denominator of the fraction in the subtrahend, and we have a new fraction 4g, which we write at the right hand of the other 9, thus, 91g. We then multiply the numerator and denominator of the subtrahend by 7, the denominator of the minuend, and we have another new fraction,

which we place at the right hand of the other 3, thus, 3. It will now be perceived, that we have changed the fractions 92 and 33 to other fractions. of the same value, having a common denominator. We now subtract as in question 26th by adding 1 (85) to 18, which makes, and from this we subtract; thus, 15-21=1, 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 5.

43. From a hhd. of wine there leaked out 123 galls, how much remained? Ans. 50ğ. 44. From $10, $23 was given to Benjamin, $3 to Lydia, $1 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 ?

48. Take from §, † from †,† from,

from .

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.

11 × 22=21376 Ans.

3. If a man receive of a dollar for one day's labor, what will he receive for 21 days' labor? Ans. $77. 4. What cost 56lbs. of chalk at of a cent per lb. ?

5 What cost 396lbs. of copperas at

Ans. $0.42. of a cent per lb. ? Ans. $3.24.

6. What cost 79 bushels of salt at of a dollar per bush

II. To multiply a mixed number by a whole number, or a whole number by a mixed number.

13. Multiply 43 by 7.

Ans. 32

OPERATION.

42

7

In performing this question, we say 7 times 3 fifths are 21 fifths, and 21 fifths are equal to 43. We write down the 32 Ans. and carry the 4 to the product of 7 times 432. Hence the following

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.

19. What cost 7lbs. of beef at 5 cents per pound?

Ans. 37.

20. What cost 23bbs. flour at $6 per barrel ?

Ans. $141.

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

22. What cost 9 barrels of vinegar at $63

23. What cost 12 cords of wood at $6.37

Ans. $417. per barrel ? Ans. $578. per cord? Ans. $76.50.

24. What cost 11cwt. of sugar at $93 per cwt. ?

Ans. $103.

25. What cost 4g bushels of rye at $1.75 per bushel ?

Ans. $7.65§.

26. What cost 7 tons of hay at $117 per ton?

27. What cost 9 doz. of adzes at $10g

28. What cost 5 tons of lumber at $3

Ans. $831.

per ton ?

Ans. $15§.

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

Ans. $114.37.

30. What cost 40 tons of coal at $ 8.37 per ton?

III. To multiply simple fractions.

Ans. $335.00.

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

39. What cost bushel ?

Ans. 1.

Ans.

Ans.

of a bushel of corn at § of a dollar per

Ans. of a dollar.

in an hour, how far

how much salt might be bought for corn?

Ans.

Ans. of a mile.

of a bushel of salt, of a bushel of 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 42 by 63.

OPERATION.

42=23, 63=20, 23 × 20=460303 Ans.

43. Multiply 71 by 89.

44. Multiply 47 by 91.

45. Multiply 114 by 8.

46. Multiply 122 by 113.

47. What cost 74 cords of wood at $5

48. What cost 7 yds. of cloth at $3

49. What cost 63 gallons molasses at lon?

Ans. 60%.

Ans. 45.

Ans. 991.

Ans. 147.

Ans. $4131.

per yard?

Áns. $2518.

23

cents per galAns. $15218.

per cord?

50. If a man travels 33 miles in one hour, he travel in 93 hours?

how far will Ans. 344. per acre? Ans. $9167113.

51. What cost 36111 acres of land at $25

52. If of of a dollar buy one bushel of corn, what will of of a bushel cost? Ans. of a dollar. 53. How many square rods of land in a garden, which is 97 rods long, and 493 rods wide?

Ans. 4810 rods. 54. If 3 of 4 of of an acre of land cost one dollar, how much may be bought with of $18?

Ans. 197 acres.

NOTE. The following questions are to exercise the foregoing rules. 55. What are the contents of a field 767 rods in length and 18 rods in breadth ? Ans. 8A. 3R. 30 p. 56. What are the contents of 10 boxes which are 72 feet long, 12 wide, and 14 feet in height?

Ans. 16917 cubic feet. 57. From of an acre of land there were sold 20 poles and 200 square feet. What quantity remained?

Áns. 2R. 1p. 22fft.

58. What cost 13 of an acre at $1.75 per square rod ? Ans. $236.92.

59. What cost of a ton at $15 per cwt.?

Ans. $49.7319.

Ans. 9184.

60. What is the continued product of the following numbers 148, 113, 5, and 101 ? 61. From of a cwt. of sugar there was sold of it; what is the value of the remainder at $0.123 per lb.?

*

Ans. $3.57.