ipt. 4-

21. When 4 boys, in 20 days, collect 1500 'bushels of apples, how many days will it require 25 persons to collect 4000 bushels ? ' ' - Ans. 8 days. +

22. What is the interest of 568 dollars for 4^ years, at 6 per cent, per annum ? Ans. 152 dollars 01 ct.

23. What will be the interest of 80 dollars for 10 months at 10 per cent. ? Ans. 6 doUara 66 f cts.

24. If 100 dollars in 12 months gain 83 dollars 38^ cts., what will be the interest of 64 dollars for 8 J months?

Ans. 15 dollars 11 cts. -f

25. If 100 dollars in one year gain 7 dollars 50 cents interest, what sum will gain 9 dollars in 4 months ?

Ans. 360 dollare.

26. What ifl ihe interest of 19 (ioUars for 5| months at 6 per cent. ? Ans. 49 1 cts. -f

27. What sum at 6 per cent, will produce 500 dollars interest in one year? Ans. 8333^ dollars.

28. A gentleman said the money he had on interest at 6 per cent., produced one dollar per day. What sum had he] on interest/ Ans. 6083 J dollars.

_^ 29. With how many dollars could I gain 6 dollars in one

\U

PRACTICE.

year, if \vith 560 dollai's I gain 5G dollars in one year and

8 month t

Ans. 100 dollars.

30. A wall wldch is to be built to the height of 40 feet has been raised 20 feet in 10 days by 16 men, how many men muni be employed to finish the Tvork in 5 days ?

Ana. 32 men.

PRACTICE.

Practice is a phort method of asceiiaining the value any number of articles at any given price per article.

TABLE OF ALIQUOT PARTS.

of

cts.

$

50 =

■■ ^ '

25

k

20

i.

o

12*

i

f*i

10

8^

1

T2

- a^ o

>— <

6}

tV

n

5.

A

4

in

*>

1

5U J

m.

Cts.

5 =

■■ i ]

1 ^^

2

1

r sfl

1

tV

1 ^

2 or 56

1 28 16 14

8 7

CWL

i

■V

I

o

CASE I.

u * <

\ When the price is i, I, }, |, or f of a cent per article, pound, y^trd, acre, ])ushel, &c.

RULE.

Divide the given smn or fjuantity by the aliquot jjarts of \ a cent for the answer in cents.

EXAMPLES

1. Wlat is the value of 124 apples at ^ of a cent each ?

2. What is the value of 1260 peaches at ^ cent each ?

i 1 124 * J 1260

Ans. 31 cents.

Ans. $6 30 cents.

-^=^

r^

rRACTicii;.

G5

iJ.. What is the value of 192 plums, at | of a cent each ? !

Ans. S144cts.i

4. AVhat in the value of 24 quills, at J of a ceut each ?

Ans. 8 cents. [

5. \\Tiat is the value of 12 cherries, ut f of a cent ?

Ans. 8 cents

6. How much will 29 come to, at ^ of a cent each ?

Ans. 7^ cents

7. How much will 11 come to, at g of a cent each?

Ans. 8^ cents

8. What is the value of 19, at J cent each ? I

Ans. 9^ cents. I

9. What is the value of 20, at 2 mills each?

Ans. 4 cents.

10. What is the value of 40, at 5 mills each ?

Ans. 20 cents.

11. Wliat is the value of 30, iit I mill each ? Ans. 3 cts.

CASE 2. Wlieu the giveli price is cent8 :

RULE.

Divide the given sum by the aliquot parts of a dollar for the answer in dollars.

EXAiMPLES.

1. What is the value of 3216, at 6^ cents?

2. What is the value of 8620, at 10 Cents?

6^

I 0

^^O

216 (Ana. $201.

10

32

I

8G20

16 16

Ans. $802

3. What is the value of 4260, at 20 cte. ? Ana. S52

4. 8264, 20 1652 6. 4264, 12 i 533

6. 5876, 50 21*38

7. 386, 25 96

8. 18626, 55 10244

cts. m. 00 0! 80 0, 00 0 00 Oj 50 0 30 0,

•m' »ipa«fwa

Ob

PUACTIOE.

9 What ia tHe value of 3542, at 45 cts

10. 1724, 37 J

11. 31925, 80

12. 3654, 18 J 18. 13854, 56i

$ cts.in ? Aub. 1593 90 0| 646 50 Ol 25540 00 0 685 12 5 7792 87 5

CASE o.

When the gi> ea prici ia dollars ftiid «:cnf« :

IIULE.

, Multiply tlie giveu sum by the dollars, aud take parU for Ithe ocDts, and add the products together for the answer in

' dollfirs.

EXAMPLES.

1. What IS the value of 420 buBhcls of wheat, at 1 dollaj- 20 Wilis per biiyhel ?

20

420 1

420' 84

504 dollars.

$ CtS. $ CtSM.

2. W^hat is the value of 2412, at 2 06icts. ? Ans. 4974 75 0

3. 1224, 3 12^ 3825 00 0 4. 5. 6. i . 8. . .

CASE 4.

When the gives gum consists of several denominations, such aa yd., qr., na., &c. :

RULE.

Set down the given price of one of the highest denomina- tion, and multiply it by the whole of the highest denomina-

870,

1181

1033 12 5

197,

4 20

827 40 0

162,

2 25

364 50 0

217,

5S7a

1166 37 5

228,

7 62^

9363 50 0

PRACTICE. G7 '

tion given; then take aliquot parts of the next lowest de nomination, continually, and add the products together foi the answer.

EXAMPLES.

1. What is the value of lOcwt. 2qr. 71b. at SIO 25 (xnU per cwt. ?

$ cts. 10 25 10 cwt.

qr.

'J.

i

lb.

"T

t

102 50 5 12i^

64

Ans. S108 26^ cte. -f

2. What is the value of 5cwt. Iqr. 141b., at 2 dollars 50 cents per cwt. ? Ans. $13 43 f cents.

3. What is the value of 7cwt. oqr. 101b., at 4 dollars 15 cents per cwt. "^ Ans. $32 86^ cents.

4. AVhat is the value of 780bu. 3pe. 2qt., at J dollar 17 ctvs. per bushel ? Ans. .$913 55 cents +

5. What is the value of 129cwt. Iqr. 101b., at 1 dollar 5 cents per cwt. ? Ans. $135 80 6m. +

6. What is the value of 25cwt. Iqr. 91b., at 1 dollar 75 cents per cwt. ? Ans. $44 32 cents, -f

7. What is the value of 2qr. 141b., at $27 10 cents per c^^t.? Ans. $16 93 1 cents.

8. W^hat is the. value of 12cwt. 3qr., at $40 20 cents per

^^^•''„,, Ans. $512 55 cents.

. 9. W hat in the value of 19bu. Ipe. of corn, at 35 ct«. per

b"^h*5l ? ^ Ans. 0 dollars 73 f cents.

10. What is the value of 810 oum^es 13dwt. 12ot., at 12 J cents per ounce ? Au^. 102 dollars 8^%ents

11. What i.s the value of 27jd3. 3qr., at ^9 65 cents per yai-d ? Ans. 207 dollars 78cts. 7m.

12. What is the value of SGOyds. Iq., at 84 cent*? ppr y^'^^J Ans. 722 dollars 61 cents.

13. What IS the value of 126yds. 2qr. 2ua., at 4 dollars 75 cents per yard ? Ans. 601 dollars 46ct3. 8m. +

14. What is the value of 17hhd. 15gal. 3qt., at 64 dol- lars 75 cenLs per hhd. ? An?, 1116 dollars 93cts. 7m.

168 ' INTEEE8T.

INTEREST.

Interest is a consideration allowed for the use of money, relative to which are 4 particulars, viz; Principal, Time, Rate per Cent, and Amount. The principal is the money for which interest is to be received ; the rate per cent, per annum is the interest of 100 dollars for one year ; the time is the nuuaber of years or months, &c., for which interest is to be calculated; the amount is the principal and interest added together.

CASE 1.

To find the int«3n3st for any number of years, or years and months.

RULE.

Multiply the principal, consisting of dollars, by the rate per cent., and that product hj the number of years ; or if there be months, take aliquot parts of a year, cut off two figures OR the right of the product for cents j or if there be cents in the principal, cut off one figure on the right as a remainder ; one more for mills ; two more for cents ; those en the left will be dollars.

CAS£ 2. To find the interest for any number of months.

RULE.

. Find the interest at 6 per cent., by multiplying the prin- cipal by half the number of months ; or at any other per cent., fiud the interest at 6 ; then state, if 6 give that inte- rest, what will the per cent, you wish to calculate give, and cut off figures in the product for cents, as in Case Ist.

CASE 8.

To find the interest for any number of days.

RULE.

Multiply the principal by the number of days j divide the product by 6, the quotient will be the interest in mills at 6 per cent. If the principal consist of dollars and cents, destroy 2 figures on the right of the product ; the balance

INTEREST.

69

nl

will be ^tho interest as before. If any other per cent, is re- quired^ 'take aliquot parts and add or subtract^ according a^ the per cent, is more or less than 6.

JVote. Case 3d is estimating 360 days in a year, which will make the interest rather large ; it may be more accu- rately found by multiplying the principal by the number of ^ days, and dividimr the 'product by a proper divisor in the , following tabie, wnich divisors are found by the following stating :

da, : 365

per

cent

. 3 da.

Thus: 4 : 100 : : 365.

Rate per cent. Divisors

4

9125

H

8111

1

5

7300

! »

i).\

6636

6

6083

6^

5615

,

0

0000

per cent. $ Again, thus : 5 : 100

Rate per cent. 7 7^

8

8^ 9

9\ 10

Divisors. 5214 4866 4562 4294 4055 3842 3650

A divisor may also be found for weeks or months, by using 52 weeks or 12 months in room of 305 days.

CASE 1.. EXAMPLES.

1. What is the interest of $500 for 1 year, at 6 per cent. per auniun ?

2. What is the interest of 40 dollars 50 cents for one year and six moiitlis, at six per cent, per annum?

3 500 6

Ans. ^s'ojbOcts.

moutlia. 6

3

cts.

40

^0

6

243

00 1

243 121

00 50

Ans. 33 64 cte. 5m.

70 INTEREST.

3. What is the intereat of 400 dollare for ouo year, at six perceut. y Ana. 24' dollars.

4. What is the interest of 600 dollars for one year, at six per cent, per annum ? Ans. 36 dollars.

5. What is the interent of 250 dollars for one year, at five per cent. ? Ans. 12 dollars 50 cents. |

6. What is the interest of 61 dollars for one year., at six. per cent. ? Ana. 8 dollars 6 cents.

7. What 13 the interest of 44 dollars for two years, at seven per cent, per annum ? Ans. 6 dollars 16 cts.

8. What is the interest of 90 dollars for thne years, ul five per cent. ? Ans. 13 dollars 50 cents.

9. What is the interest of 68 dollars for four years, at, four per cent. ? Ans. 10 dolhu-s 88 c^nts.

10. What is the interest of 1000 dollars for four years, at eight per cent. ? Ans. 320 dollars.

11. Wliat is the interest of 50 dollars for five years, at five per cent. ? Ans. 12 dollai's 50 cents.

12. What is the interest of 19 dollars for two yeai*8, at four per cent. ? Ans. 1 dollar 52 cent.^?.

13. What will he the interest of 1772 dollai-s for two years, at six per cent. ? Ans. 212 dollars 64 cents.

14. How much interest will 75 dollars draw in five years, at 4^ per cent. ? Ans. 16 dollars 87 ^ ct-s.

15. What is the interest of 100 dollars for two. years and six months, at 6 per cent., per annum? Ans. 15 dollars.

16. What will be the interest of 350 dollirs fur three years and four months, at 6 per cent, per annum l*

Ans. 70 dollars.

17. What will be the interest of 48 dollars for four years and one month, at 5 per cent, per annum ?

Ans. 9 dollars 80 cents.

18. What is the interest of 64 dollai-s for one yeai* and seven months, at 7 per cent, pei* annum ?

Ans. 7 dollars 9} cents.

19. What is the interest of 14 dollars for four years and 11 months, at 7 per cent. ? Ans. 4 dollars Sl'i cts.

CASE 2. EXAMPLES.

1. What is the interest of 40 dollars for four months, at 6 per c^nt. per annum ? Ans. 80 cents.

^Tl1

INTEREST- 71

2. What, is the iuterest of GO dollars for 6 months, at 8 j-K?! cent, per aunum ? Ana. 2 dollars 40 cts.

10 60

o

3

80 cento. 0 : 8 : : 180

8

6)1440

e2 40

3. What is the interest of 18 dollare hr six months, at Isix pjT cent, per annum? Ans. SO 54 cents.

4. What is the interest of 50 dollars for eight montha, at ,| seven ptn- cent, per annum? Ans. ^2 38f cts.

6. What is the interest of ^900 for five months, at five per cent, per annum ? Ans. 18 dollars 75 cts.

6. What is the interest of 91 dollars 50 cents for four months, at 4 per cent. "/ Ans. 1 dollai* 22 cents.

7. W hat is the interest of 80 dollars for five mouths, at seven per cent. ? Ans. 2 dolWs 06^ cents.

»^ote. When the amount is required, add the interest to the principal.

8. What is the amount of S62 50 c-ents for thirteen^ months, at 6 per cent, per annum ? Ans. ^6Q oGctg. 5m. i

9. What i* tlie interest of tlir for fourteen months, at sixi per cent. ? Ans. 5 dollars 25 ccnte.;

10. What is the intcrefct of S5 60 cents for 5^ mouths,- at six per cent, 'r Ans. 15 cents, -f-

A\)le. in this case, after finding the iuterest at six per I cent., if any other r.at^ per cent, be required, take aliquot' parts and add cir subtract, ac<v)rdif»g as the rate per cent, is!

more or lers than six. -. i

I

11. What is iheintorept of 80 dollars fnr eight moutBaJ I fit five p:i- c€ij'. "

72

INTEREST.

12. What is the iutorest of 00 dollars for four mouths, at eight per eont. ?

6 ptJF.

5 por. 1

80 4

320 int. at 6 per ot. 53^

60 o

^ 3

1 20 int. at 6 per ct 40

$1 60 cents.

Ans. $2 66f

13. Wliut in tlie iutercBt of 120 dollars 60" cents for fifteen months, at 6 pt-r cent. ? Ans. 9 dollars 4ctH. 5m.

14. What is the interest of 5420 dollars for 17 montlis, at 4 per cent, per annum ? Ans. 307 dollars 13 J cts.

. 15. What is the interest of 7200 dollars for 14 months, at G per cvjit. per anniun ? Ans. 504 dollars.

16. Yvliat is the interest of 8050 dollars SDj cents for 47 months, at 6 per cent.^ per annum ? '

Ans. 1891 dollars 95cts. 5m. !

17. What is tlic interest of 948 dollars 62^ cents for' eight months, at 8 per cent, per annum ?

Ans. 50 dollars 59 cents. 4- ,

18. What is the interest of 36 dollars for one month, at, 8 per cent, j^er ami urn ? * Ans. 24 cents,

j ]9. What is the interest of 1000 dollars for 40 months,' ■ at 0 per cent, per annum ? Ans. 200 dollars. !

! 20. What is the interest of 328 dollars for 12 months, at i 6 p.r cent. ? Ans. 19 dollars 68 cents*

i " 1

! When there is a fraction in tlie rate per cent., un 5i, 6^, I or 6 1, multiply and add i or A, (tui the case may be,) of the I pnncipal to the product, and proceed as before. i

i 21. What will be the interest of 540 dollars for 24 months, at 5 per cent, per alinum ? Ans. 54 dollars.

22. What would be the interest of 482 dollars for 84 mouths, at 6 dollars per c«nt. per annum ?

Ans. 202 ddln-?^ 44 cts.

aam

SS=B

INTEREST. ' 78

2S. "What is the interest of 325 dollars for 60 months, at 4 per cent, per annum ? Ans. $54 16 cents 6in.

24. What is the interest of 840 dollars for 63 months, at 4 per cent, per annum ? Ans. $176 40 cents.

25. What is the interest of 840 dollars for 64 months, at 7 per cent, per annum ? Ans. $313 60 cents.

26. What is the interest of 560 dollars for 4 months, at six per cent, per annum? Ans. $11 20 cents.

27. What is the interest and amount of 100 dollars for ten months, at 10 per cent, per annum ?

Answer i ^^ ^^^ ^^'^'^- \ $108 33^ amount.

28. What is the amount of 76 dollai-s 25 cents for 25 months, at 6 per cent, per annum ? Ans. $85 78cts. Im. +

CASE 3.

JVote. Multiply any principal hj the rate per (;ent., and that product by the nuniber of day 3 it haa been or interest, and divide the last product by 366. The quotient will bo the interest.

EXAMPLES.

1. What is the interest of 1000 dollars for five days, at 6 per cent, per annum ? Ans. 83 certs 3m. +

2. What is the interest of 500 dollars for 60 days, at 8 per cent, per annum ? Ans. $6 66cts. 6m. +

1000 500

5 60

6)5^0 6)30000

8313^ 2 Tr5"000

I 10665

6|66|6f

3. What is the interest of 400 dollars for 40 days, at 6 per cent, per annum? Ans, $2 66c^. 6m. -|-

'i INTEREST.

4. Wh'di is the interest of 900 dollars for fourteen dajs, Ut 6 per cent. '• Ans. $2 10 ceiilvS.

I 5. What is the interest of 1000 dollars for 4 days, at 61 I per cent. ? Ans. 66f cents, j

6. What is the interest of 500 dollara for one dav, at 6 pcT cent. ? Ans. 8 cents ';}m. 4-

7. What in the interest of 16 dollars 33J cente for 24 dsys, at 6 per cent. ? Ans. 6 cents 5ra. -\-

8. What is the inteiHist of C4 dollars 64 cents for IS days ^ai 6 per cent, per annum ? Ans. 19 cents Sm. \

9. What is the interest of 45 dollars for 22 days, at 5i jp^T cent, per annum? Ans. 15 cents. -f

10.. AVhat is the interest of 90 dollars for 51 days, at 8 {A^r cent, per annum ? Ans. 1 dollar 2 cents.

JVoie. AVhen Uio time is years, months, and days, pro- ofed witli the years and months as in Case Int, and for the tUya take niiquot parts of 30.

11. What is the interest of 50 dollars for 1 year, 2 months, and 5 days, at G per cent, per annum ? Ans. $3 54 cents.

12. What is the interest of 100 dollars for one year, 7 months, and 11 days, at 6 per cent. ? Ans. $9 68 cents. +

13. What is the interest of 21 dollars for 4 years, 4 mt-nths, and 4 days, at 5 per cent. '/ Ans. $4 56 cents. +

14. What is the interest of 5 dollars for 10 years, 3 months, and 19 days, at 6 per cent. ? Ans. ^3 09 cents. +

15. What is the intei'eet of 5 dollars 87^ cent* for 9 monthp, and 24 days, at 6 prr cent, per annum?

Ans. 28 rentf-i 7)ri. f

OASJE 4.

The amount, time and rate per cent, given to find the principal.

Find the amount of 100 dollai-s at the rate ix>r cent, and time given, y,'hich amount is the first term ; the gi^cn sum . the 2d ; 100 dollars the 3d ; proceed by the Rule of Three ; ■ the quotient will be the principal required. j

INTEREST. 75

EXAMPLES.

1. What principal at interest for 8 years, at 5 per cent., will amount to 840 dollars ?

$ 140 : S40 : : 100

100 100

Tv

500 84

8

14fO)8400IO(AaF. $600.

00

Intx^rost. 40100 100

Amount. 140

2. "What principal at interest for 5 years, at 0 per rent, per iinuuni, will amount to 650 dollars ? Ans. $500.

3. What principal at interest for 5 years, at 6 per cent, per annum, will amount to 2470 dollars ? Ans. $1900.

CA8E 5.

To find the rate per cent, when the amount, time nnd principal arc given.

RULK.

Subtract the principal from the amount; then state if the principal give the inlerest or remainder, what will 100 dol- lars give. Divide the answer by the number of years ; the quotient will be the rate per rent.

1. At what rate per cent, per annum will $500 amount t<i 8^50 in five years ?

Aiuuuot. 650 Principal. 500

V v 9

500 : 100 • • 150 150

150 intorejit

5000 100

5010)150100 Years. 5)30

Ans. 0 per cent.

J

20|00 . 210)1210

Ans. 6 years.

2. In what time will COO dollars amount to 798, at 6 per cent, per annum? Ans. 5 J years.

3. Suppose 1000 dollai's, at 4^ per cent, per annum, amount to 1281 dollars 25 cts., liow long was it at interest?

Ans. 6 years 3 months.

PROMISCUOUS EXAMPLES,

1. What is the interest of 500 dollars for one year and 2 months, at 6 per cent. ? Ans. 35 dollars.

2. What is the interei^t of 450 dollars for 2 years and 6 months, at 5 per cent., per annum ? Ans. 50 dollars 25 cts.

3. What is the inter 3st of 65 dollars 87 J cents for 9 months, at 6 per cent. ? Ans. 2 dollars 06^ cts.

4. What m the interest of 800 dollars for Ibur years, 5- months and 19 days, at G per cent, per annum ?

Ans. 214 dollai-s 53cts. 3m. +

5. AVI. at is the interef t of 18 dollars 75 cts. for 1 year, 2 months aid 7 days, at 6 per cent, per annum?

Ans. 1 dollar 33^ cents.

70 INTEREST. i

2. At what rate per cent, will 600 dollars amount to 3744 in bur years ? Ans. 6 per cent.

4. If S84 dollars, a< intere;3t 2 years aijd 6 months, | amount o $927 82^ c s., what was the nite per cent, per jinnum? Ans. 4^ per cent,

CASE G.

To find the time when the principal j amount, and rate per' cent, are given.

RULE.

Divi'^^ the whole interest by the interest of the principal, for one year. The quotient will be tho time required.

1. In what time will 400 dollars amount to 520 dollars, at 5 per cent, per anuun/ ?

409 520

5 400

AND BROKERAGE.

r-^ I

C. What is tliG interest of 90 dollars for 8 month?, at 9 per cent. ? Ans. 5 dollars 40 cts.

7. What is the interest of 6 dollars for G days, at 6 per cent. ? An 8. 6 mills.

8. V/hat is the amount of 1000 dollars 25 cts. f )r 4 years, \ months, and 5 days, at 7^ per cent, per annum?

Ans. 1326 dollars 37 cts. 3m. +

0. In what time will 1000 dollars amount to 1500 dollars,

at 8 per cent, per annum ? Ans. 6 years 3 months.

10. What is the interest of 25 cts. for 25 years, at 6 per cent, per annum ? Ans. 37 J cts.

11. What is the interest of 87 J cents for 1 year and 6 months, at 6 per cent, per annum ? Ans. 7 cts. 8m. -f-

12. At wliat rate per cent, per annum' will 1200 dollars amount to 1800 dollars in 5 3'ears ? Ans. 10 per ct.

INSURANCE, COMMISSION, AND BRO- KERAGE.-

Brokerage is an allowance to insure factors and brokers at a stipulated rate per cent., agreed on by the parties con- cerned.

RULE-

INIultiply the sum by the rate per cent. If the rate be less than one per cent., take aliquot parts.

EXAMPLES.

1. What is the commission on 500 dollars, at 5 per cent. ? •

2. What is the commission on 400 dollars, at f dollars per cent. ?

$ s

500

5

Ans. $257)0

k

400

200 100

Ans. 83 00

] 7S DISCOUNT.

8. What is the ineurance of GO doUai-s, at 3 per cent. '/

An£. 1 dollar SO cents.

4. What is the commiseiuil on 1351 dollars 50 cents, at 5 J per e«nt. ? Aus. 74 dollars 33 cents. -f

5. The gales of certain g<X)d3 amount to 1080 dollars, what smn is to be received for them, allowing 2| per cent, for commission? An.s. 1633 dollars 80 cents.

