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7

20. From of 1 take of 4.

Ans. 13 21. From of take 1 of 14.

Ans. To 22. From 7į take 37.

Ans. 316 23. From 89 take 56.

Ans. 2. 24. From 91 take 37.

Ans. 58. 25. From 10% take 1015.

Ans. III. To subtract a proper or mixed fraction from a whole number. 26. From 16 take 14.

Ans. 144. To subtract the in this example, 1 From 16 must be borrowed from the 6 in the Take

11

minuend, and reduced to fourths, (4), and the must be taken from them; 1

from 4 leaves. To pay for the 1, which was borrowed, 1 must be added to the 1 in the subtrahend, 1+1=2; and 2 taken from 16 leaves 14, and the }, placed at the right hand of it, gives the answer 141. The same result will be obtained, if we adopt the following

OPERATION.

141

RULE.

154

Subtract the numerator from the denominator of the fraction, and under the remainder write the denominator, and carry one to the subtrahend to be subtracted from the minuend.

OPERATION. 27. 28. 29. 30. 31. From - 16 19 13 14

17 Take 11 33 94 84 611 143

311 5$

1012 If it be required to subtract one mixed number from another mixed number, the following method may be adopted. 32. From 94 take 3.

5。

In this question, we Minuend 94 = 949 multiply the 2 and the 7, Subtrahend 3=3}}

the numerator and de

nominator of the fraction 534 Ans.

in the minuend by 5, the

Ans. 544

OPERATION

10 35

denominator of the fraction in the subtrahend, and we have a new fraction }}, which we write at the right hand of the other 9, thus, 91%. We then multiply the numerator and denominator of the subtrahend by 7, the denominator of the minuend, and we have another new fraction, ft, which we place at the right hand of the other 3, thus, 31. It will now be perceived, that we have changed the fractions 94 and 33 to other fractions

We of the same value, having a common denominator. now subtract as in question 26th by adding 1 (35) to }, which makes [, and from this we subtract t; thus,

- f}=, we then carry the 1 we borrowed to the 3, 1+3 = 4, which we take from 9, and find 5 remaining. The answer therefore is 534.

33. 34. 35. 36. From 124 163

19 971

8713 Take

154 183

194 211 1034

3. 7811 6 762 38. 39. 40. 41. 42. From 193 154 94 7111

614 Take 73 87 318 1312 158

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43. From a hhd. of wine there leaked out 123 gallons, how much remained ?

Ans. 50. 44. From $10, $2} was given to Benjamin, $31 to

Lydia, $ 14 to Emily, and the remainder to Betsey ; what did she receive ?

Ans. $31 Note. If it be required to find the difference between two fractions, whose numerators are a unit, the most ready way will be to write the difference of the denominators over their product. 45. What is the difference between $ and ? ?

OPERATION. 7-3= 4

Ans.

7 X 3 = 21 46. Take } from }, 7 from , f from 1, 4 from $. 47. Take from £, from 4, + from $, from : 48. Take from }, + from , from +, I from .

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Section 23.

MULTIPLICATION OF VULGAR FRACTIONS.

I. To multiply a fraction by a whole number, or a whole number by a fraction.

Multiply the numerator of the fraction by the whole number, and under the product write the denominator of the fraction. 1. Multiply s by 15.

This question may { x 4 = 185 = 133 Ans. alyzed as those in com

pound fractions. 2. Multiply 11 by 83.

OPERATION,

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OPERATION.

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11 X 2 = = 761 Ans. 3. If a man receive f of a dollar for one day's labor,

what will he receive for 21 days' labor ? Ans. $ 77. 4. What cost 50lbs. of chalk at of a cent per lb. ?

Ans. $ 0.42. 5. What cost 396lbs. of copperas at it of a cent per lb. ?

Ans. $ 3.24. 6. What cost 79 bushels of salt at % of a dollar per

bushel ?

Ans. $ 693. 7. Multiply 376 by 17.

Ans. 243

1 8. Multiply 1 by 189.

Ans. 16614. 9. Multiply 471 by itt:

Ans. 8;g 10. Multiply 871 by at.

Ans. 2347. 11. Multiply H7 by 365.

Ans. 353 44 12. Multiply 867 by 16

Ans. 6136 II. To multiply a mixed number by a whole number, or a whole number by a mixed number. 13. Multiply 4 by 7.

Ans. 321

OPERATION.

In performing this question, we say 7 43 times 3 fifths are 21 fifths, and 21 fifths

7 are equal to 4. We write down the $ 32 Ans. and carry the 4 to the product of 7 times

4= 32. Hence the following

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RULE.

Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction.; and, as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, any thing remains, let it be a numerator, and the divisor a denominator to a fraction to be affixed to the product. 14. Multiply 93 by 5.

Ans. 467. 15. Multiply 12 by 7.

Ans. 881 16. Multiply 817 by 9.

Ans. 801 17. Multiply 7 by 10.

Ans. 713. 18. Multiply 119 by 8.

Ans. 946. 19. What cost 78 lbs. of beef at 5 cents per pound ?

Ans. 3781. 20. What cost 237sbbs. flour at $ 6 per barrel ?

Ans. $ 1411. 21. What cost 8%yds. cloth at $5 per yard ?

Ans. $ 417 22. What cost 9 barrels of vinegar at $6% per barrel ?

Ans. $ 573. 23. What cost 12 cords of wood at $6.37} per cord ?

Ans. $ 76.50. 24. What cost 11cwt. of sugar at $ 9% per cwt. ?

Ans. $ 103. 25. What cost 43 bushels of rye at $ 1.75 per bushel ?

Ans. $7.65%. 26. What cost 7 tons of hay at $ 113 per ton ?

Ans. $83. 27. What cost 9 doz. of adzes at $ 10% per doz. ?

Ans. $953. 28. What cost 5 tons of lumber at $3; per ton ?

Ans. $ 158. 29. What cost 15cwt. of rice at $ 7.62 per cwt. ?

Ans. $ 114.375.

30. What cost 40 tons of coal at $ 8.371 per ton ?

Ans. $ 335.00. III. To multiply simple fractions. 31. Multiply } by .

Ans. Tz

This question may be anal{ x == 12 Ans. yzed in the same manner as in

compound fractions. Hence the following

OPERATION.

RULE.

Ans. It

CANCELLED.

Multiply the numerators together for a new numerator, and the denominators together for a new denominator ; then reduce the fraction to its lowest terms. 32. Multiply } by er:

OPERATION,
7 8 56 7

7
-X
Ans.

Ans.
8 11 88
11

11 11 33. Multiply A by 17.

Ans. 34. Multiply 1.3 by zi.

Ans. . 35. Multiply 1: by 18.

Ans. } 36. Multiply 15 by 17. 37. Multiply j by lt. 38. Multiply zis by .

Ans. 39. What costs of a bushel of corn at g of a dollar per bushel ?

Ans. į of a dollar. 40. If a man travels i of a mile in an hour, how far

would he travel in }} of an hour ? Ans. I of a mile. 41. If a bushel of corn will buy jy of a bushel of salt, how much salt might be bought for of a bushel of corn ?

Ans. 41 of a bushel. Note. If there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions. 42. Multiply 4 by 6%.

Ans. 1 Ans. IST

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