6. What is the commiseioii on 3450 doilai*8, at 4 J per cent. ? Ans. 155 dollars 25 cents.

7. When a broker sells good.« to the ainoimt of 984 dol- lars 50 cents, what. is his commigsion, at 1} per cent. ?

Ans. 12 dollars 30 cents Cm. -}-

8. What is the insurance of 1250 doilars. at 7i per cent. ?

Ans. 03 (lollai's 75 cents. 0. If a broker buys goods for me, .nmoimting to 1650 1 ■ dolhu-B 75 QQnUi, what sum must I ])ay hiin, allowing 1^ per cent. ? AuB. 24 dollars 76 ccnl^ lm.--[-

10. What if: the commission on a pnlc of goods, amount-; ing to 1184 dollars, at 5 per cent. ? Ans. 59 dollars 20 cts.

11. What is the commission on a sale of goods, amount- J i«g to 4820 doUars, at -4* per cant,?

Ans. 21C dollars 90 cents.

DISCOUNT.

Discount is an allowance? made for the payment of a sum of money before it becomes due, and is the difference be- tween that sum due sometime hence aiid its prt^scnt worth.

RULE.

Find the interest Qjf 100 dollars at the per cent, and tii*e given ; to this interest add 100 dollara, which amount is the first term ; the given sum the second j 100 dollars the third. Proceeil by the Kule of Three. The answer will be the present worth. Subtract the answer from tlie given sum, and the remainder will be the discount.

EX^iMPLES.

1. What is the discount of 500 dollars for 4 ye^rs, dis- count at 5 por cent, per annum ?

MUK-^.^* ■3»^^|l^klSa^a<MlMW!Wt3MMnM<M«»»CI<IBB«a».'*t^S^

DISCOUNT.

$

100 5

500 4

20100 100

120 : 500 : : 100 100

1210)500010

prcbciit worth. 41 G 66|

S cts. 500 00 416 (>G^

\ Discount. S83 33^1

2. Wiiat is the present worth of GOO dollars, due m 2 3'curs, diacouut at 6 per cent, per annum?

Ans. $535 7 lets. 4m. -|-

3. What is tiie discount of 590 dollars for 2 years, dis- count at 6 per cent, per annum ? Ans. $63 21 ^ ct>i.

4. "SVhat is the present worth of 480 dollars, due in 4 years, at 4 per cent, discount? Ans. 413 dollars 79icts. +

5. "What is the discount of 645 dollars for 9 months, at 6 per cent, per annum ? Ans. $27 77ct6. 6m.

6. What is the present worth of 580 dolhirs, due in 8 moaths, discount at 6 per cent, per ;innum?

Ans. 557 69 cents. +

7. What is the present vrorth of 775 dollars 50. cents, due in 4 years, at 5 per cent, per annum ?

Ans. $640 25 cents.

8. TJouglit goods amounting tu iilT) dollars 75 cent,-^, at 6 months' credit, how nuich ready money nmst be paid if a discount of 4^ per cent, be allowed? Ans. $602 20 cts.

9. Bought goods amounting to 000 dollarp, ao 4 years' credit, how much ready money mw.i be jjaid if a discount

lof 6 per cent, be allowed? Ans. $725 80 i cent6.

8*0 TARE AND TRET.

] 0. What is the discount of 00 dollar* for 1 year and ^6 \ months, at 6 per cent, per annum? Ans. $7 43 J ccntp.

■ n. What is the discount of 205 dollars, duc^in 15 months, at 7 per cent, per annum? Ans. $,16 49^ cts. +

12. A. owes B. 100 dollars, due in one year, but B. agrees to allow A. a discount of 25 per cent, per annum for presen<} payment. What sum will discharge the debt ?

Ans. 80 dollars.

13. What is the discount of 100 dollai-s, due in 12 months, at 25 per cent, per annum? Ans. 20 dollars.

JYoie. When discount is made without regard to time, it is found precisely like the interest for one year.

14. What is the discount of 800 dollars, at 6 per cent. ?

15. What is the discount of 99 dollars, at 5 per cent. ?

*$ V

800 99

6 5

Ans. $48 00 discount. Ans. U 95

16. What is the discount of 476 dollars, at 8 per cent. ?

Ans. 14 dollars 28 cents.

TARE AND TRET.

Tare and Tret are certain allowances made by merchants in selling their goods by weight. Tare is an allowance made for the weight of the barrel, box, &c., that contains the commodity bought. Tret is an allowance of 4 lb. in every 104 lb. for waste, dust, &c. Gross weight is the goods, together with the barrel, box, or whatever contains them. When the tare is deducted from the gross, what re- mains is called suttle. Neat weight is the weight of articles after all allowances are deducted.

RULE.

ist. Subtract the whole tare from the whole gross ; the remainder will be neat. -2nd. When the tai*e is so much per barrel, box, &c., multiply the tare per barrel, box, &c.,

TARE AND TRET.

81

by tlic minibGr of barrels, boxes, &c. The product will be

the whole tare. Subtract the whole tare from the whole

'grop?^, and the remainder will be neat. 3d. When (he tare

is so iiiiich per cwt., run aliquot part, or parts of a cwt.,

through the whole gross. Subtract the quotient tlicrefrom,

and the remainder will be neat. 4th. Wheii tret is allowed

with tare, subtract the tare from the gross, as before. The

SI remainder will be suttlc... Divide the suttle by 26. The

mjuotient will be tret. Subtract tlie tret from the suttle, and

! the remainder will be neat.

EXAMPLES.

1. What is the neat weight of a hogshead of toba<;co, weighing 2cwt. 3qr. 251b. gross, tare in all Icwt. 2qr. 121b. ?

* cwt. qr. lb.

2 3 25 gross. 1 2 12 tare.

Ans. 1 1 13 neat.

2. What is the neat weight of a hogshead^ of tobapco, weio-hintr 5cwt. 2qr. 151b. gross, when the tare is 3qr. 71b.?

° ^ ^ Ans. 4cw^t. 8qr. 81b.

3. What is the neat weight of 369cwt. 2qrs. 211b. gross, tare in the whole lOcwt. Iqr. 121b. ?

Ans. 359cwt. Iqr. 91b. |

4. What is the neat weight of 0 hogsheads of sugar,, each weighing 4cwt. Iqr. 41b. gross, tare in the whole IScwt. 3qr. 191b. ? !

civt. qr. lb.

4 14

6

25 2 24 whole gross weight. 13 3 19 whole tare

11 3 5 neat

5. How much is the noa't weight of 7 casks of indigo, each weighing ocwt. 2qr. 121b. gro.ss, tr.re 251b. per cask ?

TARE AND TKET.

ciot. qr. Ih. cwt. qr. Ih.

3 2 12 0 0 25

7 7

• 25 1 0 gross. 12 7 tare in all.

12 7

Ans. 23 2 21 neat.

6. What is the neat weight of G casks of raisins, each weighing 3cwt. 2qr. 101b. gross, tare 201b. per cask ?

Ans. 20cwf. Iqr. 241b.

7. What is the neat -weight of 35 keg« of figs, gross weight 37cwt. Iqr. 20ib., tare per cwt. 141b. 'I

cwt. qr. lb

lb. 14

^

37 1 20

4 2 20 quotient.

Ans. 32 a 00 neat

8. What is the neat weight of 6 hogsheads of sugar, each ij weighing 7ewt. 3qr. 141b. gi'oss, tare 201b. per cwt. ?

Ans. oScwt. 3qr. 71b.

9. What is the neat weight and value of 12 bags of coifee, each 2cwt. Iqr. lOlbs. gross, tare 181b. per cwt., ti'et 41b. per 1041b., at 19 dollars 60 cents per cwt. ?

. ( 22cwt. 2qr. 181b. neat.

^^^^^^•444 dollars 15

I 444 dollars 1 5 cts. value.

10. What is the cost of 24 casks of prunes, each cask weighing Icwt. Iqr., 231b.. gross, tare 181b. per cask, at 5 dollars 17 f cents per cwt. ? Ans. $100 79cts. 4m.

11. Wliat is the neat weight of 5 hogsheads of sugar, eaeh lOcwt. Iqr. 201b. gross, tare 3qr. 251b. per hogshead, tret 41b. per 1041b.?

civt. qr. lb. cwL qr. lb.

10 1 20 0 3 25

* 5 5

52 0 16 gTose. 4 D 13 bre.

'4 3 13 tare.

Divide by 26)47 1 3 sutflo.

13 7 tret quotient.

An;^. 45 1 24 neat.

EQUATION.

83

To find the neat weight of Pork, CBtahlished hv custom, when the gross is given.

RULE.

Place each hundred separately. Then subtract i or 25 from the firat hundred : ^ or 12^ from the second hundred. The remainders will be neat. All over the second hundred is neat. Add the remaindei-s and all over the second hun- dred together for the neat.

Note. \ must be taken from any number oi pounds L'ross, under 100 including: — ^ from all over lOa pounds^ and under 200 including.

EXAMPLES.

1. What is the neat of a hog weighing 184 pounds gross ?

2. What is the neat of a hog weighing 212 pounds gross ?

25

\

100 12.^ 25

i

84 25 10*

\

100 12* 25

I

100 12 12 J

7d 73 1

73J

75

87* 12

87J

Ans. 148^ Neat.

Ans. 174»} Neat.

3. What is the neat of a hog weighing 305 pounds gross ?

Ans. 267 *lb. neat.

4. What is the neat of 3 hogs weighing gross as follows, Az. : no. 1, 191 lb. ; no. 2, 76 lb. ; no. 3, 201 lb. ?

Ans. 375 i lb. neat.

5. What is the neat of 2 hogs weighing gross as follows, •iz. : no. 1, 219 lb. ; no. 2, 1 13 lb. :' Ans. 268 lbs. neat.

EQUATION.

EquatJuii hi used to find fhe menu time of aeverol pay- jments du.-i at dilL'reiit times.

RULE.

Multiply each payment by its time. • Add up the several i products, and divide the sum by the whole debt.

[j proc

84 EQUATION.

EXAMPLES.

1. A. owes B. (^0 dollaifj, of which 40 dolhirg is to l)e; paid at 0 montlis, aud 20 dollars at 3 months, hut thoy agree that the whole shall be paid at one tiuic. When must it bo pa\fi?

S

40x0=240 20x3= 60

6|0)30|0

Aus. 5 mouths.

2. C. owes P. nSO dollar.s, of which 100 dollars i.s (u bo paid at G months, 120 dollar.s at 7 months, and 1(30 dollar.^ at 10 month?, Init, they agree that the whole shall he paid at one time. When must it be paid ? Aus. 8 months.

3. A merchant has owing to him 300 dollai*s, to be paid as follows, viz. : 100 dollars at 2 months ; 100 dollars at 4 months; 100 dollars at G months; but they agrca that the whole shall be paid at one time. When must it bo paid-?

Ans. 4 months.

4. A merchant had pm-eliased goods to the amount of 2000 dollars, of wliich sum 400 dollars are to be paid at prcKint, SOO dollar.^ at G mwuth?-, aud the rest at 1) mOMthi; but it is agreed (<> iJiake t»nc pa} m. lit of the whole. Whvn must it bo paid? Ans. G months.

o, A. owes J. o(M) doliar.s whi( h will be duo f<'ur months hence. It is agreed that 100 dollars hhall be p:iid now, aud that the rest- remain unpaid a longer time than four months. When must it bo paid ? Ans. 6 months.

G. A. owes B. 100 dollnrs, of which 75 dollars is to be paid at 4 months, and 25 (hdlars at 2 months; but th^y aLOto that, the whole shall b<' jKud at one time. Whoni m\u'-t it he paid ? An.-^.. 3 A montili^

7. C. is indebted to a merchant to the amount of 2500! dollars, of which 1000 dollars is payable at the end of 4^ months, 800 dollars in 8 months, and 700 dollar.- in 12 »tionths; when ofiglit payment to be made if all are paid i"!tnrrcriici-y An'?. 7^ months. -f

BARTER.

BARTER.

Wi

Barter is the exchanging of one commodity for another, according to a certain price or value agreed on by the parties concerned. Questions in Barter may be solved by the Rule of Three.

When any articles, at a given price per article, are to be bartered for any other articles, at a given price per article.

RULE.

Find the value of the articles whose quantity is given. Then find how many of the other articles may be bought with that money.

EXAMPLES.

1. A. has 400 yards of cloth, at 20 cents per yard, for which B. is to give him books, at 50 cents each. How many books must A. receive ?

2. C has 100 bushels of wheat, at 75 cents per bushel, for which D. is to give him rye, at 37^ cents per bushel. How many bushels of rye ought C. to receive?

cts. cfs. yd. cts. cts. hu.

50 : 2t : : 400 37J : 75 : : 100

400 2 2

5|0)800IO 75 150

100

Ans. 160 books.

75)15000(Ans. 200 bu. 150

00

8. M. has 500 barrels of flour, at 6 dollars per barrel, for which II. is to give him salt, at 1 dollar 25 cents per bushel. How many bushels of salt ought M. to receive '/

Ans. :' 100 l)u.

4. A. has 20 pounds of sugar, at 12 J cents per pound, for which J. is to give him fowls, at 10 cents a piec( . How many fowls ought A. to receive ? An.s. 25 fowls.

liARTEIl.

5. How many Imshulb uf rycj at 40 cents per bushel, lU'e iL^oiial to 00 busi; I.s of wtoat^at i:0 .cents per biislicl?

Ads. 112 .Iba.

iy. 0. hab ICO yards of ;5tati. at 14 cents per ^-ayd,. f'r which' N. agrees to give him oats, at 220 cent.s per Ini^h! I. How many bushels of oats ought Q-.'to' receive?

Aili. .liliDU.

7. P. sold 108 yards of calico, at 10 cents per yattl, for Tvhieh E. gave him 6 dollars in money, and the rost^in iiax- seed, at 8 cents per bushel. Kow many bushels of ihixseed did P. receive ? . . Au.s. GObu.

8. How many pounds of tea, at 80 cents per pound, must be given in barter for 25 poiinds'of. coffee, 'at 22 J' cents per pound? " ^■'■•" '■'■ ^" ''.''AnsrlSf pounds.

0. A merchant has 1000 yards of cauvciss,^fit 20 cents j)er yard, which he is to barter for vsergc, at 22 Jt cents per yard. How manv vanls of serge should lie receive?

Ans. 88 8|| yards.

10. A. LVdo fjugar at 12^ cents per pound, for a quantity of which C. is to give him 450 pounds of tea, at 1 dollar per pbund. How much sugar must ^. receive ?

•'■': -' - Ans. 3()00 pounds.

11. H. has 1000 bushtils of salt,, at'l dollar 10 cents per bushel ; for which AV. is to give him 80 gallons of brand}'-, at 87-5 cci;its per gallon j" and the rest in" cotton, at 15 cents per pound. How many pounds of cdttoti mu^ II. receive ?

Ansi'6866^ pounds.

12. Vv iUit quantity of jcandles, at S9 50 cents })er ewt., must be give^ for locwt Oqr. 27ij), oi' tobacco, at 20 cents per pound? Ans. ii5cwt. oqr. 20ib. 4-

.'I'j.- Two pev.vJMi '."'ai'vi- - A. h.'i!; J7cwt. of iroii;"a,t 13*

cents per lb. — B. ;has 12001b. of cheese, at 14 dollars per

cwt. — which of tkem muBif receive money, and how much?

•' Aufj. A. 107 dollars 4 cental.

li. E. has 2iOSib. of bacon, at 10 cents per jx^und, and

'81 bushel'?! of applep, ni Tl^ 'cents per bushel, wliich ho

barters with P. thus : E. to luve 185 dollar.^ 25 cents 'in

money, and the rest in pork, at 1 dollar 58 cents per barrel.

•How many barrels it; he to j-cwivc ? Airj. 50 barrels. H-

15. K. bought of y. 1021b. of lard, at 8 J ccnta per

pound, and is to pay him as follows, viz: in c;:.sh 1 dollar 1

■cent, 20 lb. of leather, at 20 ceul-s per pound, and 40 pounds

LOSS AND GAIN. 87

of Leef, at 2 J cents per pound, and the rest in butter, at 6] cents per pound. How many pounds of Ijutter must Y receive ? Ans. o9|^ pounds

LOSS AND GAIN.

Loss and gain is us^ed to sliow bow much ia gained or lost in dealing.

RULE.

1st. Subtract the cost from the sale ; the remainder will be the gain. Or, if the coat be more than the sale, pubtraot the sale from the cost; and the remainder will lo the lo?s. 2d. Wlien you wish to sell any commodity at a certain gain per cent., and wish to know what sum it must be s<"'ld for, say; if 100 give 100 with the per cent, added, what will the firr.t cost frive ? 3d. Wlieii the amount is ffivcn at a certain rate gain per cent., to find the first cost, say; if 100, with the rate per oeiit. added, give lUO, what will the amourr. give? 4th. When any commodity is Hold at n certain rate per cent, loss, to find thk sum received, say ; if ] 00 give 100 less the per cent, lost, what will the first cost give ?

EXAMPLES.

1. What will a merchant gain by buying 95 bushels of salt, at 1 dollar 20 cents per bushel, and soiling it again, at 1 dollar 50 cents per bushel ? $ cts.

1 50 .95 bushels

1 20 80

Gain on one bushel, ^30' x\ns. $28 50 cents.

2. Bought 55 3'ardp of cloth, at 13, cents per yard, and

^old the same again for 15 cents per jnil-d. How much ^im

gained by the tiarisaction 'r' . Ans. $] 10 cts. ■

'I 3. If 1 buy 50 yards of clntir, at 25 cent's per yard; and I

soil the pamc again for 30 centiper yard, how much do 1 f

• •(. If 1 buy 100 yards of tape, ;..

si'1] It f(ir TS ecn ts p"ryar(3, ho»v^iut»vii;-«i;i ' ilio jj

tn:ri^actioiV? > Ai .r^^. i

lU ■ -' -,, , , ^- ._„^,

\SS LO^JS AND GAIN.

5. If I buy 40 saddles, at 11 dollars 50 cents eacb, aii<l sell thciTi ngiiin at 10 dollars 99 cents; how much do I lose by the sale "? Ans. 20 dollars 40 cts.

(j. Bought 12 bushels of corn, at 22^ cents per bushel, and sold it again at 22 cents per bushel. How much did T lose by the transaction? Ans. G cent:^.

7. A man bought flour, at 85 per barrel, and sold it at $5 25 ccnt« per barrel. How much did he gain on o^.o barrels ? Ans. 90 dollars 75 ets.

8. If 1 lay out 500 dolhrs in cloth, at 5 cents per yard, and sell the same again at 12^ cents per yard, how nnich do I gain ? Ans. 750 dellars.

9. If I buy a horse for GO dollars, at how mueh must I sell him to gain 20 per cent. ?

If 100 : 60 : : 120. Ans ?72.

10. If I buy 100 yards of cloth for §50, at how nnieh must I sell it per yard to gain 20 per cent, by the whole ?

Ans. GO cents.

11. If I buy 54 yards of muslin for 29 dollars 84 cents, and sell the same again at 60 cents per yard, how much do I gain? Ans. 2 dollars 56 cents.

12. If I buy 90 horses for 1800 dollars^ at how much must I sell oach horse to gain 180 dollars in the whole ?

Ans. 22 dollars.

13.* A merchant sold 40 yards of cloth, at 20 cents per

yard, and by so doing gained 10 per cent. "What was the

first cost of each yard ? Ans. 18 cents. -|-

40

20

110 : 800 : : 100 100

11|0)8000|0

Yards 4|0)72|7i

18 +

14. B )ught a quantity of tea for ?5250, and sold it for 275 dollars. What is the gain, and gain per cent.?

Ans. 25 dollars gained, 10 per cent, i

Fii I ■ 1^ II II [111 II 111 II I II 1 1 II Ml I jjxjjLJi J lUMiMiilMihilllrn iimimiaMMiil>iifW«i]<«ii«'.'««i«j!»iLnrtcil

• I'AllTNERSillP. 89

15. Bought. 190 buFhols of corn for 326 dollars, and sold the same for 870 dollars 10 cents. "What was the profit on each bushel ? Ans. 9 cents

16. Bouirbt a parcel of goods for 60 dollars, and sold thf* same iuiinediatid}'' for 90 dollars^ with 6 months' crcdil IIow juucli ])er cent, per annum was gained?

Ans. 100 per cent

17. "When a broker receives in exchange 5 cents per do] lar profit, how much is the gain per ceut. "? Ans. $5

18. A man purchased 7 pieces of cloth, at ^13 75 centi? perpieSe; but finding it somewhat damnged, he paid S3 1"?^ 'cents per piece for dyeing it. At how ranch must each pio-^

bo sold to gain 12 per cent, on tUe whole ?

• ' Ans. $18 90 ccn.^.

10. A trader bought 250 barrel.'* of flour, at S4 50 cents

a barrel.. lIow must he sell each barrel to gai-n 100 dollars

by the bargain ? Ans. $-4 90 cenws.

20. If I purchtise 16 pieces of cloth at 14 dollars per

I piece, and sell 5 pieces a-t 17 dollars per piece, and 6 at 15

d<ilhirs per piece, what must I sell the rest at per piece to

I gain 12 per ce)it. on the whole/' Ans. $15 17cts. 6m.

rARTNERSlIIP.

rartncrship is a joint interest or property, the union of two or more persons in the same trade, by which rule, per- son*? in company trading together, are enabled to make a just division of the gain or loa^i, in proportion to each man's stock.

When the respective stocks have no time^ — ]

i

RULE. I

»

Add the several shares together, which amount is thej first term; either i>erson's share, the 2nd.; the whole gnin ov[ lo.ss, the 3rd. Proceed by the Rule of Three. 2nd. When ' the respevtive stocks have time, multiply each man's stock! by its tijiic. Add the several products together, which i amount is the fu'st term; cither i/a.r(icular product^ t)n« 2iiiV ; the whole gain or lo&s, the ord. Proceed as befoi

]^'lO()^. Add together all the shares of g;iin or lobS.

jHtC* rAllTNER^HlP.. j

j LA. B. and 0. made a, Htock. A. h.^h m giO, B ^iK), jO. S40, aud by trading, tliey gained oG. ddlarH. Wiiiit was I each man's phare of the gain r

A. 20

B. 30

C. -10

Amount. 90

: 20 :

: oG.

Ana.

A.'HfiLaro U8.

90

: 30 :

: a(>.

Ans.

B.'s «hare ^12.

90

40 :

Aus.

O.'f? share 810.

Proof. ^36.

2. A. and B. purchiib^ed goods worth 80 dollars; of which A. piiys 80 dollars and E. 50 dol^a^s. ^'hoy gaiued 20 dol- lar.'^ ; Tvliat is the caiii of each ?

" . Ans. A. $7 50 cts. B. S12 50 ctH.

3. Three merchants trading together gained ^-SOO. A.'s stocli was $800; E.'s stock ^700; C.'s stock $500. What way each man's share of tUe gain ?

.Ans. A.'s share ^200; B.'s $175; C.'s 3125.

I 4. xi merchant lj<)ir>g deceased, worth, IS 00 dollars, is

Ifcniid to owe the following sums: — To A. $1200; to B.

i$500; to C. (?700. How much is each to have, iu propor-

tio!i to the debt? Ans. A. 8900; B. $a75; and C. S525.

I 5.' B. C. and D, uiado a stock, by which they gained 800

jdoiiar.-i; wdiuroof B.'s stock wmi 4U0 doiiyijiS; C/s 500 doi-

I lars ; aud D.'s GOO dollais. I demand each man's share of

the «;ai.a. 'Ans. B. 's $213^ ; C/s $2GG^ ; D.'s $820.

G. Three drovers pny amona* them 800 for ])ae:ture, into

which they put 200 cattle.; oX which A. had 50; B. 80;

1 C. 7(^ 1 would know how much each had to pay?

Ans.. A.. $15; B. $24; C. $21.

7.. F^ir menr formed a capital of 3200 dollars. They

gained in a certain 'time 05G0 dollars. A. 'a stock w:is 5G0

doilarr>; B.'s 1040 dollars; C.'s 1200 dollars ;• and P.'s

400 dollars. What did each gain ?

Am. A.'9$UM;B.'s2132; C.'s 2460; and D.'s $820.

■ 8. B. C. and '" traded together; B. put in 50 dollars

for four jiLO'jtIiRr, ') J j': ''ollars for 6 months; and D. 150

TS^

doliura for S iiiontljs. They gained 12G dollars 80 cts.; v/li-tt is cacli man's t-Iiarc of tlic'gaiu? V m.

B. 50 >: 4^200

0. 100x6 600

' D. 150x8 1200

"^^ cff!. S cts.

-i;

2000 : 200: : 126 80 ("12 68 B.

2000 : ■« GOO : : 120 80 Ans. IsS 0^ 0. . 2000 :.1200 : : 120 80 (76 08 D.

9. 0. P. and R. traded togetlier ; 0. put in 100 dollars for 2 luoutha, P. 200 dollars for four luontha, jmd K. 400 dol- lars for 5 moutbf^, and by trading together they gained 600 j dollars 50 cents. Row miich is each man's gain in propor- I tion to his stock ? LO. 40 dollars 3 ^ cents.

I . Aus. Tp. 160 dollars- 18 Scents.

(_ R. 400 dollars SS-^l- cents. • 10. A. and W. made a stock ; A. put' in '500 dollars for G months, and W. 2000 dollars for 8 months,, and by trading they gained 2600 dollars. I demand crtch man's share of the* gain '^ , f A. 410 dollars 52 cents 5m. -i-

j\.n^, I W. 2189 dollars 47 cents 8m. + 11. S. G. and Tv". made a. stock for 12 months; S. put in at first 500 dollars, and two rtionths after Tie put iij 40 dollars more ; G . put in at first ^05 dollars 50 -cents, and at tho end of ten months he took out 300 dollars; W. put in at first 600 dollars 25 cci^s, and' 4 months after he put in 100 dollars, and 6 months after that lie put in 50 dollars 50 cents more. At the expiration of 12 months their gain is 1800 dollars 50 cents; what is each man's- share of the gain? rs. Si88 89ccnts2m.

An3:^{Gv ?602 S'4 cents 7m. ,,jt-W,t,?aip OQicents Om.

KX.CIUNG„Ji.

4 far th ill: ponnj; 7/

12 pence ; . ; Jiiilling

20 shillings. . i r.nund. £

s.

92

tXCHANCE.

TABLE,

Showing the value of English Money in Federal Money

N. Hampshire,

Mas.'^achupeits,

Now York and

South (

I^arolina

New Jersey, Pennsvlvania,

Rhode Island,

Connecticut, Virginia, Ken-

North Carolina.

and Georgia.

Delaware, and

Maryland.

tucky, and Ten-

nessee.

S.

d.

^

els.

s.

d.

^

c/s.

5.

d.

$

c/s.

s.

d.

$

cts.

■

2 .

0

»

2

3. J

o

2

2

2f

3

3

3

5^

3

H

3

4

4

4

4

7

4

H

4

5^

4^

4^

4^

Tof

4^

5

H

6J

6

G|

6

6

o§

6

8i

9

9^

9

IG

9

10

9

12^

1

0

12^

1

0

2U

1

0

13^

1

0

IGf

1

6

ISi-

G

32

1

G

20

1

6

25

0

0

25

2

0

42 f

2

0

m

2

0

33^

2

28

2

48

3

30

•3

37^

2

G

31i

o

G

53^

6

33J

G

ill

0

9

34^

9

58f

9

361

2

9

451

3

0

37»

o O

0

64 i

3

0

40

0

50

3

t)

4Gf

9

80^

9

50

9

62^

4

0

50

4

0

m

4

0

53i^

4

0

m

4

6

56 i

G

m

4

^

GO

6

75

5

0

G2^

5

0

1

7

5

0

G6f

5

0

83i

610

75

6

0

1

m

6

0

80

6

0

1

00

6

9

m

G

9

1

44^

9

90

9

1

12^

7

G

mi

7i6

1

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G

1

00 7

6

1

25

10

6

1

m

10 1 6

'^

25

10

6

1

40 10

G

1

75

JYote. In calculating the above table, remainders arc not marked, being less than I, &c.

£1 of New York and North Carolina, is $2 50

£1 of South Carolina and Georgia, is $4 28 J +

£1 of New Jersey, Pennsylvania, Delaware,

and Maryland, is . ; S2 6Gt

£1 New Hampshire, Massachusetts, Ehode Island, Connecticut, Virginia, Kentucky, and Tennessee, is $3 33^ •

: -

—

EXCHANGE.

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94 EXCHANGE.

A TABLE OF OTHER FOEEIGN COINS, &c.,

WITH THEIR VALUE IN FEDERAL MONEY.

$ cts.m. cts.m.

Poimd' Sterling .... 4 44 4 Pound of Ireland.. 4 10 0 Pagoda of India... 1 94 0

j Tale of Chma 1 48 0

I Millrca of Portugal. 1 24 0 ■i Ruble of Eu^'sia... 0 CG 0

The Guilder of the ) 39 q United Netherlands ) Mark lianco of "^ 33 5

Hamburg ..... j Livre Tournois of 1 -j^^ ^^

i,xtuuic ui xiLi.Tox.. V- V.W .. , rr;)nce )

];Pvupee of Bengal . . 55 5 | Ilcid. Plate of Spain 10 0

i JS'oLe. Some persons, to try others' skill in numbers, may 'give them the multiplyiDg of pound;:!, {.hillings, pence, ka.y ; by the winie ; or the multiplying of cents by the same, &c. The following will be sufficient, thus: — Pounds m\dtiplied by pounds, gTve pounds, l^ouhds multiplied by sliiliings, | give shillings. Shillings multiplied by shillings, give the ' 20th part of a shilling. Shillings multiplied by pence, give the 20th part of a penny. Pence multiplied by pence, give the 240th part of ri' penny, &c. ; and cen^•^ Tp.nltiplied by cents, give the 100th part of a cent, &c.

EXCHANGE.

Exchange teaches to change a sum of one kind of money

to a given denominaiion Of imother kindj to reduce the

• euiTcncy 01 each (if the United States to dolhu'S and cents,

|| or Federal Money.

' HULL. ' !

Ilcduco the sum to peace ) to the pence ;iunex two ciphers ; 1 then divide by the number of pence which make a dollar in, that state or country. The quotient will be cents; which] 1 reduce to dollars. 1

vYo/e. This rule ..fipplie.-\to the currency of any state or,', I! country,' if its cuiT(in<*l be in' pounds, shillings, pence, o:c.

i;XA3U'LLS.

1. Ill UO povLuds .N.,'W England, Virginia, Kentucky andj

I EXCHANGE.

I

^h^i^r^'^r,!^'^''^' ^""'^ "'''''^ '^''"^'' ''""^ centP, a dollar

90

is 00 12

s.

I ' 72)21G0000(.S300 00

I 21(3

0000

2 liring 12 pound., ^ sliiiiiiigs: and 0 pence to dollar J aud cent, sainc^cTurenoy. a^3. g^O G2^ ct J

3. Keduce 19 shillings and 10 pence to dollars and cents = same cnrroncv. ^ . . A,i^ «Rq ^^n.f > ';•

i y ^-,..t' , , • -^iife- WO Ducts. 5m. !

-4. in roo pounds how many dollars, cents and mill, : same currency r W$2548 83cts. in :(.

0 Keduce S0£ and Ss. to dollars and cents, same cm- 1

c7't. o^p o ^ ,„ . Ans. 8100 50cte.l

.nd \V.fCr i- "''' ^-^^^^^J dollars and cent., New York ^ a.Kl Aoxth Oarohna currency, one dollar being 90 pence?

- . ill oO£ how many. dollars and cents, same currency? s Tn <)r tr 1 ,„ • Ans. S75 00 ct«.'

,e,;vf '""' "''"^' ^^^^"^"-^ =^"'^ <^^"<^^ ^"me. cur-

I ^'^ T,. ^'Hr r V r r ' Ann. ,Sf^4 50 c(8.

M-^rvl nri' >;'^ ' 7 '^'''"''' ^^''^"-^y^^^'^ia, Delaware and

f'-k T tor- T -^vn^. O-'OlL {JO ct:;.

1^. in 12£ how many dollars and ccuta, same currency?

Jl. I.i 8fi:< Of<. 5(1. how miny dollnrs, een^s and rrll- ' same currcncv ? ' \ nt, «oQn i o ^ o "' I

12. Tn 5(U, :-^::,uI, (.':ir..lio:, .ndOenmacm-rencv'how mamy dollars and eent^, bcin. i>G pence in^ dollnr ? ^^

11 IS T, oiri , n , An::. 8240 00 cts.

! ""• ^'*"y^>^'l'''»'--^'?»nd cents, same currency?

L- ^ - , '^J»s. 890 00 cts. I,

96 EXCHANGE.

{ 14. In 460j£ and 16s., sterling money, liow many uollars and cents, being 54 pence in a dollar? Ans. §2048 00 ets.

To bring dollars, or dollars and cents, to pounds, shil- lings, &c.

RULE.

Multiply the dollars, or dollars and cents, by the number ■ of pence 'which make a dollar of the currency into which you wish to bring the given sum. The answer will be pence, which bring to pounds.

JVo/e. If there be cents in the given sum, two figures must be cut off from the right of the product, before bring- ing them into pounds, &c. -

EXAMPLES.

1. In 33 dollars how many pounds, &c. sterling, a dollar being 54 pence ?

S

83

54

182

165

]2)1782d. 210)14|8— 6d. Ans. 7£ 8». 6d

2. 1,000,000 dollars how many pounds, same currency?

Ans. 225,000£.

o. In 150 dollars 25 cents how ninny pounds, <tc.. New

'■ Eiidand, Virginia, Kentucky and Tennessee currency, a [

! dollar being 72 pence? Ans. 45£ Is. 6d.

I 4. In 2070 dollars. New Enghmd, Virginia, Kentucky

and Tennessee currency, how many pounds, <ltc., a dollar

being 72 pence? Ans. ()21£.

5. In 24 dollars 50 cenis how many pounds and shillings,

&c., in New YorK and ^orth Carolina cnrroucy, a dollnr

being 96 cents? Ans. 0£ 16s. Od.

VULGAll I'RACTIONS 97

6. In 2512 dollars, how many pounds of New Jersey, Pennsylvania, Delaware, and Maryland currency, a dollar being 90 pence ? Ans. 942£.

7. In 90 dollars, how many pounds South Carolina and Georgia currency, a doliai' being 66 pence ? Ans. 21£.

To change the currency of one state or country into that of another.

RULE.

Place the sum you wish to change, in the third place — the number of shillings in a dollar of that currency into which you wish to change it, in the second — and the num- ber of shillings in a dollar of that currency you wish to change, in the first. Proceed by the Kule of Three.

1. What is the value of 60£ Tennessee currency, in New York ?

S. S. £.

6 : 8 : ; 50

8

6)400

Ans. 66£. 13s. 4d.

2. What is the value of 500£ Massachusetta currency, in Pennsylvania? Ans. 625£.

3. What is the value of 100£ South Carolina or Georgia currency, in Kentucky? Ans. 128£. lis. 5d.-{-

4. What is the value of 750£ New Hampshire currency, in North Carolina? Ans. 1000<£.

VULGAR FRACTIONS.

A Vulgar Fraction is a part of a whole number, and is read by first mentioning the upper part of the fraction, and then^ the^ lower, thus : i, |, &c. The upper part of the fraction is called the numerator, and shows the part o( a whole number expressed by the fraction. The lower num- ber is called the denominator, and shows the number of such pai'ta contained in a whole number. Vulgar Fractions ai'c either proper, improper, compound, or roixeS. A proper

98 vulgXh tractions.

fraction lias its numerator less than its denominator, m |, |, &c. An improper fraction has its numerator greater than its denominator, as f, *, &c. A compound fraction is a fraction of a fraction, with the word " of ^' expressed between them, as J of s, of |, &o. A mixed number b a whole number and a fraction, as 5i, 81, &o. ,a^. ,,-.

REDUCTION OF TULCtAR FRACTIONS.

CASE 1.

To reduce a fraction to its lowest terii».

Di^'ide the numerator and denominator continually by j an J number that will divide them both without a remainder. i When they cannot be divided by any number without a re- j mainder, the fraction is then at its lowest terms.

EXAMPLES.

1. Reduce |f to its lowest terms;

24)11= ^Ans.

2. Reduce ai to its lowest terms. Ans. ^.

3. Reduce {| to its lowest terms. Ans. J.

4. Reduce j f | to its lowest tenne. Ans. f . 6. Reduce /g%. to its lowest terms. Ans. ^. 6. Reduce ||f to its lowest tcn»9. Ans. -fj.

CA«E 2.

To reduce a mixed number to an improper fractioB.

RULE.

Multiply the whole number by the denominator of^the fraction, and add the numerator to the product for a new| numerator, uuder which place the given denominator.

EXAMPLES.

1. Reduce 11| to an imi>roper fraction. Ane. Y-

New numerator. 57 Denominator. 5

VULGAR I'HAOTIONS. 99

2. Reduce 8^ to an improper fraction. Ana. Y-

3. Reduce 14 J to an improper fraction. Ans. V-

4. Reduce 99|?j- to an improper fraction. Ans. 'f|^.

CASE 3.

To reduce an improper fraction to a whole or mixed number.

EULE.

Divide the numerator by the denominator.

EXAMPLES.

1. Reduce \y* to its prop^* terms.

17)400(An3. 23A. J 34'

"60 51 '

9

2. Reduce ^y to its proper terms. • Ans. 22 1

3. Reduce J i to its proper terms. Ans. 5j'^

4. Reduce '*^/;i^ to its proper terms. Ans. 2^j

JVbte. Case 2d. and" 3rd. prove each other.

CASE 4.

To reduce compound fractions to single ones.

RULE.

, Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; "which reduce to their lowest terms.

EXAMPLES.

1. Reduce J of § of J oj a to a single fraction. Ans. J.

1x2x3x4= 24 =

24) (J.

2 + 3x4x5= 120

100 VULGAR FRACTIONS,

2. Reduce ^ of | of f to a single frnction. Ane. f .

8. Reduce | of | of ^ to a single fraction. Ans. -^.

4. Reduce |f of | of J to a single fraction. Ans. y\.

CASE 5.

To find a common denominator, viz : one whose denomi- nators are all alike.

RULE.

Multiply all the denominators together for a common denominator, into which divide each denominator, and mul- tiply the quotient by its own numerator for a new nume- rator, and place the new numerator over the common de- nominator.

EXAMPLES.

1. Reduce J, f and f to a common denominator. .

iff 12 X 1 = 12

3 8x2= 16 new numerators. — 6x3= 18 12

2

— m

Divide hy 2, 8, 4. 24 common denominator.

Ans. 2 4? 2*; 'if'

2. Reduce J, | and ^ to a common denominator.

At1<5 2.1 11 56

3. Reduce |, |, |, -f , to a common denominator.

Anq :!^-^ l^^ ^^^ ^*-5-

4. Reduce J, §, |- and |, to a common denominator.

An<? I"! 15.2 210 25.2 xxua. .rtis) 2 8 8> asaJ 28 8*

CASE 6.

To reduce the fraction of one denomination to the fraction of another, but greater, retaining the same value.

RULE.

Make the fraction a cf^mpound one, by comparing it with all the denominations between it and that to which it is to be reduced; which fraction reduce to a single on6.

VULGAR FRACTIONS. 101

EXAMPLES.

1. Ilcdiicc I of a pennyweight to the fractioifof a pound, Troy.

2. Reduce | of a nail to the fraction of a yard.

Ans. y|j yd.

3. Reduce f of a cent to the fraction of a dollar.

Ans. yl^ dollar.

4. Reduce | of a pint to the fraction of a hogshead.

Ans. -^-^^ hhd. CASE 7.

To reduce the fraction of one denomination to the fraction of another, but less, retaining the same value.

RULE.

jNTultiply the given numerator by the parts of the deno- miiintor between it and that to which it is reduced, for a new imnicrator, and place it over the given denominator, which reduce to its lowest terms.

EXAMPLES.

1. Reduce -^^^ of a dollar to the fraction of a cent.

Ans. f cent. els.

_1 y 100 — 9IO^>C|iL — 1

2. Reduce ^j of a pound, troy, to the fraction of an ounce. Ans. f oz.

3. Reduce ^^^ of a cwt. to the fraction of a pound, avoirdupois. Ans. ^ lb.

4. Reduce y^y^ of a day to the fraction of a minute.

Ans. j^ min.

CASE 8.

To reduce a fraction to its proper value.

^, RULE.

^Multiply the numerator by the next lowest denomination, and xlivide by the denominator.

" n ■■■■ "^ "r-T— TTT-u-TTTTT-

* t ■ ■ ' T^— ' ■

102 VULGAR FRACTIONS.

EXAMPLES,

1. Itediige J of a dollar to its proper value.

i 300

5)400

Ana. 80 ccuta.

2. Reduce f of a dollar to its proper value.

Ans. 75 cents.

3. Keduce | of a day to its projSer quantity.

Ans. 6 hours.

4. Keiluce | of a mile to its proper quantity.

*' -^^' Ans. 4fur. 125yd. 2ft. lin. •;.

5. Reduce /^ of an acre to its proper quantity.

Ans. IR. lOr.

6. Reduce -j^q of a year to its proj^cr quantity.

Ans. a28aa. 12Lr.

CAKE 9.

To reduce any given value, or quantity, to a fraction of any greater denomination of the same kind.

RULE.

Reduce the given sum to the lowest denomiaation men- tioned for a numerator, and the denomination of which you vnah to make it a fraction to the same name for a denomi- nator.

EXAMPLES.

1. Reduce 60 cents to the fraction of a dollar.

Ans. ^ dollar. 2t0)/vij = f

2. Reduce 90 cents to the fraction of a doWar.

Ans. -/^ dollar.

3. Reduce 9 ounces, troy, to the fraction of a pound.

Ans. f lb.

4. Reduce 9oz. Sdr. |, avoirdupois, to the fraction of a pound. "' Ans. 4 lb.

5. Reduce 8qr. 3na. to the fraction of a y'c^rd. Ans. if.

6. Reduce 7 months to the fraction of a year.

Ans. /j year.

VULGAR FRACTIONS. 103

ADDITION OF VULGAR FRACTIONS.

RULE.

Reduce the fractions to a common dnnominator; then add all the numeratora together, and place their sum over the common denominator. If fractions be of different denomi- nations, i5nd their value separately, and add as in Compound Addition.

Note. If mixed numbers be given, reduce them to im- proper fractions, or only use the fractional part in perform- ing the operation. Then add the whole numbers, as in Simple Addition. If compound fractions be given, reduce

Ans. I.

Divide by 8, 2, 4)64

2. Add %, and y'^, together. Ana. ^,''^.

3. Add £, I-, fj^, and t, together. Ans. y/^?^.

4. Add j\j /^, -j^fj and y-^p together. Ans. j^.

5. Add j, ^, and f, togetner. Ans. Ij.

6. Add 3}, 8f, and ^, together. Ans. 11 1;,^^.

7. Add T^, and 5}, together, Ans. 13/^.

8. Add i of an acre to -^\ of a rood. Ans. 2R. 10.

9. Add f of a mile to j\ of a furlong. Ans. 6fur. 28P.

10. Add 3 of ^ and ^ of J^ together. Ans. f *.

11. Add i of 1 and I bf is together. Ans. ff

them to single ones.

EXAMPLES.

1. Add J, if, and ^, together.

i J \ 2

8 32

8

16

8

fl

MULTIPLICiTION OP l^LGAR FRACTIONS.

\ULE.

Multiply lie ^rsrirttcci 'ADgethcr for a jew numerator, and the deao«i»<iOfi fo/i i aeii (iionomin»tor.

104 VULGAR FRACTIONS.

J^ote. If compound fractions be given, reduce them to single ones ; or, if mixed numbers; rgduce them to improper fractions; and proceed as before.

EXAMPLES.

1. Multiply i by t, i X t=f 2)|. Ana. h

2. Multiply i by |. Ans. f^.

3. Multiply Vv by h Ans. ^j,

4. Multiply 4| by |. Ans. 8*.

5. Multiply J of f by j\ of jj. Ans. /j^.

6. Multiply J of 7 by i. Ans. If. }XiXj=f 4)7

1^

SUBTRACTION OF VULGAE FRACTIONS.

RULE.

Reduce compound fractions to single ones, and mixed niimbers to improper fractions. Then reduce these frac- tions to a common denominator, and subtract the less numerator from the greater, and place the difference over the common denominator.

JS'ote. When the fractions are of different denominations, reduce them to their proper value, each separately, and take their difference by Compound Subtraction.

EXAMPLES.

1. From I take / Ans. ^\,

8 12x5=60 8X6=40

Divideby8,12)9G

4)if=A.

2. From |- take | . Ans. J,.

3. From ^^ take -^^. Ans. f .

4. From y^^ take A. Ans. ^\.

5. From ^ of | take | of f . Ans. i. G. From f of ^\ take \ of |. Ans. ^. 7. From J of a league take f^ of a mile.

Ans. Im- 2fur. 16p. — —^——^————————^'^

VULGAR TRACTIONS. 106

8. From ^ of a yard take ^ of an inch. Ans. 5} in

JVote. When fractions or mixed niimLcrs are to be sub- tracted from whole numbers, subtract the numerator of the Iraction from its denominator, and under the remainder place the denominator; then carry t)nc, to be subtracted from the whole number.

9. From 5 take /^. Ans. 4-j-\.

Ang. 9-f\.

Ans. 3^.

Ans. -1.

DIVISION OF VULGAR FRACTIONS.

RULE.

Reduce compound fractions to single ones, and mixed numbers to improper fractions. Then invert the dividing term, and multiply all the numerators into each other for a

dividend, and denominators for a divisor.

«

EXAMPLES.

1. Divide | by f . Ans. i

inverted f X h 2)^ = |.

2. Div* - " •

3. Div

4. Div

5

8 1 4

1..

8

4

tV

10.

From 10 take J5,

11.

From 9 take 5^.

12.

From 25 take 24f^.

5. Div

6. Div

7. Div

8. Div 0.- Div

de (> by J. Ans. 48.

de {i by 3. Ans. -r-'^.

de H by §. Ans. l|f

de ^ by i. Ans. 19f

de I of i by ^ of f Ans. %^}.

de f of .} by ^ of f Ans. 1^.

de ^of iby| of ^. Ans. 16^

de4iby5.of4. Ans. 2^V

10. What part of 335V is 28 jj? A^s."!.

RULE OF THREE, IN VULGAR FRACTIONS.

RULE.

State as in whole numbers. Then invert the first term, and multiply all the numerators together for a dividend,

106 VULGAR FRACTIONS.

and denominators for a divisor. If mixed numbers be given, reduce them to improper fractions ; or compound fractions to single ones. If a whole number, place it thus: |-, J, &c.

EXAMPLES.

1. If f of a yard of cloth cost f of a dollar, how much will f of a yard cost at that rate ? Ana. $1 60 cts.

Inverted f X ix f X 510)810

^1 60 cts.

2. If f of an ounce of indigo cost J of a dollar, how much will I of an ounce cost? Ans. 23-^^ cts.

3. If If bushels of corn cost $1J, how much will 60 bushels cost at that rate ? Ans. $38 57| ets.

4. If 2i bushels oats cost 50 cents, what cost 13 J bushels at that rate? Ans. $2 65 cts.

5. How many yards of linen, ^ widS, will be sufficient to line 20 yards of baize, that is f of a yard wide ?

Ans. 12 yd.

6. If ^ of a pound of cinnamon bring f of a dollar, what will If lb. come to? Ans. $2 74f cts.

7. What will i of 2i.cwt. of chocolate come to, when 6 J lb. cost f of a dollar? Ans. $10 76|| cts.

8. When 10 men can finish a piece of work in 20f days, in how many days can 6 men do the same ? Ans. 34^ da.

9. How many pieces of stuff, at $20 J per. piece, are equal in value to 240A pieces, at $12 J per piece ? Ans. 149^/-!^.

10. If ^ of # of f of 60 cents will pay for a bushel of potatoes, how many bushel will $1 60 cts. pay for ?

Ans. lOjbu.

DOUBLif RULE OF THREE IN VULGAR • FRACTIONS.

RULE.

Prepare the terms, if necessary, by Reduction. State as in wlioie numl.iers. Then invert the two dividing terms, and multi[>ly all numerators together for a dividend, and the l|denominators for a divisor.

DECIMAL TRACTIONS. 107

EXAMPLES.

1. If i of a dollar, in /.^ of a year, gain ^. of a dollar interest, how mueli will I o{ a dollar gain in ^'of a year ?

Ana. 05 ct«. 8 y. 8 Principal. * : /^ ' - jV lufeerest. I :f Inverted J X V x | X f X ^3 = 108|00)(>00l00=5§.

MO

.60

2. If 21 yards of cloth, If yards wide, cost ^3j, what is the value of 38 i yards, 2 y^ds wide ? Ans. itO 50 cts.

3. If $50 in i^^ months gain 2^ dollars interest, in what time will $15 J gain m ? Ans. 12if J months.

4. If 4 men in 5| days cat 7j lb. of bread, how many poiuids will 20 'men eat in | of a day? Ans. 5-"^ lb.

5. If 90 dollars in | of a year gain $4i interest, in what time will 900 dollars gain 20 dollars interest ?

Ans. 4:^j months.

DECIMAL FRACTIONS.

A Decimal Fraction is a part of a whole number or unit, denoted by a point placed to the left of a figure or fipires ; us .2, .18, .110. The first figure after the point denotes so many tenths of a unit; the second, so many hundredths; the third, so many thousandths ; and ho on.

Decimal Fractions are read in the same manner as vulf'ar fractions. .5 is equal to, and reads as j% .10 j-^^, .120 j'^'^'^^, {and so on. A mixed number consisting of a whole num- ber and a decimal, as Di/', ; thus 12.5. Whole numbers, counting fiom" the right towards the left, increase in a ten- fold proportion ; but detumale, countina from, the left towards the right, decreajse m & tenfold proportion, as will bo better (Exemplified in the fWIowing iahh :

108 DECIMAL TRACTIONS.

TABLE. '

;i^ ;r; ;^ ;=; ^ H W H U? h >-i h r-< th S rn ,-^ rH 222 2 22221 122222222

Whole numbers. Decimals.

J^ote. Ciphers annexed to decimals, neither ii) crease or decrease them; thus, .4, .10, .50, being y\j, rf^% ^y^, are of the same value ; but ciphers prefixed to decimals, decrease them in a tenfold proportion; thus, .04, .010, .050, being

T^5> i ioT57 iooo? ^'^'

1

ADDITION OF DECIMALS. '

RULE.

Wriic down the given nunibers under each other, viz, : — j Units under units, tens under tens, &c., and add as in addi- i tion of Tvhole numbers ; observing to set the point in the answer under those of the given number.

EXAMPLES.

(2.) 30:12 (3.) .7324

3.112 .0962

.12 .132

16.182 • .09

18.078 55.534 1.0500

4. Add 56.12, .7, 1.314, 5837.01, and .15, together.

Ans. 5895.294.

5. Add 361.04, .120, 78.0006, 101.54, 8.943, and" .3,

together. Ans. 5 19.9436. j

DECIMAL niACTlONS. 109 (

MULTIPLICATION OF DECIMALS.

RULE.

Multiply as in whole numbGrs, and point off as many figures in the product for decimals as there are decimals in both factors. If there are not so many figures in the pro- duct as there are decimal figures in both factors, place ciphers to the left of the product to supply the deficiency.

EXAMPLES.

1. Multiply 5.11 by .122 6.11

122 122 610

.62342

2. Multiply 54.20 by 38.63. Ans. 2093.7460.

3. Multiply 4560. by .3720. Ans. 1696.3200.

4. Multiply .285 by .003. Ans. .000855.

5. Multiply 3.92 by 196. Ans. 768.82

6. Multiply .28043 by .0005. Ans. .000140215,

SUBTRACTION OF DECIMALS.

Place the numbers aa in addition, with the less under the greater; and subtract as in whole numbers, setting the point in the answer under those in the given numbers.

EXAMPLES.

1. From 32.456 <ake 1.83 1.33

Ans. 31.126 2. From 18.16 take 9.125." Ans. 9.035

3 Frcm 100 take 25. Ana. 99.75

flTO DECIMAL FRACTIONS.

4. From 441.2 talie 128.9 Ans. 812.3.

5. From 456.1 take tll.Q Am

■ ■■< tma^m. — *«iXw<wMB<**Mi

3-14.2,

DIVISION OF DECIMALS.

EXILE.

Divide as in whole numbers; then observe how many 1 more decimal figiirea tllere are in the cli\idend than divisor,. [ and point off that num])cr of decimal figures ia the answer.

Or if there be not figureB enough in the answer, annex

ciphers until there be a sufficient nmnber.

JVb^e. If tiie diA^dend be not lai'gc enough to eontain the divisor, annex ciphera until it will be > or if there be a. re- j mainder, proceed in like manner.

EXAMPLES.

1. Divide 148.63 by 4.21

4.2lVl48.(>3(Ans. '6bMi^ 126.3

n

105

128.0

126.S

16.84 160

2. Divide 19.25 by 88.5 * Ana. .5.

8. Divide .2142 by iJ.2 Ane. .066. +

4. Divide 210. by 240. Ajis. .875.

5. Divide .1606 by 4.4 Ans. ,865.

6. Divide 3. by 4." Ans. .75.

7. Divide 275. bv 3842. Ana. .OTIS'/'?, -f

fcdB».' ■"iJftl*-3

M» « rri-TiitwMWMM I . l»«Mp— ■■! mi I iiiiii iiMaii ij i imn 1 1 ■ 1 1 ■■—— ■aaa— B— aai

DECIMAL rs ACTIONS. Ill

REDUCTION OF DECIMALS.

CARE 1.

To reduce n vulgar frnctlpn to a decimal.

1

; i\jinex ciphers to the numerator, and divide by the de- nominator. If compound fractions be giTCD, reduce them to single ones, and then to a decimal.

EXAMPLES.

1. Heduce | to a d«^cimal. ^ Ans. .5.

55)1.0

5

2. Reduce J to a decimal. Ans. .333

3. Reduce f to a decimal. Ans. .75

4. Reduce f to a decimal. Ans. .375.

5. Reduce ^ of f to a decimal. Ans. .333. -4-

CASE 2. To reduce any sum or quantity to the decimal of a higher. |

RULE.

Reduce the ^ven sum to the loweat denomination men- tioned for a dividend, and one of tliat denomination of which you wish to make a decimal to the same denomination for a divisor. The quotient will be the answer.

EXAMPLES.

1. Reduce Sqr. to the decimal of a yard. Ans ,5

vd. 1 4)20

5

4

2. Reduce 2qr. 2ua. to the decimal of a yard.

Ans. .625.

3. Reduw 2qt. Ipt. io the decimal of a hhd.

Ans. .00992 +.

as

112 DECIMAL FRACTIONS.

4. Reduce lOgr. to the decimal of an onnce, apotliccaries' weight. Ans. .02083. +

5. Reduce 5 minutes to the decimal of an hour.

Ans. .08*333. -f

6. Reduce 2r. 4p. to the decimal of an acre. Ans. .525.

CASE 3. To reduce a decimal fraction to its proper value.

RULE.

Multiply the given fraction continually by the next lowest denomination than that of the given sum, for the proper

value.

EXAMPLES.

1. What is the value of .75 of a doUai-? Aur. TGcts.

100

75.00

2. What is the value of .375 of a dollar? Ans. 37^cts.

3. "What is the value of .9 of an acre ? Ans. 3r. 23p.

4. What is the value of .436 of a yard ?

Ans. Iqr. 2na. .976.

5. What is the value of .71 of 4 ounces, troy ? ,

Ans. 2oz. lOdwt. 19.2gr.

6. What is the value of .86 of cwt. ?

Ans. 3qr. 121b. 5oz. 1.92dr.

7. What is the value of .07 of a ban-el of 32 gallons ?

Ans. 2gal. 1.92pt.

8. W^hat is the value of .235 of a day ?

Ans. 5hr. 38min. 24sec.

RULE OF THREE IN DECIMALS.

EULE. ^

State as in whole numbers, only observing when you multiply and divide, to place the decimal points according lo the rules of multiplication and division of decimals.

involution; dRji. iiAibiNQ of rOWERS. "'"113

EXAMPLES.

1. If G.-l lb. of coffee cost l-'22 dollars^ what cost 25.6 lb. 6.4 : 25.6 : : 1.22 ? ^ Ans. U 88 ceut.s. M

2. If 1.4 lb. of sugar cost .10 of a dollar, witat will SOcwt. Iqr. 22.5 lb. come to? Ans. $389.77Lh-

3. If I sell Iqr. of cloth for §2.345, wliat ir, it per vard ?

Ana. i9M.

4. Iiow many pieces of cloth at $20.8 per jsiece ai'e equal in value to 240 pieces at $12.6 per piece*/

Ans. 145.38. -\-

5. How loiag will 3 nieii be ia performing a piece of work which will occupy 5 nien for 40.5 days?

Ans. G7.5 days. Ifuw luuch niusiin .75 of a yard wide will line 25.5

6.

yardi'

of c]ulJi that is 5 l!^uartcrs wide ?

Ans. 42.5 yards.

INVOLUTION; OR, RAISING OF POWERS,

A power is the product produced by multiplying any giveu number iuto it,self a certain niunber of times.

Thus, 3 X 8=:: 9, the square or second power. SxSx 8=27, the cube or third power of 3. 3 X 3 X 3 X 3 X =81, the fourth power of three, &c

The number which denotes a power is called its index. Any nuiubei multiplied by the same sum one timo, the pro- duct is its square. Thus, 2 by x2 = 4, the square of 2^ SiQ... Any number multiplied into its square, the product will be the cube. Thus, 2x2 X 2- 8, the .cube of 2. When ' any power of a \T.ilgar fraction is nnpiirod, first raise tlie numerator to the required power for a now numerator, and thea^ajijSe the denominator to 1 he required power for'Aiiew 4<}U9*Riaa.toA\ Tl^jfis, A|je ihird pow^f of | x f x t~.

c;- ^ Ans. .^^ ^^^ required powf^re, ,

^■^Ej

==1

IM

^QTjAliE HOOT,

TABLE OF THE FIE8T NINE PO\VeKS.

t^

rfJ

o

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tri

a>

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CO

^

^

c

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ft-

B-

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1

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1

1

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2

4

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16

J?^ 64

12>8

266 512!

3

9

27

81

24» 721^

2187

6561! 19683!

4

1&

64

256

1024 409e

16384

(I'^ryM 262144i

1 5

25

125

625

312i>, li>62i>

7-^125

i 3t.K3ei25i 19531251

6

36i216

1290

7770' 4(')056

279936

' 1679616^ 100776901

7

49'3i3;2401

.UM)? 117649

e2a543

i 5764801 j 40353607!

8 9

64512: 4Ci9(7

o27G8 262144 121)97 15x1

16777216:134217728!

8i:729i,a50i

59040 5i3144i!47S2f>i>94:]04072i;38742()489i

EXAMPLES.

1. "VVTiat Ls the sqiua-e of 8? Au's. 64.

2. What in the square of 9? Ane.Sl. What h the cul^e of 4 ? Ana. 64. What h the cube of 5 ? Ans. 125, What is the cube or thiiti power of .263 ?

Alls. .018191447. What is the Gth pow^r of 2.8 ? Ans. 481.890304.

What i.s the 8tk power of

Aufs.

zjT, n •

The root of a uiunber is that which y,'ill produce that n amber by b*'.iug multiplied by itself a giTen number of time-a ; thus, 2 ie the gquore root of 4, because twice 2 make 4 J and 4 is the cub<> rc^ot of 64, kx'ause 4 X 4 X 4= make 64 ; and so on.

SQUAKE BOOT.

"N^lien the square root of any given number ia required.

RULE.

Separate the given number into periods of two figures

each, begining at the units* place, find the gi'eatest square

,| contained in the left hand period, and set its root on the right

«)R>aiisn«r*n««i«ai«M

• SQUARE KOOT. 115

of tlic given number. Subtract said square from the left hand period, and to the remainder bnng down the next period for a dividend, iid. Double the root for u divis-jr, and tiy how often this divisor is contained in the dividend, omitting the last figure, and pkce th(^ result to the right of the asoertaiucd root ; and to the right of the number pro- duced by doubling the ascertained root. Multiply and sub- tract as in division ; and bring down the next period to the remainder for a dividend. Doul^le tlie ascertained root for a divisor, and pi-oceed as before, till all the penoda are bro\ight down.

JYoie. If the square root of a whole number and decimal .'iro roquu*ed, point the whole number from right to left; then l>egin with 'the decimal, atid point from left to right; if there be only one figure at the last, place a cipher to ita right to make an even period.

EXAMPLKf.

1. What in the sfjuare root of 451581 i*

'45.15.8 l(Ans. 672 root. SG

127)915

sm

1342)2684 2684

2. What is the square root of 106929 ? • Ans. 827.

3. AVhat is the square niot of 6.9169 *r* Ans. 2.63.

4. What is the squai'c root of 393756 ? Ans. 627. -f

5. What is the square root of 10.4976 ? Ans. 8.24.

6. What is the square root of 18.3021 ? Ans. 4.28. -j-

7. What is the square voot of 1'60000 ? Ans. ioO.

8. W^hat is the square root of .250000 't xiug. .500.

9. "What is the square ryot of 5 ? Ans. 2.2S. -f

AVc. When the squai*e root of a vulgar fraction is re- quired, extract the squai'e root of the numerator for a new

jilt) tJQUARE ROOT. ' ^

uunierator^ aud^ the square root of the dcnoiniuator fur a new Je nominator. If tliere be a remainder, cither to the! numerator or denominator, reduce the fraction to a decimal, and extract the square root thereof; or if there be a mixed ' number, reduce it to an improper fraction, and proceed as before,

10. Whut is the square root of \m? Ana. 4.

1 1. What is the square root of flf ^ '/ Ans. i-

12. AVhat is the square root of ^^^j ? Ans. |.

13. What is the square root of f^g ? Anu. f .

14. What is the square root of 27A? Ans. 5^

15. What is the square root of 30^ ? Ans. 6/5.

»

16. A certain yoHng man gave 484 apples to a number of gii-ls, each girl received as many apples as there were L':irls ; how many girls were there ? An?. 22.

17. A person being desirous to lay off 3 acres, 2 roods, 5 poles of land, in such ^ manner as to form a square field, what must be the length of one of its squares ?

Ans. 23.76 poles. +

18. The square of a certain number is 124600, what is that number ? Ans. 352. +

J^ote. To find the longest side of a right angled triangle. I Squai-e each number, and extract the s([uare root of their sum. If the shortest side be required, extract the square root of their difference.

10. Suppose two men depai-t fr^m Baltimore; one of them travels due east 90 miles; the other duo north 40 miles; how far are they asunder? Ans. 98.48 miles. +

20. Suppose a wall be 20 feet high, and be suiTOunded by a creek 50 feet wide ; how long luu.s't a line be to reach from the top of the wall to the opposite bank of the creek ?

Ans. 53.85 feet. +

21. Said James to Joseph, I see a tree known to be 100 feet high, ajjd from the spot where T stand it is 40 feet to its root, but I demand the distance from where I stand to its top? ' '*!> •■'^' ' Ans. 107.70 feet.

22. A certain castle which is 45 feet high, is surrounded

CUBE HOOT. 117

by a ditch CO feet broad. What k>ngth mu»t a ladder be to reach from the outside of the ditcli to the top of the castle ? Ails. 75 feet.

28. What is the height of a st^.eple, when a line 204 feet llciRg -will reach from the top of the steeple to the opposite )>ank of a river, known to be 41 feet broad ?

Ans. 199.83 feet. +,

24. A certain general has an army of 5625 men; how many must he place in rank and file to form them into a square ? Ans. 75 men.

25. Suppose a ladder, 60 feet long, be so planted as to reach a window o7 feet from the ground on one side of the street, and without moving it at the foot %vill reach a win-^ dow 23 foet high on the other side. What is tlie breadth of the sti^eet? Ans. 102.64 feci

CUBE ROOT

When the cube root of any number is required.

RUIiE.

1st. Separate the given number into periods of three figures, each beginning at the units' place. 2nd. Find the greatest cube contained in the left hand period, and set its root on the right of the given number, ord. Subtract said cube from the left hand period ; bring down the nest period to the remainder for a dividend. 4th. Squai-e the root and multiply the sc(uare by 3 for a defective divisor. 5th. Try how often the defective divisor is contained in the dividenrl, omitting the two right hand figures, and place the number of times it is contained to th(! right of the ascertained root, and its square to the right of the defective di^'isor, supply- i ing the place of tens with a cipher, if the square be less than 10. 6th. Multiply the la.st figure of the root by all the figures in it previously ascertaiued; multiply that pro- duct by 30 ; and add tlieir products to the divisor to com- plete it. 7th. IMultiply and suTjtract, as In Division. 8th. x\nd to the remainder bring down the next period for a new dividend. 0th. Find a divisor as before : and thus proceed until all the pcriM.,- are brought down. '•*

118

SINGLE POSITION.

JVote. "W^Iien remaiuderrf occur, annex ciphers for decimal periods; and*f)oint decimald as in the Squjire Root.

EXAMPLES.

1. What is the cube root of 10793S61 ?

Ans. 221

10.793.861(221. 8

Defective divisor and square of 2 — 1204)2793 + 120 = complete divisor 1324)2648

Defective diviRorand square of 1 = 145201)145.861 -f 660 r~. complete divipor 145861)145.861

2. What is the cube root of 16194277 ? An8. 2

3. What is the cube-root of 5735339 ? Ans. 1

4. What is the cube root of 7532641 ? Ans. 196.

5. What is the.cube root of 12.113847 ? Ans. ^:29.

6. What is the cube root of .378621 ? Ans. .72.

I-

53. [ 79.

+ ! -f

JS'otc. When the cube root of a vulgar fraction is required, reduce it to its lowest terms, and extract the cube root of the numerator and of the denominator. If there be a re- mainder to the numerator or denominator, reduce the frac- tion to a decimal, and extract the cube root thereof When mixed numbers are given, reduce them to improper frac- tions, or to a decimal, and proceed as before.

7. What is the cube root of f f^^ ? Ans. -f.

8. What is the cube root of ^f^foV ? Ans. ^^

9. AVhat is the cube root of -|^ ?

Ans. 3.32. -f

10. There has been a cellar dug, out of which has been taken 3456 cubical feet ; what is the length, breadth, and depth of it? Ans. 15ft. -f-

SINGLE POSITION.

Single poBition is used when it Ih required to make use of only one .supposed numI)or to find an unknown number.

RULE.

Suppose any number most suitable, and proceed with it

SINGLE POSITION.

119

as if it were the true one ; setting down the result, which is the firat term; the given number the second; the supposed number the third. Proceed by Rule of Three. The quo- tient will be the number sought.

EXAMPLES.

1. A person having about him a certain number of dol- lars, said, if a J, a J, and a J, were added together, the sum would be 90 ; how many hyd he ?

12 (SuppoMed.) 1

2

120

40 30

20

9 : 90 : : 12 (Ans. S120. $90 proof.

2. A merchant received a number of dollars, said }, ^, ^, and I of the number is 90; what number of dollars has he? Ans. 75.

3. A. nnd B. having found a purse of money, disputed who should have it; A. said that 4, y\,, and -^^ of it amoimt- ed to 35 dollars, and if B. could tell him how much was in it he should have the whole, otherwise he should have nothing ; how much did the purse contain ? Ans. $100.

4. A person after spending } and J of his money, had 265 dollars left, how much had he at first? Ans. $160.

5. A certain sum of money is to !)e divi<led among 5 men, in such a manner Ibat A. shall have ], B: -J, C. yV, D. v/^, I and E. the remaimlcr, which is 40 dollars; what i:^ Ihe rumi" ^ v\ns. .<?100.

6. A gentleman being asked his age, replied : if the years of my life were doubled, and f^ of the product divided by 3, the reiiult would be 14 ; what was his age? Ans. 35 years.

7. In a certain web of cloth there is 4 blue, ■}. black, and 9 yards white, how many yards are there in the web ?

• Ans. 54 yards.

8. A. Yoiitl) wiio was desirous to know the age of a fair Miss, to whom lie had made iiis addresses, was replied to in the following manner : If you multiply the years of my life by .'>, ^ of the product will be three times the square root of llv What wa3 her age? Ans. 14 years.]

120 DOUBLE rOSITION.

DOUBLE POSITION.

Double Position teaches to find the trae number by

making u«e of two supposed numberf^.

RULE.

Suppose two numbers most suitable, and work with each according to the nature of the question, observing the errors of the result. Multiply the errors of each operation into the contrary supposed number. If the errors- be alike, i. e., both too much or both too little, take their dijGference for a divisor, and the difference of the products for a dividend ; but if the errors be unlike, that is, one too great, and the; other too small, take their sum for a divisor, and the sum of the products for a dividend. Proof as in Single 'Position.

EXAMPLES.

1. A. B. and C. would di\dde $100 among them, so as that A. may have 5 more than B., and B. 10 more than C. The share of each is required.

Suppose A. 60 Again suppose A. 45

B. 45 B. 40

C. 35 C. 30

130 115

100 100

30 error too much. 15 error too much 2d suppo£ed No. 45 SOletEuppos'dNo

150 750

120

error 30 1350 error 1 5 750

difference 15 15)600(

600 Ans.

0

Proof 100.

■<Ba^<m"^w^<— I II naiB!»t>'»WBM

.

ALLIGATION. X21

2. A laborer engaged himself for 60 days upon these conditions ; that for every day he worked he should receive one dollar; and that for every day he was idle he should forfeit 50 cents. At settlement, he received $27 50 cents How many days did he work, and how many was ho idle ? '

^ -R I., 1 .u ^ ^°^- Worked 85, idle 15 days.

d. Bought cloth for a coat at $6 per yard, and linen to

me It at U per yard The number of yards was 12, and

the whole cost $42 ; how many yards were there of each ?

/t A /• 1. . , . , ^^•^- ^ 7^'^^^ each.

for them all, $320,- being paid at the rate of $24 pgr ox, $16 per cow and $6 per calf There were as many oxen as cows, and four times as many calves; how many wereii there of eax^h ? Ans. 5 oxen, 5 co;s, and 20 calves.

D. A man, when driving sheep to market, was asked where he was going with his score of sheep? who answered he had no scoje; but if he had as many more, half as many more, and two sheep and a half, he would have a score. How many had he? Ans. 7 sheep.

ALLIGATION.

Alligation IS a rule for mixing simples of different qualities m such a manner that the composition may be of a middle quality When the quantity and rates of the simples are given to find the rate of mixture, compounded of their

RULE.

Find the value of each quantity, according to their re- spectiye costs; then divide their whole valu? by the sum of the several quantities.

EXAMPLES.

1. If 4 pounds, at 20 cents per pountJ, 6 pcmnds, at 25 cents, and 8 pounds, at 30 cents per pound, b^ mixed toge- tner, wliat will a nound of th^ mi-rfnt.^ h^ «,^«*u » ^

-^ — .J w^v* ^ I.UIXUUC5, ai ov cents per pound, be mi tuer, what will a pound of the mixture be worth ?

^ ■'-'■'i li iiiii'- II II , ,1

AEITHMETICAL PROGRESSION. Jh. Ctt.

4 at 20 = 80 6 at 25 = 150 8 ai 30 =: 240

18 i8)470(AnB: 26 cente. -f

86

110

T08

2. If a pcraon liave 4 lb. of tea, at 90 cents per lb., 8 lb. at 75 cents per lb., and G lb. at 110 cents per lb., to mix

\ together, what will a pound of the mixture be worth ?

Ans. 90 cents.

3. If 4oz. of silver, worth 75 cents per ounce, be melted with Soz., worth 60 cents per ounce, what will loz. of the mixture be worth ? * Ans. 65 cents.

4. A ffij-mer mingled 20 bushels of wheat, at 50 cents per bushel, 36 bushels of rye, at 40 cents per bushel, with 30 bushels of corn, at 20 cents per bushel, what is the worth of one bushel of the mixture ? Ans. 35^ cents. +

5. A grocer has 2cwt. of coffee, at $25 per cwt., 4cwt. at ,S20 50 cents per cwt., p^nd 7cwt. at ^18 62^ cents per cwt., ■1 which he will mix together; what will Icwt. of this mixture I be worth? > Ans. ^20 l#i cent;?..

AiRITHMETieAL PROGRESSIQ-N.

Any mnk or series of numl^ere increasing or decrc-asmg, lid by a c<.'mmon diflcrence in Arithmetical Progression^ as

I, 2^,3, 4, 5, 6^ — 6,5,4,3,2, 1;— 1, 3, 5, 7,9, 11 j —

II, 9, 7, 5, 3, 1. There' are live things to be particularly ^ attended to in Arithmetical Protri-es&ianj the first and last <§ tennri; thf> uiimbfU" ol' It-rniH; lh»' roinip.nn diffenMiov ;uul th^• 5um of fill thr Lt.-nii ■.

The lirat teirm,, coramoii difference, and number fti\ termsjj beicg giyec, to fhid the but term and Bum cf all t.he t^rms-jj

AlUTHMETICAL PROQREtihilON. 12U

EULE.

Multiply the number of terms less one, by the common difference ; to that product add the first term ; the sum is the last term. Add the first and last tenns together, and multiply their sum by the number of termp, and half the product will be the sum of all the terms.

BXAMPLlBS.

1 . What in the laat term and sum of all the terms of an Arithmetical Progression, whose first term is 2 j the com- mon difference 4, and number of terms 13 ?

number of tenns 13 — 1 3= 12 2 -f 50 = 52 first & last terms, common difference 4 18 number of terms.

48

156

first term. -|- 2

52

the last tt^rm. 60

2)676

Sum of all the terms. '

838 Answer.

2. A man sold 40 yards of linen, at 2 cents for the first I yard, 4 cents for the second, increasing 2 cents every yard ;

what did they amount to ? Aup. ^16 40cts,

3. Bought 15 yards of linen, at 2 cents for the first yard, 4 cents for the second, 6 cents for the third, &c., increasing 2 cents every yard ; what was the cost of the last yard, and what was the cost of the whole ?

Ans. The last yd. cost 30cts,— the whole $2 40cts.

4. Twenty persons gave charity to a poor woman,; the I fii'st gave 6 cents, the second 8 cents, and so on in arithmo- I tieal progression ; how much did the last person give, and j what sum did the woman receive ?

i Ans. The last person gave 44 cts, — she received $5.

5. A man on a journey travels the first day 10 miles, the second 14 miles, increasing 4 miles every day ; ho"v^ many miles did he travel the tenth day, and how many miles did he travel in all ?

Ana. Teoth day 46 miles, — in all 280 miles.

ARITHMETICAL PROGRESSION.

6. Suppose a number of stones were laid a yard distant from each other for the space of a mile, and the first a yard from a basket ; what length of ground will that man travel over who gathers them up singly, returning with them one by one to the basket ? Ans. 1761 miles.

CASE 2.

When the two extremes and the number of terms are given to find the common difference.

RULE.

Subtract the less extreme from the greater, and di^ade the remainder by one less than the number of terms; the quo- tient will be the common difierence.

EXAMPLES.

7. The extremes being 20 and 40 ; and the number of ^ terms 6 ; what is the common difierence ?

Ishimber of terms 6' 40 r Extremes.

1 20 }^^^.^

One less 5 5)20

Ans. 4 Common.

8. A man had 10 sons whose several ages difiered alike ; the youngest was 3 years old, and the eldest 48 ; what was the common difference of their ages ? Ans. 5 years.

9. A man is to travel from Boston to a certain place in 9 days, and to go but 5 miles the first day, increasing every day by an equal excess, so that the last day's journey may be 37 miles. Required the daily increase.

Ans. 4 miles.

10. A man received charity from 10 different persons- the first gave him 4 cents, the last 49 cents, in arithmetical progression; what was the common difierence, and what did the man receive ?

Ana. Received $2 65cts. — common difference 5cts.

GEOiMLTRICAL rROGKESSlON

11. When a debt is paid at 8 different pavments in an hmetol progres^on, the first payment to K^^the last §l/o; what 13 the common difference, and what pa.h payment, and what was the whole debt ?

Am. Common difference, ?22-Socond payment 8-13- Third payment, §65, &e.-The whole sum, 8784 '

GEOMETIUCAL niOGRESSION.

j Oeonietrical rrogre,ssion is the increase of a series of

«umber.s by a common nmltiplier, or decrea.sc by a common.

divisor, as 4 8, 10, 'jo, iU-U, 32, l(i, 8, 4. Thomul I

.pher or d.vsor by which any 'series is iLroascd or de

crcSgcd, is called the ratio.

I CASE.

To End the lawt term aud sum of the series.

RULE.

liaise tlie ratio to a power whose index is one less than he number ot terms given in the sum. Multiply the pro duct by the first t<3rm, and that product by the ratio. FrC this last product subtract the first term/and divide the r^ mainder by a number that is one less than the ratio. The quotient will be the sum of the series.

EXAMPLES.

fi !* /^^ Y'^1 1^ ^"^^^^^^ ^^ ^^'^^^ and pay 2 cents for the

to the last^ how much must I pay ?

126 GEOMETRICAL PEOGUEtSBION.

o

j Eatio2, -i, 8, 10, ;>2, 6i, 128, ' . 128

1024 256

128

i^

tw

tw

Uh

u

Cj

O)

o;

<y

<a

^

^

^

fc

^

a

a

o

a

9

T3

•=!-(

.c?

rd

►xa

^

d

ti

♦ '

4J

■*i

?i

CO

-^f'

ViTi

ts>

t-

16884 14th power, 8 iird power.

131072 ITtli pov.-Hr, 2 Fir^t term.

2 Katio.

524288

2 Fii'st torni.

Divide by Katiu 2 — 1 =: 1)524286

Au3. 15242 86 cte.

2 A man taught Bckool 21 days, aad received for the iirst day 1 cent, for the second 2, for the third 4, and so on, until the last. What sum did he receive ?

Ans. 20,971 dollars 51 cents.

3. A gentleman, wliose daughter wiis married on a New Year's day, gave her 81, promising to triple it on the &st day of each month in the year. What did her portion amount to ? Ans. ^265,720.

4. What sum would purchase a howe with 4 shoes, and six nails in each shoe, at ^ of a cent for the first nail, a half for the second, a cent for the thii'd, &c., doubling to the last? Ans. $41,943 03| cts.

5. A merchant sold 20 bushels of clover seed, at 1 cent for the first bushel, 4 for the second, 16 for the third, and

COMPOUND INTEREST, IJY DECIMALS. 127

SO on ; in quadruple proportion. What sum did be receive, and how much did he gain by the talc, supposing he gave !$5 per bushel for the seed i' '

. ( ^3,GG5,038,750 25 cts, sum received. -^^^- I ?3,GG5,038,G59 25 eta. gained.

COMPOUNl) IxNTEREST, BY DECIMALS.

. The ratio in Compound Interest ia the amount of 1 dollar for 1 year, which is found ;is follows :

100 : 104 : : 1 (101 amount for 1 year at 4 per cent.

.Yote. The 4<h root of the ratio will be the quarterly amount — the s-^uarc r(>ot the half 3(^arly amount — and the product arising from the half yearly and quarter yearly, multiplied together, the three quarter yearly amount, as

follows :

Thus: V 1.04 — 1.009853, quarterly amount; and V 1.04=: 1.019804, half yearly amount; then 1.009853 X 1.019804 = 1.029852, amount for 3qrs. of a yeai-, at 4 per cent. «

.Xotc. The 4th root is found by extracting the square root of the square root. The ratio involved to the power, whose index is the time, ia the amount of one dollar for that 'time, as a square for two years, a cube for three yeai-s, &c.

Thus : 1.04 X 1.04 X 1.04 = 1.154864, amount of 1 del- lar for three years, at 4 per cent.

When the ratio is to be involved to years and quarters, the power for the years must be multiplied by the quarterly amount.

Thus : 1.1910160 x 1.014674 ==. 1.2184929, amount for 3 J- yeai's, at 6 per cent.

The power of 1 dollar may also be obtaino<l for months and days, nearly, by adding the monthly simple interest of

di

128 COMPOUND INTEREST, BY DECIMALS.

1 dollar, or proper pcirts thereof, to the amount of the quarter next preceding the given time, for what that time exceeds the said quarter, as follows :

Amount for | year, =1.0295-63: For 4| years, =1.318873

Int. of.nforlmo., = .005000 .005000

One sixth for 5 days, = .000833 .000833

For7month9,5days=1.035396.for4y.l0mo.5d.=1.324706

TA.BLE I.

9moimt of $1 for a year, and for Quarters j at Compound

Interest.

Rate

For three For two

For one

Simple Int.

pr. ct.

3

Ratio.

Quarters.

Quarters.

Quarter.

of $1 for 1 month.

1.03

1.022416

1.014889

1.007417

.002500

3^

1.035

1.026137

1.017349

1.008637

.002917

4

1.04

1.029852

1.019804

1.009853

.003333

4^

1.045

1.033563

1.022252

1.011065

.003750

5

1.05

1.037270

1.024695

1.012272

.004167

5i

1.055

1,04097^

1.027132

1.013475

.004583

6

1,06

1.044671

1.029536

1.014674

.005000

6*

1.065

1.048364

1.031988

1.015868

.005417

7

1.07

1,052053

1.034408

1.017058

.005833

COMPOUND INTEREST, BY DECIMALS.

1:^9

TABLE 2, Showing the amount of one dollar from one year to fortj"?

5^ per cent

1

2

8

9

10 11 12

il31 141

4 per cent.

15 1 10

;i7

1 18 19 20 21 122 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

4 4 404

.0400000 .0816000 .1248640 .1698585 .2166529 .2653190 .3159317 .3685690 .4233118 .4802442 .5394540 .6010322 .6650735 ,7316764 ,80(/l)43r-) .8729812 ,9479005 ,0258161 1068491 1911231 2787680 3699187 4647155 5633041 6658363 7724697 8833685 .9987033 .1186514 .2433975 .3734324 .5080587 .6481831 .7943163 .9460889 4.1030325 4.2680898 ,4388134 ,6163659 ,8010206

4i per cent.

ToTsoooo

.0920250

.141166111

.19251861

5 per cent.

"^0500001) 1

.1025000 1

1576250!l

.2461819 3022601 .3608618 4221006 .4860951 1.5529694

.6228530

.6958814

.772J961

.8519449

.9352824

.0223701

.1133768

.2084787

.3078603

.4117140

,5202411

,6336520

,7521663

,8760138 3.

,0054344

,14(16790

,2820095

,4296999

,5840364

7453181

9138574

,0899810

,2740301

4663015

6673478

8773784

0968604

3262192

5658990

8163645

.2155062

.2762815

.3400956

.4071004

.4774554

.5513282

.6238946

.7103393

.7958563

.8S56491

.9799316

.0789281

.1828745

.2920183

.4066192

.5269502

.6532977

.7859625

.9252607

,0715237

2256999

3863549

5556726

7334563

9201291

1161356

3219423

5380394

7649414

0031885

2533473

5160152

7918101

0314009

3854772

7047511

0399887

.0550000

.1130250

.1742413

.2388246

.3069698

.3788426

.4546789

.5346862

.6190939

.7081440

,8020919

,9012069

,0057732

,1160907

,2324756

,3552617

4848011

6214652

7656458

,9177563

0782329

2475357

4261502

6045885

8133919

0231279

2443999

,4778419

7241232

9839469

2580671

5472608

8523600

1742398

5138230

8720832

2500478

6488004

0694844

5133060

6 per cent.

1.0600000

1.1360000

1.1910160

1.2624769

1.3S82256

1.4185191

1.5036302

1.5938480

1.6894789

1.7908476

1.8982985

2.0121964

2.1329282

2.2609039

2.3965581

2.5403517

2.6927727

2.8543391

3.0255995

3.2071355

3.3995636

3.6035374

3.8097496

4.0489346

4.2918707^

4.5493829

4.8223459

5.1116867

5.4183870

5.7434912

6.0881007

6.4533867

6.8405899

7.2510253

7.6860868

8.1472520

8.6360871

9.1542523

9.7035074

10.2857178

180 COMPOUND INTEREST, BY I)E0Ii\fAL8.

Oompound Interest in that in wliicli the interest of 1 year is added to the principal, and that amount is the principal for the second year, and. so on for any number of years.

CASE 1. The principal, time and rate given to find the amount.

RULE.

Multiply the principal by the ratio involved to the time, which may be taken from table 2, and the product will be the amount, from which subtract the principal for the com- pound interest,

EXAMPLES.

1. What 13 the compound interest and amount of 1300 for 3 years, at 5 per cent. ?

1.05 X 1.05 X 1.05=1.1576250

800

r $347.28.7.5000 amount! Answer. ) 300

( S47.28. 7 interest.

2. What is the amount of $500 for five years, at G per cent.? Ans. S669.11.2.

3. What is th« compound interest of ^100 for four years, at 5 per cent. ? Ans. $21.55.

I 4, What is the amount of five dollars for 20 years, at «ix per cent. ? Ans. $16.03.5.

5. What is the compound interest of 1000 dollars for thirteen years, at six per cent, per annum ?

Ans. $1132.92.8.

6. What is the amount of 50 dollars for 11 yeai*s, at 6 J per cent. ? Ans. $94.91.4m. -f

7. What ia the amount of 12 dollars for one half year, I at 6 per cent. ? Ans. 812.85.4.

I'EKMUTATION. — COMBINATluN, 131 1

CASE 2. _ I

The amount, time, and rate per cent, giveu to find the I principal. }

RULE.

Divide the amount Ly the ratio involved to the time in j table 2.

EXAMPLES.

1 . What principal, put to interest, will amount to $400 in five year^j at 6 per cent. ?

1.3382256)400:0000000 Ans. $298.90.3.

2. What principal, put to interest, will amount to ^1500 in 7 years, at 5^ per^cent. ? Ans. 81031.15*. -f

PERMUTATION.

Permutation iri.uscd to show how many waya things may be varied in place or succesBion.

RULE.

■ Multiply all the terms of the series continually, from one to the given number, inclusive, and the last product will be the answer required.

EXAMPLES.

■ 1. In how many diflferent poyitions can ten persons place themselves round a table ?

Ix2xs!v4'>c5x6x7x8x9x lO^Ans. 3628800

2. The church in Boston has 8 bells; how many changes may be rung on them ? 'Ans. 40320.

3. In what time will a person make all the changes that! I the fir.st 12 letters of the alphabet admit of, allovring 151 i seconds to eaeli change, and 365 J days to a year.

I _ Ans. 227y. 248da. 6h.

COMBINATION. '

Combination is used lo filiow how many different wayj' a less nuiubor of lhinn;3 can be combined oul uf a greater, I as out of the figures 1, 2, 3, 4; four combinations, 12, 21, I'oi and 43, may bo VLilbrmKl

132 DUODECIMALS

RULE.

Take a series proceeding from and increasing by a unit up to the number to be combined. Take another series of as many places decreasing by unity from the number out of which the combinations are to be made. Multiply the first continually for a divisor, and the last for a dividend, the (j^otient will be the auswsr.

EXAMPLES.

1. How many combinations of 4 persons in 8 ?

1x2x3x4= 24 24)1680(70 Ans.

8x7x6x5 = 1680 168

0

2. How many combinations of 10 figures may be made out of 20? . Ans. 184756.

3. How many changes may be rung with 10 bells out of 20? Ans. 184756.

DUODECIMALS.

Duodecimals are parts of a foot; the denominations of which increase continually by 12. The denominations are,

♦ 12 fourths ("") make ... 1 third.'"

12 thirds 1 second."

12 seconds 1 inch. in.

12 inches i foot, ft

AD'DITION OF DUODECIMALS.

RUL'E.

Proceed as in Compound Addition, observing to cairy one for every 12. -

DUODECIMALS. 13^

EXAINIPLES.

,^^ ft *?' ft' in. '

8 10 9 11 i!2 8 7 1 '4

13 7 10 8 15 11 9 8 10

1^ 1^ 5 2 13 0 0 1

Ans. 49 2 3 5 Ans. 150 "e 6~"^ 9 3. Three planks measure as follows: 16ft. Sin —14ft 6in.— 17ft. 9m. 2". How many fe< .t do they conta In ?

Ans. 48ft. llin. 2".

SUBTRACTION OF DUODECIMALS.

RULE.

Proceed as in Compound Subtraction, observing the 12's.

EXAMPLES.

Jt. lit. fl l^ II III ,,n

17 5 10 11 4 887 9 6 14

Ans. 32 9 0 9 9 A:is. 12 11 1 9 8

41ft.. 7m., how much wiU be left? Ans. 21ft. 9in,

MULTIPLICATION OF DUODECIMALS.

RULE.

Set the multipHer in such a manr er that the feet thereof may stand under the lowest denom nation of the riultipli- cand; multiply and carry one for jyery 12 from one de- nomination to another; and taie parts for the inchts, as lu

JVofe. Feet multiplied by feet, gi 76 feet

Feet multiplied ^ inches, give inchei. Feet multiplied by seconds, give seconds. Inches multiplied by inchc s, give seconds. Liches multiplied by eeoor ds, give thirds. Seconds multiplied by seconds, give fourths ^f= "

i.>4 niOMISCUOTJS EXAMPLES.

EXAMPLES.

L Multiply 5ft. 6m, by 2ft, 4m.

ifu ft. in. 4 I si f 5 6 •

=^

o.

11 0

1 10

- Alls. iSft.'iOiii.

J.Iultiply 54ft. lOin. by 5ft. 7m. Aus. SOGft. liu. 10'. jMultiply Oft Till, by oft. Gin. Aiis. 33ft. Gin. G".

4. V/hat are the contents of a dooi'; measm'iug in length 6ft. Oin. 3", and in width 3ft. Sin. ?

- . Aps. 23ft. lin. 7" 3'".

5. A certain partition is 81ft. lOin. 4" long, and 14ft. Tin. 5" hi<'b. How many yards does it contain ^

Ans. 132yd. 8ft. Tin. 9" T" 8"".

G. If a lloor be T9ft. 4in. by 38ft. llin., bow many square feet arc there in it? Ans. 3100ft. 4in. 4".

T. How many square feet in a board ITft. Tin. long, and Iff. 5iu. wide? Aus. 24ft. lOin. 11".

8. AVhat will be the expense of pla^t^riug the walls of a room 8ft, Gin. high, and each of the four gidee IGft. oip. lonp;, at 50 cents per square yard ? ' ; Ans. ^30 69. 4-

9. In 40 planks, 13ft. long and 8iu. wide, how many feet? tAif :'.'H<I<.)' • Ans. 34Gtft. 1 10, lu 49 plauk.s, 22ft. long and llin. wide, how many I feet? ^ ' Ans. 988ft. 2in.

11. In 17 plankn, 12ft. long and 5in. wide, how mrmy ^■fect? '>A^s. 85 feet.-[{i

: PROMISCUOUS EXAMPLES.

1. How many bushels of cora^ at 22 cents per bushel, can I have for 40 dollars-? ,,r.x»^ ri ^ A.ns. 181y\l)u.

2. If a B?4a's yearly inq9pie^"bo $7777, how much is it :per day? , •• ,,; ' \ v,:,. • Ana. $21 SQeta. 6m. + .. C. My ^eut sends mu woid ho hai; bought goods to the

4*:^

11 TROMiscuous examples;. llj5

value of 500 dollars 54ct.s. upon my ax^count; what will I ins commission come to at 4 per cent. ?

A A 1 J. .. Y , . Ans. 20 dollars 2cts.+

4. A man had m his desk 2176 dollars 55 cents, he drew

out at one tmie 13 dollaxs 6^ cents, at another time 49 lol^

ars 1 cent, and at another 61 dollar's 21 1 cts., after which

, he deposited at one time 88 dollars 884 cts.: how much

I had he in desk after making the deposit ? '

I r^ A • Of: ,. T. . Ans. $2142 14i cents.

5 A. IS 25 years old B. 15 years older than A., and C

1}LT'" '^^"' '^"" ^- ^^^ '-^Ses of R and C. are re- ^ TVm«v.i . , . Ans.B.40y. a52y.'

6. Sold 6 bnles of doth, 5 of which contained 10 pieces eacOi and m each piece were 28 yards; the other bale con- tamed 16 pieces, and m ejich piece were 20 yards. How many pieces and how many yards wore there in aJl ?

7 T^ J , . t. . , ^^"^' ^^ V^^^^s, and 1720 yds.

7. If goods which cost 44 doUajs, be sold for 62 dollars what IS the gam per cent. ? Ans. 40|^ per cent!

«. If 4 of an ounce cost | of a dollar, what will % of a

^TjTI, 11 ^ . Ans. ^19 (fo cts.

y. It I of a gallon cost 1^ dollars, what will -« of a ton

I """"Tn I s. . ^"^- ^^10 90 c^s. 9m. +

, W. Al^erson who was possessed of f of a store, sold ^ of his share for 551 dollars 62} cents, Uat was the whole store worth at that rate ? Ans. 1241 dollars 15^ cents.

u Wliat will 27cwt. of iron come to at U 56 cts per

lo T^ V 1. -.n. Ans. 3123 12 cts.

12. If I buy 100 yards of cloth, at 50 cents per yard, at how much must I sell it per yard to gain 100 per cent. ?

iQ "o i-i . „ Ans. $1.

id. Bought a quantity of soods for ^400, and 5 months afterwards sold them for $650. How much per cent per annum was gained by the transaction ? ^ , "^- P^r

1/1 wTi. A-'^T- . . Ans. 150 per cent.

14. What IS the interest of ??51 62^ cents for 2 years 3 months, and 13 days, at 7^ per cent ? ^ '

i I'. TTnwnff ij , Ans. S8 85 cents. -f

fn. L t7 ^^^^"^ould a wagon-Wheel turn round in roll- bo^fiOO n .f "^^^J"^./,^ Baltimore;, suppose the distance to

, be. 600 miles; admitting the wheel be 5 feet in diameter ?

Ans. 201600 times.

iOU

136 PROMISCUOUS EXAMPLES.

16. A person has two yilver cups of unequal weight, having one cover for both which weighs 5oz., now if the cover b<^ put on the less cup it will he double the weight of rhe I reater cup, and put on the gi'eater cup it will be throe times as heavy as the less eup, what is the weight of each cup? -Ans. The less 8 oz., the greater 4 oz.

17. A man had $20, which he wished to lay out as fol- lows : viz., in sugar at 10 cents, coffee at 14 cents, and rice at 11 cents per pound; so as to have an equal quantity of each. How many pounds must he have ? Ans. 57^ lb.

18. A Gom-erib is 5f c. wide at the bottom, and 7ft. wide at the top, tell me how wide it is on an average ?

Ans. 6 feet.

19. When .^25 are n;ultiplied by 125, how much money is there in the product? 'Ans. $625.

20. "When $25 are multiplied by 25 cents, how much money is there in the p :'oduct ? Ans. $6 25 cts.

21. When 25 cents are multiplied by 25 cents, how much money is there in the p:oduct? Ans. 6 J cents.

22. How much will 18| bushels of corn come to at ISf cents per bushel ? * Ans. $3 51 cts. 5m'. -1-

23. "What will 2^ pounds of beef come to at 2 J cents per pound? Ans. 6j'cents.

24. In 48 planks 8 inches wide and 10 feet long, how many feet? Ans. 320 feet.

25. A house is 20 feet long, and 18 feet wide. How many feet of plank will be required to cover the floor ?

Ans. 360 feet.

26. What is the neut of a hog weighing 294 pounds gross ? . Ans. 256| lb. neat.

27. If A. can drink ;i pint of whiskey in 20 minutes; B. oje in 80; and C. one ;n 40; in what time can they drink a pint, when all drinking together ?

rivideby20, 30,and40. Suppose 120

3

• 4

6

13)120(Ans. 9A min. 117

rdk ^

PROMISCUOUS EXAMPLES. IXi]

J\ytc. Jn imy question like the above, suppose an}^ num- ber into which all the given numb ts may be diviied with out any reniRindcr, then add together theu' quotients, b) which sum divide the same dividend. The quotient will be the answer.

28. Three young ladies mot at their neighbours' for the pm-pose of tinishing a fine quilt. J^ aid M., I can fi jish it in six hours; said E., I can do it in four hours; said L., I can do it in three hourn; })ut wo will all work t-ogether. In what time can we finish the quilt ? Ans. 1 1 hours.

29. There \s a cellar dug, that is 20 feet every way in length, breadth and depth. How many solid feet of earth were taken out of it ? An?. 8000 feet.

30. How many bricks, 9 inches long and 4 inches wide, will pave a yard that is 300 feet long and 40 feet ^vide"?

Ans. 480C0 bricks. •81. What sum will produce sa much interest in five years, as §^500 would in 8 years an \ 4 months ?

Anr. 8833 J. 32. A guardian paid his ward ;?3500 for I25C0, which he hnd held in possession 8 years. What rate of interest did he allow him ? Ans. 5.

83. A. owes B. 100 dollars, payr.ble in o\ montlis; 8150 in 4| months, auvl $204 in 5f months; but is williiig to make one p.nyment of the whole. In what time should the payment be made ? Ans. 4mo. 23 day.i. +

34. In what time will any sum of money double itself, at 5 per cent, simple interest? Ans. 20 years.

35. If E. can do a piece a vfork alone in 10 dayj, and 0. can do it in 19 days, iti what time can they finish it, both working together i* • Ans. r>|| days.

36. A. E. ani 0. found a pui^^ of money, containing ?60; where^)f A. is to h&^i f, B. i, and 0. i. What will be the sliare of each '/

C A.'s share ^27 69 cents 2m. +

Ans. i B.'s sLare $18 46 cents Im. 4-

(C.'s sh-ire ^^13 84 cenfs 6m. +

87. A. and B. traded to^etii-??; A. put in 320 dollars for five months ; B. pnfc m 480 dollar? for 3 months; and they

U* --- ^ i

138 I'llOMISCL'OUS EXAMPLES.

gained 100 dollars. What was cacli man's share of the ggiu? . , ( A.'a share ^53 69cts. Im. +

^^^' I B.'b share $46 30cts. 8m. + 80. What is the difTeroncc between tlie interest of ^1000, at 6 per cent, for 8 years^ and the discount of the same sum for the same timO; and at the same rate of interest?

Ans. The int. exceeds the discount by ^155 GTcts. 5m.

39. Said I)ick to Harry, I ca* place four nines in such a manner that they will make precisely an even hundrgd. Can you do so too ? Ans. 99||-.

40. What is the sum of third and half the third of 6} cents? Ans. 3^ cents.

41. How many dollars are there in £200, Tennessee cur- rency? Ans. $6(56 61| cents.

42. The clocks -of Italy go on to 24 hours. How many strokes do they strike in one complete revolution of the index? '"' Ans. 300.

43. A line 40 yards long will exactly reach from the tojD of a fort, startling on the ])vink of a river, to the opposite bank, known to be 25 yards from the foot of the wall. What is the height of the wall ? Ans. 31.22yds.

44. What is the value of a slab of marble, the length of which is 5ft. Tin. and the breadth 1ft. lOin., at ^2 per foot?

Ans. §20 47cts. +

45. Shipped to New Orleans 40001b. of cotton, at 7^ cts. per lb., and 513 yards of muslin, at 62^ cts per j^ard; in return for wJiich, I have received 87cwt. 3qr. of sugar, at 12^ ceftts per pound, and 44 pounds of indigo, at 20 cents per pound. What remains due to me ?

Ans. ^83 33 1 cents.

46. If the flash of a gun was observed just 1 minute and 20 seconds before the report : What was the distance, sup- posing the flash to ])e seen the inst^it of its going off, and admitting the sound to fly at the rate of 1150 feet in a second ? Ans. 17m. 3fur. 15p. 4yd. Oft. 6in.

47. There is a certain pole, ^ of which is in the water, I in the mud, and 6ft. on dry groimd. What is the whole length of the pole ? .^ Ans. 30ft.

48. When J^ of the number of an Assembly, and 15, were met, there were J and 10 absent. How many did that branch of the legislature consist of? Ans. 150.

ril03IISCU0US EXAMPLES. 139

40. Bonglit goods for ^500, and sold the same imiuo- liatcly for §400. What was the loss per cent. ?

Ans. 20 per cent. 60. Wliat is the interest of $15,000,000 for one niiuute, at 6 per cent, per annum? Ans. ^1 71 cts. 2ra.4-

51. If the earth be 360 degrees in circumference, and each degree 60 miles, how long would a man bo in travel- ling round it, who advances 40 miles a day, reckoning 365^ days a year? Ans. Iv. 174da. 18hr.

"52. Sold 12 yards of cloth for SI 5 20cts!', by which was gained 8 per cent. What was the first cost of a yard ?

Ans. $1 17cts. 2m. 4-

53. Ijought 12 pieces of white cloth for $16 50cts. per piece; paid 32 S7cts. per piece for dyhig. For how much must I sell them each, to gain 20 per cent. ?

Ans. $23 24cts. 4m.

54. When T, by disposing of a yard of cloth at §7, gain 56 1 cents, what would I gain by selling 3 pieces, which cost me 8400 'i Ans. 32 14:lcts. +

55. The yearly interest of Charlotte's money at 6 per cent, per annum exceeds one twentieth part of the principal by $100, and she does not intend to marry any man who is not scholar enough to tell her fortune. I'ray what is it ?

Ans.^ ^10,000.

56. There is a cistern having eight pipes to discliarge it. By the first it may be emptied in ten minutes ; by the second in 20 ; by the third in 40 ; by the 4th in 80 ; by the 5th in 160; by the 6th in 320; by the 7th in 640; and by the 8th in 1280. In what time will all eight running together empty it 'I Ans. 5^^^ minutes.

57. In 140 planks, each 12 feet long and 9 inches wide, how many feet? Ans. 1260.

58. At a certain quilting, I of the girls are eating, I of them cooking, and 5 at work; I would know how many girls there arc at the place ? • Ans. 30.

59. A hare starts 12 rods before a hound, but is not per- I ccived by him till she has been up 45 seconds, .^he scuds

away at the rate of 10 miles an hour, and the dog on-s'iew, n'akes after at the rate of 16 miles an hour, llow long will the course hold; and wliat space will be run over from the spot whence the dog started, until the hare be over- taken ? * Ans. 228Sft. and 97 J sec.

140 PROMISCUOUS EXAMPLES.

60. Bought a -^^atch at 10 per cent, under its value, and sold it at 10 per cent, over its value, and by so doing gained $10. How much was the watch worth ? Ans. $50.

61. Bought a horse and saddle for $100. The horse was worth seven times as much as the saddle. How much was the horse worth, and how much was the saddle worth ?

. ( H. $87 50. ^^^' \ S. $12 50.

62. A. owes B. 100 bushels of com, the tub out of which they expect to measure the same, contains Ibu. Ipe^ Iqt. Ipt. How often must it be filled to make the 100 bushels ?

Ans. 77/-^.

63. A merchant purchased 200 yards of broad cloth, at $3 per yard. A customer who was desirous of speculating, projwsed to take $300 worth of the cloth, at $2 75 per yard, and then give $3 25 for the remainder. What would the merchant gaiu or lose by the transaction ?

^ Ans. He would lose $4 54 ,\.

APPENDIX.

MENSURATION OF SURFACES.

To find the area of a ParalleJogram, Square, Rhombus or Rhomhoid.

3Iultiply the length by the perpendicular height or breadth.

EXAMrLES.

1. How many square feet arc there in a floor 23 J feet long and 18 feet broad ? Ans. 23 J X 18 = 423.

2. What are the contents of a piece of ground 66 poles square? Ans. 4356po. or 27a. 36po.

3. What are the contents of a rhombus, whose sides are 60 feet, and perpendicular 50 feet?

Ans. 3000 feet.

4. How many acres are there ^^ in a field in the form of a rhom- boid, the sides of which are 50 poles, and perj)endicular distance 25 poles ? Ans. 7a. 3r. lOp.

5. How many square feet are there in a plank 13 feet long and 7in. broad? Ans. 7ft. 84in.

6. How many square foet are there in a plank 1 8 feet long, 12 inches at one end and 8 inches at the other ?

Ans. 15 feet.

12 + 8 = 20^2=10

18 feet.

9 6

15 Ans.

(141)

11-2 .\J ENSURATION OP SURFACES.

7. How many square feet are there in 20 planks, 15 feet long, and each 9 inches wide ? Ans. 225 feet.

JVote. When there is a number of planks to he calculated of the same length and breadth, multiply the width of one in inches by the number of i^lanks, divide the product by 12^, and multiply by the length.

9 X 20 = 180 ^ 12 = 15 X 1^.= 225.

8. How many square feet are there in 50 pieces of scant- ling, 4 inches by 3, counting "one side and edge, and 20 feet long? Ans. 583^ feet.

4 + 3 = 7 x50=350-H-12=:29ix20=583Heet.

9. How many square feet are there in 30 pieces of scant- ling 14 feet long, 4 inches by 2 ? Ans. 210 feet.

To find the area of a Triangle.

Multiply one side by half the perpendicular from the opposite angle.

EXAMPLES.

1. If A. B. be 65 poles, and the per- pendicular 31 poles, how many acres are contained in the Triangle ? ^^ — — (is^

31 4^ 2 = 15 J X 65 = 1007ipo. or 6a. Ir. 7^p.

2. How many square feet are there in a triangle whose base is 120 feet and perpendicular 75 feet? Ans. 4500.

To find the circumference of a circle from its diameter.

Multiply the diameter by 3.14159; or multiply the dia- meter by 355, and divide the product by 113.

EXAMPLES.

1. If the diameter of the earth be 7930 miles, what is the circumference ? Ans. 7930 X 3.14159 = 24912.8 miles.

:.iE.NSURA'nON OF SUKi'ACKS.

U^

2. How many miles does tlic earth move, iu rcvohduir round the sun; supposing the orbit to be a circle whose diameter is 190 millions of miles? \urf 59G OO'^ 604

!| To find the diameter of a circle from its circumference. .

_ Divide the circumference by 3.14150; or multiply the circumference ll;5, and divide the product by 355.

EXAMPLES.

1. What is the diameter of a tree which is 5.] feet round ^

o -r^,, . , 3.14159)5.5000000(1.75 Ans.

-.. it the circumference of the sun be 2.800.000 miles

what is its diameter? ^^s^ 891.2G7'

To ffid the area of a Circle. Multiply the square of the diameter by the decimals .7854.

EXAMPLES.

1. What is the surface of a circular lish-pond which is lO^^poIes in diameter? lOx lOx .7854=^78.54 Ans.

2. What is the area of a circle whose diameter is 623

^^'t' ,, Ans. 304836.

o. How many acres arc there in a circular island whose

diameter is 124 poles ? Ans. 75a. 76po.

To find the area of an elipsis or oval

Midtiply the longest diameter by the shorto^5t, and that

product by 7854.

EXAMPLES.

1. What ift the area of an oval who.<^e (greatest diameter is 36 feet, and least 28 ? — - -2BjiM>( 7854 = 791.68 feet Ans

144 MENSURATION OF BOLIDS.

MENSURATION OF SOLIDS

In Bolid measure 1728 cubic inches =1 cubic foot. 282 cubic inches =1 ale gallon. ' 231 cubic inches =1 wine gallon.

150.42 cubic inches=l bushel.

1 cubic foot of pure water weighs 62 J pounds.

To find the solidity of a piece of hewn timher, box, Sfc Multiply the length, breadth, and depth or height,

EXAMPLES.

1. How many solid feet are there in a piece of square timber 3 feet by 2, and 20 feet long ?

3x 2 X 20=120 feet Ans.

2. How many cubic inches are there in a piece of marble in a cubic form, which is 12 inches every way ?

12x12x12=1728 Ans.

3. How many cubic quarters of an inch are there in one cubic inch ^ Ans. 64.

4. What ia the solidity of a wall 'J2 feet long, 12 feet high, and 2 feet 6 inches thick "^ Ans. 660.

5. How many cubic inchcvS are there in a box 2 feet at the bottom,* 3 feet at the top, 4 feet high, and 6 feet long ?

Ans. 108680.

together

To find the number of bushels or gallons contained in a corn-house or box, ascertain how many cubic inches are con- tained ivt^the box or house, and divide them by the number of inches in a bushel or gallon. If the house contain ears of com, divide the number of bushels by 2, which will I give the number of shelled corn.

EXAMPLES- *

1 . How many ale gallons are there in a cistern, which is

-J

In all such ejcaniplcs taice the average width or length.

MENSURATION OF 30LIDS. 145

11 feet 9 inches deep, and whose Ivasc is 4 feet 2 inches square ?

. f The cistern contai is 352500 cubic^ inches.

^^' I And 352600 ^ 2 ;2 = 1250 gaUons.

2. now many wine gallons wil fill a ditch 3 feet 11 inches wide, 3 feet deep, and 462 f( et long ? Ans 40608.

3. How many bushels of corn aie there in a crib 5 feet wide, 5 feet high and 10 feet long, : illed with ears ?

Ans. IGObu. lip. -f

4. How many bushels of com ar > there in a cril 20 feet long, 10 feet deep, and 6 feet wide '{ Ans. '^81|. -{- 1

N'ote. As complete accuracy is cot to be expected from any rule to gauge a crib, the following is recommended as being accurate enough for practice. ' Multiply the number of cubic feet in a crib by 2, and d vide the product by 5. Take the above example,

2 X 10 X 6 = 1200 X 2 = 2400 -rf 5 = 480.

5. How many bushels of com ar.? there in a crib 16 feet bag, 10 feet high, 8 feet wide at tha bottom, and 6 at the top? Aia. 480.

6. How many bushels of coal wlI a coal bed contain, 14 fijat long, 4 feet wide, and 3 feet 6 mches high ?

AnB. 166^^.

Ab/c, In suob examples, it will produce very near the true result to multiply the number Df cubic feet bj 4, ani[ divide the prodtiot by 5.

To mate a box large enough to c mtain a given fpiantity, multiply the number of bushels or ;^11ods to bo contained by the number of cubic inches in a, bushel or gallon. If the box is to be in a cubic form, extract the cube root of the product. If the side or end of the box be given to ascer- tain how long or wide it must be, d vide the product by the number of square inches contained oj the side or end.

EXAMPLES.

1. It is required to make a box in a cubi« form krgo

;146 MENblJRATION OF SOLIDS.

enough to contain 1 bushel. How many inches must it be

every way ?

The cube root of 2150= 12.9 i- in. inako it 18 in. every way.

2. How large a box in the form of a cube will contain** I bushel? Ans. 10.29 4- or lOi in. nearly.

3. How large a box^ in a cubic form, will contain 5 bushels ? Ans. 22 -f in.

4. How long must a box be made to contain 60 bushels, which is to be 4 feet wide and 3 feet high ?

Ans. 5 feet 2.2in. 2150x50=:=107500-r-172S=62.2==5ft.2.2in.36x48=^1728

5. What must be the length of a box, the end of which is 3 feet by 2, to contain 20 bushels? Ans. 5 feet l|in.

6. How wide must a box be made, which is to be 10 feet long and 5 feet deep ? Ans. 4 feet 11.72 in.

To Jind the iolidity of a Cylinder Multiply the area of one end by the length.

EXAMFLLB.

1. What is the solidity of a cylinder whose length is 60. I inches and diameter 20 inches ?

20 X 20=400 X .7864=3141600 X 60=18849.6 Ans. What is the solidity of a cylinder whose length is 121 ;inchea and diameter 45.2 inches? Ane. 194156.6.

j 3. The Winchester bushel is a hollow cylinder 18 J inches in diameter and 8 inches deep? Ans. 2150.42.

' 4. How many cubic feet are there in a log of timber 2 •feet in diameter and 20 feet long? Ans. 62.83.

5. A gentleman has a bushel measure which is 15 inches in diameter and 12 inches deep, how much is it too great or too small? Kn<^ i 29.84 inches, or a little more

'"I than a pint, wine measure.

6. A gentleman has purchased a gallon measure in the fonn of a cylinder, which is 6 inches in diameter and 10 inches deep. He was told it was a wino measure by the merchant. Is it a correct measure ?

, f-It ^ontaaib 282.7 cubic inches: "^ ^ * ' therefore it must l>e ale mearave.

GAUGING OF CASKij. 147 i

Tojind t/ie contents of a vessel in the shape of a frustrum

of a cone.

Square tlie diameter of each end, multiply tlieir squares together, and extract the square root of their product, to which add the two squares, and then multiply by the deci- mals .7854 and i of tho length.

EXAMPLES.

1. How many cubic inches are contained in a vessel 9 inches deep, 4 inches in diameter at the bottom, and 3 feet at the top { Ana, 87.18 cubic inches.

4 X 4==16 3 X 3=9 X 16=144 the square root is 12 9^16-fl2rrr37x. 7854=29.0598x3=87.13 cubic in.

2. A measure which has been made for a wine gallon is 6 inches at the bottom, 5 inches at the top, and 10 deep. Is it a correct measure ?

. f It contains 238 cubic-inches, 7 cubic * ( inches too much, or 1 gill nearly.

3. A measure which has been made to contain ^ bushel is 12 inches at the bottom, 15 inches at the top, and 15 1 inches high. Is it a correct measure ?

Ans. It contains 1019- 7 cubic inches, 56 too little.

4. How many gallons, wine measure, will a large crout tub contain, 9 feet high, 4 feet at the bottom, and 3 at the top? Ans. 87.18 cubic feet, or 652.15 wine gallons.

GAUGING OF CASKS.

There are commonly reckonod four varieties of casks, for eflxjh of which some have a different rule, but the following t I rule will apply to all :

To calculate the contents of a cask, reduce tlie dimensions Ito inches; subtract the head from the bung diameter, multi- jply the difference by the decimal .7, if there be much curve

;of the .staves betwixt the head and bung, by .67, if a little jmore than common, .6, if common, .57, if but little, .52, if jnonc. To this product add the head diameter. Square

' "- '•■ "■• •' •■ '-- - • •■■"'^ ' • ■ • ^ ''

jT? •T.

1248 TONNAQ.i or FLAT BOATS.

their suia, which -mul tip' j by the decimals .0028, when ale^, aiid .0024, when wine giUons are required, and the length of the cask.

A^ote. .0028 and Ml 4 are the results of dividing .7854 by 282 Lnd 231.

:XAMPLE8.

1 W lat is the capaciij of a cask which has much -curve b( twixt ohe head and I ung, 30 inches long, head diameter 18, and bung 24 inches 1'

Ais. 60.26 wine, or 41.3 ale gallons.

24— 18r=6x 7=4.2 -f J 8=22.2 x 22.2=4928.84 x .0084 = 16.75656 X 30=50.239680 gnllons.

2. How many wine j;.allons will a casl^ contnin, of com- mon curvature, which i,- 30 inches long, head diameter 18, and buu;^ 24 iiiches ? Ans. 45.9 gallons.

8. What is the capac}vj of a cask without curvature be- twixt thi) head and bung, 30 inches in length, head diameter 13, and oung 24 inches '

j\.nB. 37.3 ale, or 45.3 wine gallons.

4. Hew many wine gallons will a cask contain, of the

Jc^mmon form, whose lei gth is 27 inches, head diameter 21,

and bun*,' 23 inches ? Ans. 46.24 gallons.

TONNAGi: OF FLAT BOATS.

The quantity which any vessel will carry is equal in weight to the quantity of water which the vessel displaces by loadi?igj therefore tha number of cubic feet of water dis- placed b7 loading a ves^^l, multiplied by 62^, will give the number of pounds whic i that vessel will carry.

To aj' certain how m;ny tons, barrels, &c., of % certain (weight, a Flat Boat will carry

TONNAGE or iXAV BOATS; 149

RULE.

Subiraot ^ the lake or rakes tiv a the length. Multiply the remainder by the 'depth to wiich she is suik by the load, and that product by the width measured 'a*om the outside of the gunnel.-^. If the pi oduct is not ir feet, i-e- duce it to f^Qt, which multiply by 52^, which will give tlje number of pound?, which reduce to tons, or divicie by the I weight of a barrel, &c.

JEX^lMPLES.

t 1. How much will a flat boat c*a:ry which is 50 feet long, 'rake 10 feet, 12 feet wide, and wil bear sinking 1| feet? I Ans. 22 tons 12 e\t

i50 — 5=r:45X l^r:::67^V 12=:81C X 62A:r= 50625 ^112 rn

452-20=22 ton. 12 cwt.

2. What number of flour bai-rels; which weigh IC 6 pounds each, will a flat boat carry which i? capable of being suik 1 foot 3 inches, 50 feet long, one lake 10 feet, tho other 8 f(yA, 15 foot wide? Ans. 515.

r^>ii,iin irfiii, mil I inn l»»»j*

TABLES.

Of the present state of real and imaginary monies of the

most commercial parts of the world, with tlie United States, and reduced to the value of the monies thereofjin Dollars, Cents and Mills,

This mark t is prefixed to the imaginary moiicy« or money of account.

This mark ::= is make,^ or equal to.

In the column of Mills, wherever a tij^are is preceded by a point {.) it coni'crta it to decimals : I'hus 6.8 means $ix mills and eight-tenths of a mill.

A-miBMlCA,

UNITED STATES,

A

5 i\lills = a half cent .

10 Mills a cent^

S^Centg a half dime 2 Halfdimesa dime ..

25 50 10 '2\ 5 10

Cent^

Cents

Dimes

Dollars

Dollars

Dollars

a I of a dollar a half dollar .

a dollar

a 4 eagle .... a 1 eagle .... an eagle

Doils. jCentB.l Mills.

1

2

5

10

1 5

10

I 25 50

50

Accounts, in the United Statps^ are kept in Dollars and Cents.

CANADA, NCn^A SaJTlA, &c.

A "fFarthing . .

4 Farthings = a penny . 12 Pence a shilling*

60 Pence a dollar. .

1

20

4.1

6f

(i^C)

TABLES or iOREIGN MONEY.

15)

CANADA, NOVA SCOTIA, ^c.

(continued.) *

20 Shillings =^ a pound 4

30 Shillings a moidore ' 6

40 Shillings a half Joe | 8

50 Shillings a Federal Eagle 1 10

AccouatK are kept in pounds, shillings^! and pence; but they are also kept in some | parts of Canada in IJvres, sous, and deniers, ; according to the ancient system of France, | and is called Old Currency.

MEXICO, PERU, CHILI, kc.

5iE^Accounts are kept here, and all other partj: of Spanish America in Pesos and Dol- lars of 8 ideals, the Real being divided into halves and quarters; this Real is occasion- ally divided into IG parts, and ?'iSO into 34 51arf,vedis of Mexican plate.

DollH. iceuts.JMill/

BRAZIL.

Account* are kept here u^ in Portugal, in jReas, 1000 making the Milrea; 100,000 I being 100 milrcas; and 1.000,000, one

thwii»and Milreas, commonly called n

Con to of Mih-cas.

:sti»OPJ3.

.NOKUifcttN PAKT8.

ENGLAND AND .SCOTLAND. ;

LomJov, lAirrpcoI, .Bristol, Edinhnnj^ t Glasaow, (f!:c. !

! A fEarthing

I 2 Farthings ~- a halfpenny j 2 Halfpence aj.enny...

4.(

8*

mtmmmamtan

ngTW IT BtrwirtafigUJ

TABLES or FOREIGN MONEY.

nl

ENGLAND AND SCOTLAND. | (continued.) i

4 Pence ~ a groat ,

6 Pence a half shilling

12 Pence a shilling . =

54 Pence an American dollar .,.,*.

5 Shillings a crown

20 Shillings a ^ound sterling .......

2 1 Shillings an English guinea

Accounts* are kept in Pounds, Shillings, Pence, and Farthings.

jYote. AUhoiigh the English crown at the par of exchange is $1.11 1 . 1, yet in the United States it passes only for $i 10 cents, and the gold coins, instead of passing at their par value, are now regulated by the rate of exchange between the two countries.

mELAND.

Dublin, Cork, Londonderry ^ Sgc.

A fFarthing

2 Farthings = a halfpenny

2 Halfpence a penny

12 Pence a shilling

13 Pence an English shilling . . . 58 1 Pence an American dollar , . .

20 Shillings a pound

22| Shillings an Englbh guinea . . .

Accounts are kept in Pounds, Shillings, Pence, and Farthings.

BREMEN.

Dolls. I Cents

MiliB.

7 \ 11 22

11 44 66

4

1.1

2.2

1.1 4.4 6.7

A tPfening

IJ 2 Pfennigs = a sware 5 Swares a grote

4.3

t iipi ■

TABLE3 OF POllEIGN MONEY.

163;

BREMEN.— (coxTixNUED.)

3 Grotes -^ a double shilling

24 Grotes a mark

48 Grotes u double mark

72 Grotes or

3 marks a tdxdollar

Accounts arc kept in Kixdollahs and Grotes.

Dc /<».

HANOVER.

A jPlcnii)^,

3 Pfenings ~

8 Pfenings

12 Pfenings

8 Groshen

16 Groshen

24 Groshen

32 Groshen

34 Groshen

a dreyer

a marien

a tgrosh

a half guilden ..........

a guilden

a |rixdollar

a double guilden

a ducat

Accounts are kept in RixdoUars,Groshen, land Pfening-s.

AUSTRIA AND SVVABIA.

Vienna^ IHes^^ jlugslnirg, Blenh$im, Sfc

A |Phening

2 'Phenings ~ a dreyer

4 Phenings a |creutzeir

14 Pheuingd a grosh ,

4 Creutzers a batzen

1 5 Batzen a |gould or f florin .... iK) Creutzerg a rixdoilar

C nl8.

3 25

51

76

' 2

3 26 52 78

5 10

3

3

52

78

!«<SS

2. V

4

H

5 ft

io^i

TABLES OF FOREIGN MONT.Y.

AUSTRIA AND SWABIA. (continued.)

30 Batzen = a specie dollar' 60 Batzen a ducat

Doils.

Cents.

5 10

Accounts are kept in Florins, Creiitzers, and Phenings. j

!

•Although the par of exchange makes a j specie dollar 1 dollar and 5 cents, yet lu the United States it is worth but a dollar.

OLLAND AND ZEALAND,

Sinstcrdairij RoUerdam, Middleburg and Flushing.

A "j Penning

8 Pennings =:= a gwte

2 Grotes a f stiver

6 Stivers

20 Stivers

50 Stivers

60 Stivers

105 Stivers

6 Guilders

a seal in a Iguilder . . . , a rixdollar . . . . a drey guilder

a ducat ,

a pistole , . . ,

Accounts are kept in Guilders, Stivers, *nd Pennings.

SOUTHERN PARTS.

PORTUGAL.

A -fRm

10 Rcas «=ft half vintin. . .

20 Reas A viatin

5 Vintias a teetoon

'—^-"—T- II ] ' i7~i Ml I

1

2

12

40

1

1

20

2

10

2

40

1

2 V2

niimii^friii t\iu

TABLES or rOREIGN ^lONEY.

156

PORTUGAL.— (continued.)

4 Ti'stooDs ==: a crusad of exchange. .

24 Vmtins a new crusado

10 Testoons a "fmiilrea

48 Testoons a moidore

64 Tjstoons a Johannes

Accounts are kept in Millreas and Reas.

FRANCE AND NAVARRE.

Paris, Lyonsy Marseilles^ Bardeaux^ \ Baycmne^ S^c.

I A teenier

I 3 D rniers ^-^ a hard

i 2 Liards a dardene

: \2 Deniern a j&ol

j 20 Sols a tlivre tournois

'■ 60 Si-ls an ecu of exchange

I 0 Livres s.n ecu or crown

1 10 Livre^- a pistole

1 24 Livres a Louis d'or

!

I Accounts are Icept in Livres, Sous, and P«niers.

j Since 1795 accounts are kept in Fiance I of 10 Decimes or 100 Centimes. The J Livre and Franc were formerly of tlie same value: but by a decree of 1810, the follow- , ing proportion has been established : Pieces of 48 Livres at 47f. 20c. of 24 £t 23 . 55

of 6 at 5 . 80

of^ 3 &t 2 . 75

The modern .^^olJ coins are Napoltons of 40 and 20 Fraiics, and Louis cf tli©

Dolls.

Cents.

50

60

1

25

6

8

!

! 1

18

1

55

i 1

11

1

86

! 4

44

*

1 1 1

Mills.

2.3 4.6

H

5 6 1 i

4.4

tftn»»ra«a— » *itf»Lliwiii ■

— w»— I nm^iiii^i

156

TABLES OF FOREIGN MONEY.

JVote. French crowns at the par of ex- change are estimated at 1 dollar 111.1 cts., but they only pass for 1 dollar 10 cts.

SPAIN AND CATALONIA.

Madrid^ Cadiz, Seville^ Sfc.

NEW PLATE.

A f Maravedi ,

2 Maravedis = a quartit

*34 Maravedis a |Real

2 Reals a pistareeii

8 Reals a piastre of exchange

10 Reals a tdollar

375 Maravedis a ducat of exchange .

32 Reals a pistole of exchange

36 Reals a pistole

Accounts are kept in Dollars, Reals, and Maravedis.

Dolls.

Gibraltar* Malaga, Denia^ 6$c,

VELON.

4

34 15 512 GO 2048 70

A fMaravedi 2 Maravedis

Maravedis

Maravedis

Reals

Maravedis

Reals

jMaravedis

Reals

an ocnavo ....

a quartil

a treal velon . . a f piastre of ex.

a piastre

a pistole of ex. a pistole of ex. a pistole

Account are kept in Doilars, Reals^. and lilaravsdis.

Cents. Mills.

10 20

80

10

18

72

79 79 18 .18 72

2.9 5.8

as

att;

TABtiES OF FOREIGN MONEY.

167

BarceloTUty Saragossa, Valencia, Sfc,

OLD PLATE.

A t Maravedi

16 Maravedis = a soldo

2 SoldoB a "frial, old plate

16 Soldos afdollar

20 Soldos a libra.

24 Soldos a ducat

60 Soldos a pistole ...........

There are also Ducats of 21 aid 22 Soldos.

Accounts are kept in Dollars, Reals and Maravedis.

JS*ote. — Although 60 Soldos are ecual to 3 dollars and 75 cents, the Spanish Tistole is worth but 3 dollars and 60 cents

ITALY. Genoa, JVowt, 4rc., Corsica, Baska^ Sfc,

A fDenari .-

12 Denari = a "fsoldi

4 Soldi a chevalet • . ....

20 Soldi ' a flira

30 Soldi a testoon

5 Lires a croisade

115 Soldis a pezzo of exchange. .. .

6 Testoons a genoine ....

20 lires a pistole

Accounts ai'fi kept in Lires, Soldis, and

Denaris.

DollB.

C«nts.

.

Leghorn^ Florente, 4r**

A jDenari

4 Denaris = a quatrini

14

6 12

25

50 60

a

15 23 79 92 44 18

168

TABLES 01 FOKEiaN MONEY.

ITALY, &.C.— (continued.)

12 Denaris = a |Soldi

5 Quatrinis a craca

a qiiilo

a jlira

a piastre of exchange . . , a ducat

18 Cracad 20 Soldi 6 Lires 7J Lires 22 Lires

Dolls.

a pistole ............. j 3

Accounts are kept in Liresj Soldisy and Denaris.

ASZJL

BENGAL.

Calcutta^ Callictttj Sfc,

A [Pice • . . .

4 Pices = a fanum

6 Pices a viz

12 Pices an ana

10 Anas a piano

1 G Anas a rupee

2 Rupees a French ecu or crown ....

2 Rupees an English crown

56 Anas a pagoda .

A Lack IS 100,000 rupees.

Accounts are kept in Rupee^^ Anas, and Pice.

CHINA.

Pekin, Canton^ ^c.

A jCash

10 Cash = . a fcandareen

10 Candareens a f mace

10 Mace, 1 oz. 6 dwt. 16 grs.'= a ftale

Accounts arc kept here in Tales, Mace, ;| Gandareen?. and Cash.

Cents.

Milts.

1

10 15 92 15 44

j7.7 i2.8 2.8 4.3 5.9 7.3 14*. 4

1 1 3 34 55 11 11 94

1 14

48

2.9 1.6 7.3 4.7

6.8

1.1 1.1

4.4

1.4

4.8 8

BBUSBi

kMMWaateAM

iTtsni

TABLES OP FOREIGN MONEY.

159?

MocJia.

A tCarat

6 Carats = a commarsee

Carats a | caveer

Commarsees a cofTala

Coflalas a fMocha dollar

Mocha Dollar a Spanish Dollar

Coffalas a sequin

Sequins a tomond ,

)Vecounts are kept in Piastres or Mocha Dollars, and Caveers.

ISLAND OF JAVA.

Batavia.

A tDoit

4 Doits = a Istiver

8 Doits a cash or dubbettjees . , . 3 Doits a satalie or schilling .... 3 Satalies a sooka

9 Cash a sooka satalies

15 Cash a current rupee

24 Cash a fPardaoor rixdollar . . .

60 Stivers a dollar

13 Schillings a ducatoon

J^ote, — A new system of monies has been established by the king of the Nether- i lands.

The unit is the new Gulden or Florin of the Netherlands, and instead of decimal divisions is divided into 4 Schillings, 12 Dubbels, 24 Dutch Stivers, 30 Indian Sti- vers, or 120 Doits.

DoUfl.

Cents.

MilU.

1 1

15

1 1 6 "83

66

1 1 10 20 30 50 80

30

160

VABLES OS FOREIGN MONEY.

Isle of jBourhoHy and Isle of France.

A Denier . ». , ,

12 Deniers = a "fSoiis

20 Sous a flivre

IQ Livre* a dollar ,

EGYPT.

Old and JSTm Cairo^ Mexandria^ Sttyde, Sfc.

An |A«per

3 Aspers = a tmedino

24 Medini an Italian ducat.

80 Aspers a piastrs ._.

30 Medini a dollar

96 Aspers an ecu

32 Medini a crowii

200 Aspers a suttaiiin

70 Medini a Parzo dollar

Accounts are kept ia Piastres, Medini, and Aspsis.

iBARBARY.

JilgieTSy TimiSj Tripoli^ Una, ^c.

Bolls.

Cents.

An f Asper ,

3 Aspers = a mediuo

10 Aspers a reai^ old plate a fdoul le ....

a doUai

a silver chequin a dollai

2 Reals

4 Doubles

24 Medini

30 Medini

180 Aspers

15 Doubles

a zequiJi a Pisto.^ e

Accounts are kept in Doubles and Aspers.

10

1 3

74 88

10 10 22 33

1

3

12

25

74

9G 72

Mills.

0.4 5

0.3

0.8

9

TABLES or roiiiiil?!*^ MdpSrE-ir:

Igi

WBST INDIES.

Jamaica and Bermudas.

A Farthing

4 Fanhiug = a "jpeiiny

1\ Pence a real or bit

2 Bits a pistereen

12 Pence a t-shilling

20 Pence a J of a dollar .......

80 Pence a dollar

1 6 Shillings a half English guinea .

20 Shilling.'; a tpound

40 Shillingij u moidore

53^ Shillings a half joe, I) dvvt

Accounts are kept in Pounds^ Shillings, and Pence.

JVo/e.— -As the currency of JTamaica ,is 1 .407., its proportion to sterling is as 7 to 5. Hence \l. sterling = 17. 85. currency; and U. curreycy — 145. 3J«7. sterling.

Barhadoes.

A Farthing

4 Farthings = a penny

7 J Pence a real or bit

2 Bits a pistareen

12 pence a shilling

75 Pence , ^ dollar.

20 Shillings a pound

27j Shillings a moidore

50 Shillings ,u half Joh{innea ......

. A<'-covsiUs are kept in Pounds, Shiliings, Pence, aud Farthincrs.

Dolls. Cents. Mills

1

10

20

15

'25

33

1 10 20 IG

20

i6-2

TABLES OF rOEEIGN MONEY.

Bafiamas.

A f Fiirthuig

4 Fanhiiigs =:= a fpcnny

0 Pence 12 Pence 90 Pence 20 Shilllrigs 48 Shillings 64 Shillings

a bit

a "fshiiling . , . .

a dollar

a tpound . . . . . a nioidore . . . .

a half Johanncjs

DolU.

Cents.

Mills. 1

•

2.6

1

10

04

12

5

1

3

6

•

8

Accounts are kepi in Poundis. Shiiihigs, Pence, and Farthings.

Sl Barthohmews, St. Kitts^ JSTevis, Antigua and Montserrat,

A fFarthing ,

4 Farthings ~ a tpenny

9 Pence a bit

12 Pence a jshilling

8\ Shillings a dollar . ,

1 1 Bit? a dollar

20 Shillings a fpound

66 Shillings sl half Johannes

Money of account, Pounds, Shillings, Pence^ and Farthings.

Dominica^ St. Vincents^ Grenada^ St.

A fFarthing

4 Farthings = a |penny .

9 Pence a bit ... .

12 Pence a fshilling

I

9 12

40

n

8 11

2.3

H

3.3 1.1

"•■(W

l^^^^^lhMMM

;v;-t^' g;

«i >-iii"'1 Ttit r rt WJm III I At III ■■»»»<—>1rteifc&

TABLES or FOREIGN MONEY.

163]

Dominica y Sfc. (continued.)

13 Bits = a dollar . 20 Shillings a fpound

Dolls.

Accounts are kept in Pounda, Shillings, Pence, and Farthings.

Martinique, St. Lucia, Guad^tloupCy Sfc,

A Denier

13 Deniers = a sol

15. Sols an escalin

20 Sols a livre

3 Escalms a J gourde

9 Livres a piastre gourde ..,.,.. 12 Escalins a piastre gourde

8 Gourdes a J Johannes, 9 dwts. . . .

J of a Quadruple = 4 dwts. 6 grs

J of a Quadruple 8 dwts. 12 grs. . . A Quadruple 17 dwts

jMoney of account, Lirrcs, Sols, and Deniers.

St, Domingo, (Spanish part,) CuhOf Porto Rico, Sfc,

A Cluarter Real

A tHalf Real

4 Quarters 3= a freal '

2 Reals a Peso Medeo . .

4 Reals a jpeso or dollar

Accounts are kept in Pesos or Dollars* Reals, and Half Reals.

1 1 8 4 8 16

Cents.

Mills.

22 12.2

8 11 25

3

6

12

35

Oi

H

1.1

H

5

I II m II n

fi04

TABLES OF FOREIGN MONEY.

St. Domingo, (French part.)

In the French part of St. Domingo or Hayti, accounts were formerly kept in Livres, Sols, and Deniers current; and the Dollar was then reckoned at 8 Livres 5 Sous current; but at present accounts are mostly kept in Dollars and Cents, as in the United States.

Si. Emiaiia^ St, Martin^ Curaqoa, S;c.

A Farthing

4 Farthings = a |penny

9 Pence a bit

12 Pence a fshilling ,

8 1 Shillings a dollar .... .... ...^,, . .

11 Bits a dollar '..'*. ... ..

20 Shillings a fpound

Money of account, pounds, ShiUingSj Pence, and Farthings.

St. Thomas^ St. Johriy Santa Cruz.

A jStiver

5 Stivers = an old Bit

6 Stivers a jgood bit

8 Good Bits a fpiece of I

12^ Good Bits,

or 15 Old, a dollar ........ , .,. . . .

75 Good Bits a moidore . . . .'i';-;*/ ..V".

100 Good Bits a half joe A 9tK

' Accounts are made out in Pieces of f^ iBits, and Stivers.

Dolls.

Cents.

Mills

1

9 12

40

H

I

8 64

3^

61

■■!■ ■■■ I J ■

TABLES OP FOREIGN MONEY.

1G5

Surinam, Berhice, Demerard, Sfc.

A fDiiit

1 G Duits ;r= a stiver

20 Stivers a guilder , . , .

2i Guilders a dollar

5 Guilders ^ Johannes

1 5 Guilders a moidore

20 Guilders a half Johannes

Accounts are kept in Guildei*s, Stivers, and Duits.

Canary and Madeira Isl({^ds.

A tHce

62| llees = a sixteenth of a dollar . . .

62| Rees J of a pistareen

125 Rees | of a dollar

125 Rees J of a pistareen ........

250 Rees J of a dollar

250 Rees a pistareen

1000 Rees a milree

Accounts are kept, a? in Portugal, in Rees and Milrees.

JVo/ff.-T.A pistareen, which is wortli I only 20 Cents, passes in Madeira, the same as a quarter of a Dollar, which is worth 25 Cents

Dolls.

Cents.

Mills.

3

40

lii

6 5 12 10 25 20

2i

??s_ ^ ■ ■■ .. - . ii:ij.>j^^

SHORT METHOD

TO

CALCULATE INTEREST.

RULE.

Multiply the sum by half the number of days,* that pro- duct being divided by 30 will give the interest in cents.

EXAMPLES.

V ^at is the interest of 165 dollars for 16 days. 165 dollars 8 half the number of days

30)1320(44 cents 120

120 120

REDUCTION OF COINS.

Tl e Dollar having different denominations of value throrghout the United States, some simple rules for re- ducirg the respective nominal values to Dollars and Cents may not be unacceptable.

The Dollar is valued at 6 Shillings in the states of New Hampshire, Massachusetts, Rhode Island, Connecticut, Y^^^" , ginia, Kentucky, and Tennessee.

To reduce the Currency of these States to Dollars and Cents, take this

RULE.

Add a cypher to the right hand of the pounds, and divide * Counting 360 days in a year.

KKDUCXIUN or C^Jl.NS. ItiT i

by 3, the quotient will I)o-dollarf^— If there are sbillinga io I the sum^ ud-i 1 dollar 5or every G^*.

KXAVi'J^fc.s..

1 . Kedxioe lOiil t> vl<>llar6 aud otuts.

o^

Keducc 4t>.^. 1;')^. Ikl to dolbn; :iud centa. 3>i60

15o.o3^

Ansv/er 6155.96 acarly.

The Dollar U valaod at 7^. OrZ. ia the States of Pennsyl- vania, New Jcrt?ej, Mary knd,. and I>elaware; to reduce which to Dollar.'?, take the followinjr

RULE.

Multiply the pouurit^ by 8 ; d^^^diug that product ])y 3, i I ,'^lvoa the doJlftTK; and where there arc shillings add" one |

i '■Joll-ir for tvt^vv "ir. i^yj. \

I

i

l?e.l

uce 80/. 30

3j2l0

1/v.

to dollars

and

C€nt8

15

80

AnsTPer ^82

168 REDUCTION OP COINS.

The Dollar passes for 8 shillings in the States of New York and North Carolina.; to reduce which to Dollars, ufae this

RULE,

Multiply the pounds by 2 J, and the product will be dol- lars; and where there are shillings, add one dollar for every Ss,

EXAMPLES.

Reduce 30?. 12s. to dollars and cent^. 30 12s.

H

60 15 12s. = 1.50

Answer $76.50

In ttee States of South Carolina and Georgia^ the Dollar passes for 45. and Sd. to reduce which into Dc liars, take

RULE,

■

Add a cypher io the right hand of the pounds, then multi^ plv by 5, and divide by 7, and the quotient is the dollars ; and it mere are shillings, add a dollar for evwy 4$. 8d.

EXAMPLES.

Reduce 10Z. lOs. to dollars and cente 100 3

7)300

42.85.C 9.<f. 4d. - 2. 8f .14.2

Answer $45.00.0

ramiXMammiimmmtf

n 'i ' ~il Ti' Ti ' ■ < «ii'in rii ' I ii«ir 1 1, n "'■Tliid ' n ^

A TABLE,

Exhibiting the standard weight, and Federal value of the Gold Coins, that pass current in the United States, with their value in the currencies of the respective States.

-?^? ?ri

ts-* P-

P- P- S-

a « a 5? o

^ 5- ^ ^ g . p . . .

o

CD

o

p-

J3

o

p-

p p

CO

8

a.

•I

P5

a- ?

CD

•^

^

Co

w

o

o

to O^ I-*

^

s

O en o QftJ

CO Ot CO ><^ >i:^ O GO 05 -Jl-'OiCnOSOOO

CnbOCOtOOiOOO

ti o« o

(yt o o

o o o

o o o

fcOOOtO-^OOOSOOCi 000050000

O M CO t^

Oi o • O J«

O O O fX

Standard Weight.

Federal Money.

New England States, Virgi- nia, Kentucky and Tennessee

MC;iMMH-»b0 05<:75 H-ibOtf^t*<

OOOOOOOO

O O O J» O O O ft.

New York and N, Carolina.

h^^>^}^i-itZ>ZOC^ OH-*COt*<

OO ti> — 1 >+* O^ C/« O O OOOOiOOOO

00 -1 en ?»

O O "O ft.

New Jersey, Pennsylvania, Delaware, and Maryland.

OCOOH*HJ|-»fcO>f^ 0»-*b©t^

OOO^IM(-*COOO OOOSCJ^CDOOO

H-* CO Ci o» OO t^ 00 ft,

South Caroli- na & Georgia.

*The Standard for Gold Coins of the United States is i eleven parts fine, to one part aljoy; Silver Coins 1485 parts ■ fine, to 179 parts alloy.

^ ■x-ai>!,iini>ii«ftMii I

t 'tit^iNiaratf^tiMu:^

f IVO f.- /

:|L'

ri5

<

I ABLE

o

so

is*

P 00 jcv^

^ *^ »^ 5z; (^"^ ic-i

-^ Ir-I IOC ItT:

O "--' t'-^

Tj^ ICO

^ Ice

0^1 r-<

iCO jvN i»0 ■■'7~1

o

02 ^^

to

(ji o cc ICC'

ICv5

CO

o o

CO CO

CO iO

CO |:.:

IcO (M i'M

CO

<5 CI H

CC jO-l

|(M 'lr->i J!— *

V»%i— I jo ■^ OO i«0

■^1 Oi

C3 r-<

iC^

|X>

jr^, jo |u-0

!:-> Ico i'O

i i :co

ir-l vO IO

;cTj r^ jco ; .."0 CO

CO -co

JO CO

CO o

CO CO

M^ CO CO CO O I--.

CO Ctt) IcM

jr^ pO CO

CO c<i ca

>j^o '^ r-" o >-o 1^ '"I' fc»2 k^i !c;4 !t=s .'S CI GO rv£> jco ''-D CO o jt-- h* H cr^ Ji; '"":.; ic^^ CO ico '71 <:■? ci i— .

'S O 05

,-1 \ta> kd 1"^ M4 .:o

CO <r> 'co lO {^ kj< CO CO I^O !g4 '^-nJ

i^!c-i

C 1 ifH T— s J— 1 j

^ .- ;^ »ro l««* h^ Ico !co \oi irH .S '-^ h^ «o jco iO 1I-- i-v?* i^ Use

.iC, i v^i ^CO iC«i '?! ■■•! CI P"^

J i

b- jcp to jo

u^ c

0 'O Irti

O

iTt*

"i jO ?^ !^ ''**' I'X) i'*i>

jco CO. ICO C^ i'^i \Q^ r^

to o o hf hjf (:o Icri

O ?— -" I.— I l.go O T'^^

! I

&4

a

uo k^ O-

< ^ .-^ t-5 •-< (©2

I . i ( -4 ..... !, I

tj — -ft

CO

iTMir iijr- iB>»i

Pi

fcX)

s

a. o

•♦J

03

S

s

a.

<»

DC

CD

> — 4

^

O

o

I

TABLE OF INTEREST,

Pcj day, at 6 per cent, on anj number of Dollars, from One to Twelve Thousand.

D.

1

2

r, O

4 5 6 7 8 9

10 11 12 13 14 15 10 17 18 19 20 21

oo

23 24 25 26

27

i. 2f

M. I 016 038 049 066 082 099 115 182 148 164 I8i 197 214 230 247 203 279 296 312 329 345 362 37« 395 411 427 444 ^.60 477 498

2!

o

D. 31

'32 33- 34 35 36 37 38 39 40 41 42 48 44 45 46 47 48 49 50 51 52 153 II 54 55 56 57 58 59 60

M.

510 526 542

559 575

592 608 625 641

658 674 690 707 723 I 740 , 756 I

< i O '

789 i

808 i

822

838

855

871

888

004

021 I 937 ' 053 I 970 : 986

^"

D.

61

62

64 65

66 67

68 69 70 71

72

73 I

74 j

75 !

/O .

«/ I 78 j 79 80 ' 81 82 I 83 84 85

, 8^

l! C^

fssj

89 \ 90

C.

1,

1

1,

I.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1

I. •

1. 1. 1. 1. 1. 1. 1. 1.

M.

003 019

036

052

068

085

101

118

134

151

167

184

200

216

233

249

266

282

299

315

332 11

348

364 !•

381 jl

397 |!

414 I!

447 '1

468 I 479 I

5^

•^•

D.

91

92

93

94

95

96

97

98

99

100

200

300 ^

400

500

600 j

700 I

800 I

900 '

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

•oannM^UMa

D. C.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

3.

4.

6.

8.

9. 11. 18. 14. 16. 32. 49. 65. 82. 98. 16. 31. 47. 64. 80. 97.

M.

496

512

529

545

662

678

695

611

627

644

288

932

575

219

863

507

151

795

438 1

877

815

763

192

630

058

507

045

884

822

260

A PRACTICAL SYSTEM

©F

BOO K-K E E P I N G,

FOR

FARMERS AND MECHANICS.

Almost all persons, in thS ordinary avocations of life, unless they adopt some method of keeping their accounts in a regular manner, will be subjected to continual losses and inconveniences ; to prevent wliich the following- plan or outline is coiifposed, embracing the principles of Book-Keeping in the most simple form. Before the pupil commences this study, it will not be necessary for him to iiave attended to all the rules in the Arith- metic; but he should make himself acquainted with the subject of Book-Keeping, before he is suffered to leave school. A few examples only are given, barely sufficient to give the learner a view of the manner of keeping books; it being intended that the pupil should be required to compose similar ones, and in- sert them in a book adapted to tiiis purpose.

Book-Keeping is the metiiod of recording business transac- tions. It is of two kinds — single and double entry; but we shall only notice the former.

Single entry is the simplest foym of Book-Keeping, and is employed by retailers, mechanics, farmers^ &c. It requires a Day-Book, Leger, and, where money is frequently received and paid out, a Cash-Book.

DAY-BOOK.

This book should be a minute history of business transac- tions in the order of time in which they occur; it should be ruled with head lines, witli one column on the leil hand for post-marks and references, and (wo columns on the right for dollars and cents. The owner's name, the town or city, ^nd the date of the first transaction, should stand at the head of the first page. It is the cuat<»n of tnany to continue inserting the name of the town on every page. This, lirnvever, is unneces- sary. It is sufficient to write only the month, day, and year, I at the head of eacii page after Llie first. This should be writ- ten in a larger hand than the entries.

(L7^4

FORM OF A DAT-BOOK.

iO

On commencing an account with any individual, his place of residence sliould be notod, provided it is not l\v?, same as that \vh(;re the hook is kept. If it be the same, this is unnecessary. As it often happens that dillerent persons bear tiie same nan^e, it is well, in such castas, to (Jesitrnate the individual with whom the account is opened, by L^fating his occupation, or particular place of residence.

When the conditions of sale or purchase vary from the ordi- nary custo«is of the place, it should be stated. Every month, or oftener, the Day-I^ook should be copied or posted into the Legcr, as hereaftjer directed. The crasses, on the left hand column, show that the charge or credit, against which they stand, 19 posted, and the tigures show the page of the Leger whore the account is^pposted. Some use the figures only as post-marks.

Every article f=old on credit, except when a note is taken, should be iiiunediatcly charged, aa it is always unsafe to trust to memory. Also, all bbour performed, or any transaction whereby another is made indebted to us, should be immediate- ly entered on the Day-Book. If farmers and naechanics would strictly observe this rule, they would not only save many quar- rels, but much money. In this respect, at least, follow the example of Dr. Franklin, who never omitted to make a charge as soon as it could be done. Never defer a charge till to-mor- row, when it can be made to-day>.

Edward L. Peckham.

• Jan. 1, 1840.

+ 2 +

James Murray, Jr Dr.

To Igall. Lisbon wine $1,92

" {) yds. C'Jlico, a '.M^ els <.- - '2.^5

" 2}Ms. Broadcloth, aS4,50 y,00

Robert Hawkins, Blacksmith Dr.

To 217 Ibg. Iron, a 8 cts.

:^4-

Thomas Yoeman . . . • Cr.

By Casli

.3 :

Archihdd Tracy. Salem Dr.

To Oiie jwece Droadololh, containing 2D yds., a $3 per yd., S!0 days' credit

Jwacs Warren^ Wartland Dr.

To J cask A'ojIs, 2-2j lbs., a 8 cts

Cr.

By :i7 lbs Cheese, a 10 cts $3.70

" 41 \h^. Fcalhors, a 70 cte ■ 28.70

IJalance to be paid in Corn, at market price.

18

17

3G

75

00 00

32 40

^5-"^

J II. -M \v . ■!-

2 + 2-h

rORM OF A DAY-BOOK.

Isaac Ikomas^ Brattle Square To 32 palls. Molasses, a 50 els

J)r.

William AngelL

7'a 300 IbP. Porh, at 7 ots. '■• 30 bu. C<MH, o 45 CIS. .

Dr.

$•21,00 I 13,50

10

C 00

■ H 3-}! 50

Samioel Stone Dt.

I'o 50 lb.s H.irncsa Leather, « 20 cts. •• 7 Tons Hsy, « 810

$15,00 \ , 70.00 i I

George Corpenier

To 17 Brooms, t 1:3 ctg

" 7 lbs. Butter, a 20 cts

" 4 lbs. Cheese, a 10 cts

35, 00

3-f

3 +

1 +

Jesse B. Swuei. ■''

To 1 hM. Molaese?, &8-^ ^ H2 /rails., a 30 cts.

Dr. \ I

. 1.40 i' I ■ ,40 |!

Dr.

]■ 27i 60

Or.

By C.Hsh

Jesse Metcalj]

To 20Ca!f-S.kiiis, a$.^.. •' 59 Dried Hides, a ^.

60 days' credit.

Dr.

$100,00 200,00

James Murray y Jr Cr.

By 20 !>u. CJorn, a CO cts. " 4 bu. Oats, a 40 cts. .

$13,00 l,«iO

* James Warren . . ! To 24 bu. Corn, a CO cts.

Dr.

Archibald Tracii, Dr.

To 1 cord Wc/d

" 30 lbs. Feathers, a 70 cts.

$6,00 21,00

1 +

Robert Haivlcins Cr.

By shoeinu my HT)rs>e. " " " Oxen .

$2.00 3,00

— i

Samuel Stone Dr.

To 2 yds. Broadcloth, a $4 " 4 pr. Shoes, a $1

$8,00 4.00

15

1 00

300

i - i

00

1 t

1 ''

CO

14

1 i

4t)

27

00

5

t

.00

! ! 12

00

FORM OF A I>AY-BOOK.

Jaji 5, 1840.

17 o'

2-f

Thomas Yeomans Dr.

To 200 bu. Corn, a 70 cts.

?! C

110 yo

To 30 quiiitaM Fiab, a $3,75

> ^ i Archibald Tracy Br.

i To'^bbls. Flour, agllO $20,00 j

. I •• 25 bb!5. Lard, « 10 cts 2,50 |

I " 3I)U. Satt.at^U.-t? lr'8 !

I)r.

•^-1, Gcorgr. Carpenter Dr.

ToQOO lbs. t'hc^sc, a r cia $10,00

•• 1 flrkin Butlo.r, 7H lbs., weitfhl of lub, 10 lb9.»66,

a SI) cts. • 13.20

112

SO

ea »

! 2i

^-f

Isaac Thomas Dr.

To 50 yds. Cnlico, n "Tl cts .'$11,00

" 75 yda. brown Shcotiiii;, a J 1 't-< 10,50 |i

Cr.

By Order on Goodrich St Lnrd. for ^U.

12

3H

2 +

Jesse Melcalf Dr.

To 500 pr. Men's Bhoos, a 95 cts \\ 475

. 10

Thomas Yeomans . , Di\

Po3 bbls. Flour, c !;^,50 %^

Robert Hawkins .'. Dr. j

'^o ViO ib'J. bii3tered Stetil, a ij cls S^.CO j

*' W) lbs. ltu.ssi,-. Iron, a 5 cts 5,00 jj

28

14

James Murray, Jr Dr, \\

To 10 lbs. Suj!Hr, a 11 cts 81. 10 ll

" iG lbs. Cotiee, a 15 cl.s. 3,00 jj

" 6 gallB. Molasses, o 37 cts • 2.^2

WUliam Angdl Cr.

ny 200 lbs. L.ird, a (j eta $12,00

" :},50 Iba. Ilacon, a V. cts 42,00

18

50 80

oc»

50

60

32

541 00

^1'76

LEGER.

Jan. 9, 1840.

3 +

+

James Hammond Dr.

To 1 bbl. Flour $10,00

" 3 bu. Corn, a 65 cts 1.95

" f. palls. Wine, a 1,25 7,50

" 3 lbs. Coffee, ff 1(> els .■ 48

" 4 bu. Salt, a 70 cts 2,80

" 1 Jb. Y. H. Tea 1,25

" 14 lbs Sugar, a 12 cts 1,68

" 3 vds. Broadclotli, a $,2,')0 7,50

" 12 yds. Shirting, a 19 cts 2,28

13

Jame^ Murray^ Jr Dr.

ToG lbs. Raisins, n 20 cts. .* $1,20

" 5 galls. Currant Wine, « 75 cts 3,75

35

44

95

LEGER.

This book is used to collect the scattered accountB of the Day- Book, and to arrange all that relates to each individual into one separate statement. The business of collecting these accounts from the Day-Book, and writing* them in the^Leger, is called posting. This should be done once a month, or oftener. Debts due from others, and entered upon the Day-Book, are placed on the side of Dr. ; whatever is on the Day-book as due to another is placed on the side of Or.

When an account is posted,* the page of the Legor, in which this account i.s kept, is xvritten in the left hand column of the Day-Book.

Every Leger should have an alphabetical Index, where the names of the several persons, whose accounts are kept in the Leger, should be written, and the page noted down.

When one Leger is full, and a new one is opened, the accounts in the former should be all balanced, and the balances transferred to the new Leger.

EXPLANATION OF THE LEGEE, AND THE MANNEil OF POSTING.

It will be seen that the name of James Murray, Jr., stands first on the Day-Book; of course, we shall post his account first. We enter his nanie on the first page of the Leger, in a large, fair hand, writing Dr. on the left, and Cr. on the right. At the top of the left hand column, we enter the year, under which we write the month and day when the first charge was made in the Day-Book, and in the next column the page of tjse

f-

FOPvM OF A r.KOER.

177

Day Book where the charge stands. apti':le3 ia the first chrirg-e, instead

Then, as there are several

of specifying each article,

J as in the Day-Book, we merely say, To Sundries, and enter

] the amonnt in the proper columns. This charge being thus

i posted, we write the page of the Leger, viz., 1, in the left hand

■column of the Day-Book, and opposite to it a -f, to show'

i more distinctly that the charge is posted. We then pass a

finger carefully over the names, till we again come to the name

\ of James Murray, Jr., which we find on the second page; but,

las this is credit, we enter it on the credit side, with the date

I and page in their proper columns. We then enter the Loger-

; page and cross, as before, and then proceed again in search of

! the same name, until every charge and credit is transferred

; into the Leger. The next name is to be taken and proceeded

with in the same way as the first; and so continue till all the

accounts are posted.

As it is uncertain how extensive an account may be when once opened, it is better to take a new page for every name, until all the Leger pages are occupied. By this time, it is pro- bable, several accounts will have been settled, we may then enter a second name on the same page, and so continue till all the pages are full.

Whenever any account is settled, the amount or the Iwlance is ascertained, and the settlement entered in the Leger. The settlement may also be entered in tiie Day-Book; and many practice this, although it is not essentially necessary. But it ia es.senlially necessary that one, if not both the books, should show how every account is settled, whether by cash, note, order, goods, or whatever way tiie amount or balance m liqui- dated.

N. B. In making out bills, the Leger is used as a reference to the charges in the Day-Book, which must be exactly copied.

FORxM OF A LEGER.

D

r.

James Murray^ Jr.

Cr.

Jan. 1. " 10. " 13.

To Sundries, do. do.

13 0 4

951

1829.

Jan. 5.

" 15.

2

$•21

4-1

By Corn and Oats, By Cash, to bal.,

«24

D

r.

Robert Hawkins,

Cr.

18ii9. Jan. 1. " 10.

To Iron,

" Sundries,

c I 1829.

17361 14 GO,

$31 UGl

Jan 6. " 12.

By Work,

" Note, aGOdays,

2G

$31 96

[iii

rirf Till iiiiMinini II - — -dirr-

rOIlM OF A LEGER.

Oi

L^l

Dr.

Thomas Yeomans.

Cr. .

Jan. 7. •• 10.

To Corn, ". Flour,

$ \c 14000

2850'

« 168 50

18^9.

Jan. 1.

" 11.

By Cash, " Check for bal

$ c

75175

. 9* 75

S1C850

Br.

Archibald Tracy,

Cr.

1829. Jan. 3. « 6. 9.

To Broadcloth, " Sundries,

do.

a

(•

18^.

87

00

Apr. 2.

'i7

00

24

"IF

$138

48

By Cash.

138

D)

James Warren.

Cr.

■ 1829. Jan. 3. 6.

To NaiJs, Corn,

1800 1440

$32|40

: ifej9. Jan. 3.

By S^indrieB,

32

40

Dr.

Isaac Thomas.

Cr.

1829.

Jan. n.

". 9.

To Molasses, " Sumlrios,

50

1829.

Jan. 9.

" 20.

By Order, " Note, a 90 days,

12180

2470

|37l.^i

Dr.

Willmm An sell.

Cr.

1829.

Jan. 4.

" 1(5.

To SiindrieR, " Cash,

34

19

I $54

c 1| 1829. 50 Uan. 10. 50 1

00

.'>4!00

Dr.

Samml Stone.

Cr.

1829 Jan. *.

To Sundries. do.

1S2^">. 85'00|lJan. 30.

00

By CaeU,

97 00

Dr.

George Carpenter.

Cr.

182'. Jan. 5. 9.

To Sundries, do.

$ i e I)

3,84 29 20

833:04 1

1829. Jan. 15.

I $ i r Ov note, a 30 daye 33 04

■MM«tHk«aaiMMCiaHm>N0M

CariX;nt''J' Grcoigti 2

i T

Thomas, Isaac 2

H

Tracy, Archibald 2

Hawkins, Ilobcrt , , . ]

IlaiTiuioiid, James • . • 3

W

M

Murray, James 1

y

Yeomann, Thomas 3

Mctcalf, JcBSO • 3

CASH-BOOK.

Thif book records the p^ymeiUG ttuJ receipts of casft.

It 18 kept by maki'^ff cash Dt. lo catJi oi; hand and what in rscei vied, and Or. by whatever ia paid cut.

! At the end of every day or v/aok, aa may beat suit the nati;fc of tha bjBinese, the cash on hand is c cuntod, ,~nd entered on th« O. side.

If there is no on-cr, luu wii! maku th<i bum of the Dr. equal to t!iat of the Cr. A bclancc i* t.ion tftruok, iir,<l the c^aii on Land curriMl a^ain xi^n tao Ih. side.

»'»-'«r<u'i "rTir nri

TX^

4 BILLS.

FOEM.OF A CASH BOOK. CASH.

Cr.

To Cash on hand

" J. Thompson

" Hart, paid acc't.

" H Palmer on note

*' S. Snowdou

" f. Mcrvin on acc't.

*' 8. Crane Sixies of Merchandise

Casii on hand,

637150 37194

651-13

m\2S

84,73

1790

100 'JO

311 18

1382

550

86

(55

I 1827. Jan. 2

By rent of store for one quarter, paid Thomas Taylor, " Paid note to R.

Thacher, " Family expenses, " Merchandise bo't

of T. Thamor, Cash on hana,

62

127

27

614

550

1382

Form of a Bill from the preceding Work.

Mr. Jambs Murray

To Edward L. Peckham, Dr.

1629.

'an. 1. To 1 gall Li;;l'f>n VVm-:

" 6 vds. Calico, a 37J- els. . . ' " " 2 yds. Broadcloth, a §4.50.

2 26 9^00

10 To 10 lbs. Sugar, a 11 cts i ,10

" " 6 flails. Molasses, c 37i ct3 "2,22

" " 20 Ibd. Coffee, a 15 cts 3,00

12 '■ .C Ibg. Raisins, a 20 ctB 1,20

" " 5 galls. Currant Wine, a 75 cts 3,75

Cr.

5 By 20 bu. Corn, a 60 cti = . . . = 12,00

" " 4 bu. Oats, a 40 cty ] ,00

15 " Cash to balance 10,04

Errors o.vcpputil,

KinVVARii I. PECKHAM. Juniutry 1/";. h.m

13

17

32

95 !

I

44

44^

2d Form. Mr. Jesse Metcalf

To E. L. Peck HAM,

1829.

ian. 5. To 20 Calt-SkiBs, a $5

•• " •' 50, Dried Hides, a $4 *

"" •' " 500 pr. Men's Shoes, a 95 eta

JDr.

Received payment, by his check, on N. E. Bank. 3S775

^pril 7, IdiJ. EDWARD L. PECKHAM

9 c

100 200 475

j Ao. 1. Mgotiabk JVwi

?i^- --^- *Wai^ 25, 1827.

Oo,„ a^"" ^'""-^ w'-^ ?r'^^.*^ £*^ ^^^^^« Lorraine, or jO.'uor, Seyenty^ight BoUai^ Fifty 6ent8, with Interest, for JTalue received, '

JAMES HONKSTUS.

Ab. 2, Aote payable to Bearer.

Sept. 17, 1827.

Six months from date, I promise to pay A. B.. lie&rer, Forty Dolkra for value received.

or

SIMEON PAYWELL. .

•^<?« 3, ^o^g 5j^ fjffQ Persons.

!5^' -- Oc^ 28, 1827.

, For value received, we, jointly and severally, pro-

mise to pay C. D, or Order, on demand, Five Hundred Dollars, with Interest.

HORACE WALCOTT. JAMES HART.

^0' 4. JSpoU at Bank.

!1^ - Fed. 25, 1819.

Ninety-fivo days from date, I promise to pay Tbo- m^ Andrews or Order, at the Phoenix Bank, One Huu,imi and i^lfty Dollarfl, for value received.

JOHN REYNOJ..W

wj'^^aian I

' ' "i" ■■^^f|V

; iirmiuM » |-p-..,-. ^, -Mi-iar ■iiifirtMnri<>.iiirwii<rr»j--»«wr«»>iitin»i«ir»»wraaMa«iagiM<<aiMa»»M^^

182 MERCANTILE FORMS;

Remarks relating to JSfotes of Hand,

1. A negotiable note is one which is made payable to A. B. or order. — It ie otherwise, when these words are omitted.

2. By endorsing a note is understood, that the person to wlwra it is payable writes his name on the back of it. For additional 1 soojrity, any other person may afterwards endorse it

3. If the note be made payable to A. B., or order, {see No. 1,) th'cn A. B. can sell said note to whom he pleases, provided he endorsee it ; and whoever buys said note may lawfully demand payment of the signer of the note, and if the signer, through inability or otherwise, refuses to pay said note, the purchaser may lawfully demand payment of the endorser.

4. If the note be made payable to A. B., or bearer^ (see No. 2,) then the signer only is responsible to any one who may purchase it. -j

6. Unless a note be written payable on some specific future i time, it should be written on demand; but should the words! on demand be omitted, the note ie suppo.sed to be recoverable i \Tj law. I

6. When a note, payable at a future day, becomes due, it is ■ XfiiE'.dered on hilercst from that time till payed, though no men- j \ion be made of interest.

7. No mention r.oed be made in a note of the rate of interest : that particular is s^jftled by lav^, and may be collected according to the laws of the f/ate where the note is dated. In some states! it is 6 per cent, ; in others, 7.

8. If twc p€'ff<-ns, jointly and severally, {see No. 3,) sign a note, it may iK; collected by law of either.

9. A nAe if. liot valid, unless the words for value received be expressed.

10. "When a note is given, payable in any article of mer- jchandise, or property other than money, deliverable on a speci- fied time, such articles should be rendered in payment at said [

jtirae, othefvvise the holder of the note may demand the value in 'money.

MERCANTILE FOBMS. 18^^

Account unih Interest

Mr. Thomas I. Spencer

To H. Tlsd.ill, Dr,

l816-~Nor. 1. To 3 yards Cloth, a §7,50 per yd. . $22,50

IQIO ?^- ?•" ^i^'-^J^^- Wine, a 4,25 per gall. 25,50

1810— Jan. 1. '' Balance of Interest ..... . . 5,80

^53^

' I

Supra, Cr.

1817— Nov. 1. Bv Cnsh $226ol

1819— Jan. 1. Ihtto in full *.'* 31^301

^^3^1 v.- Jan. 1, 1819. H. TI«DALL.

Receipt for Money on Account. j

Re^p.iYed of Jamea Wardell, Three Dollars on account

SIMEON BB.ANJ>T. w. - /wne21, 1816.

^ -- Dec. 31, 1827.

A General Receipt.

nOR.VCE EITTKB

Rec^^ived of Jonathan Andrewfl, Fonrt<Mia I^nara Jo

fuU of all account*.

Receipt for Money paid on a JSoie,

Received of L(=^onard Teraple, Seventy-two Pounds and Eleven Shillings, on hi^ noto for t]j3 m\m of One Hundred and Sc-Tonty-two PoimAs, and diitcd at Enfield, Oct 27, 1826.

D.THOMAS. ,,

}^ Boston, August 27, 1828. ij

«-.rK^ .» iiauw MiHI,i^lWa—^BWl^HaSWBCfal-JMU . I .. IM 11 Mini ' ■!.. HI .!■ .11 1 1 ■ i ^F— **

HEECANTILE FORMS, 1

An Order for Mone^c

BIesses. E, PottES & Co.

Pay Jamc.^s Tliotiias, c? Ote, ^8t«ii iss^^liere^ iSkd this shall be yoiir receipt for the samOo

SHEELAH SPBNCEE. BepL % 1828.

o^n Order for GcoiSo

Mr. -Alexon N. Olney,

Pay the Bearer Scventy-one Dollars^ m Goods from ; ■jyour store^ and charge

Your obedient Rervant,

Oxford, Dec. 31, 1827. R. RAYNALL.

«» A receipt gketi in full of &U accounts cuts off aoeounta only ; but a receipt given in full of all demands 0iste off not Guly all accounts, but all demands whatever.

An order, when- paid, should be receipted on the back, by the person to whom it is made payable, or by some one duly siithorised to sign for him ; but when it is made payable to be&refj or to A. B. or hearer^ it may b^ received by any one who preeeate it for pajmeci

7BS IHJD.

>''TqTr.,'.«V'..:>:T'gr^.*y.'»X.Strf.j:*t^-iJ3MJ^

^m4

r»

^ ti