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34. Multiply 27 by 3}. 35. Multiply 63 by 10%.

Ans. 90. 36. Multiply 75 by 12%.

CASE II.

37. A man owning of a ship, sold of what he owned. What part of the ship did he sell?

Analysis - $ of is is; for, multiplying the denominator

by any number, divides the value of the fraction. (Art. 113.) Now 2 thirds of is twice as much; that is, 1x2=, which, reduced to its lowest terms, is Ans.

Again, the example may be performed thus :

Since he ownedž, and sold f of what he owned, it is evident he sold for of the ship. Now sof} is a compound fraction, whose value is sound by multiplying the numerators together for a new numerator, and the denominators for a new denominator. (Art. 123.)

Operation. x}=15, or. Ans. Hence, 135. To multiply a fraction by a fraction.

Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Obs. It will be seen that the process of multiplying one fraction by another, is precisely the same as that of reducing compound fractions to simple ones. 38. Multiply by

Ans. *=. 39. Multiply by . 40. Multiply z by f. 41. Multiply is by . 42. Multiply 13 by

136. In multiplication of fractions, the operation may often be shortened by canceling the factors common boih to the numerators and denominators, as in reducing compound fractions to simple ones. (Art. 123.)

Quest.–135. How is a fraction multiplied by a fraction?. Obs. To what is the process of multiplying one fraction by another similar ? 136. How may the operation in multiplication of fractions be shortened?

Obs. 1. This, in effect, is dividing the product of the numerators and that of the denominators by the same number, and therefore does not alter the value of the answer. (Art. 116.)

2. Care must be taken that the factors canceled in the numerators are exactly equal to those canceled in the denominators.

43. Multiply by Operation.

The factor 3 is common to the numerator 2 1 of the first fraction and the denominator of the 6 4 2 second. Also the factor 4 is common to the 18Xy9 denominator of the first, and the numerator of 3 3

the second fraction. The product of the remaining factors in the numerator is 2; that of the remaining factors in the denominator is 9. Ans. g.

44. Multiply & by f. Ans.
45. Multiply by . and $. Ans. is.
46. Multiply ka by and
47. Multiply 3. by
48. Multiply 4 by 3% and .
49. Multiply 3i by , and
50. Multiply 7by 3}.

Solution. 71, reduced to an improper fraction, becomes , and 3} becomes . Now x1=150, or 25. Ans.

137. Hence, when the multiplier and multiplicand are both mixed numbers, they should be reduced to improper fractions, and then be multiplied according to the rule above.

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EXAMPLES FOR PRACTICE.

1. What will 12 apples cost, at } of a cent apiece ?

2. If a bushel of wheat weighs of a hundred weight, how much will 10 bushels weigh?

3. If a man earns & of a dollar per day, how much can he earn in 12 days?

Quest.Obs. Does this alter the answer? Why not? What is necessary to be observed with regard to canceling factors ? 137. When the multiplier and multiplicand are mixed numbers, how proceed?

4. If a family consume of a barrel of flour in a week, how much will they consume in 15 weeks?

5. If I burn s of a cord of wood in a month, how much shall I burn in 12 months ?

6. If a man can reap iż of an acre of grain in a day, how many acres can he reap

in 9 days? 7. If a pound of powder cost 6 shillings, how much will of a pound cost?

8. If a gallon of oil cost 7 shillings, how much will of a gallon cost ?

9. When beef is 10 dollars a barrel, how much will of a barrel cost?

10. What will of a firkin of butter cost, at 15 dollars a firkin ?

11. At { of a dollar a cord, how much will the sawing of 20 cords of wood amount to ?

12. What will 16 pounds of cheese cost, at 83 cents per pound?

13. What cost 9 dozen of eggs, at 123 cents per dozen ? 14. What cost 15% yards of cambric, at 15 pence per 15. What cost 8; cords of wood, at 2 dollars per

cord ? 16. At 12 cents a pound, what cost 2 pounds of pep

yard ?

per ?

17. At 5 shillings a pound, what cost 12% pounds of tea?

18. What will 6 pounds of starch come to, at 12} cents per pound?

19. What will 18 ounces of nutmegs come to, at 64 cents an ounce ?

20. At 124 cents a yard, what will 17 yards of cotton come to ?

21. At 34 dollars a yard, what cost 16 yards of broadcloth?

22. What cost 158 yards of ribbon, at 10 cents per yard ?

23. What cost 22 pocket handkerchiefs, at of a dollar a piece ?

24. At s a dollar a yard, what will & of a yard of lace cost ?

25. Ats of a dollar a yard, what will y of a yard of muslin come to?

26. At of a dollar a bushel, what cost 15 of a bushel of wheat ?

27. What will y of a pound of tea cost, at of a dollar a pound?

28. What cost 66 bushels of apples, at 184 cents a bushel ?

29. At 62} cents a yard, what cost 12} yards of balzorine ?

30. What cost 18% yards of tape, at 64 cents per yard ?

31. What cost 13 bushels of oats, at 184 cents per bushel ?

32. What cost 31} yards of sheeting, at of a dollar per yard?

33. At iz of a dollar a quart, what cost 83 quarts of cherries?

34. At 38 shillings a yard, what cost 7 yards of gingham ?

35. What cost 143 bushels of potatoes, at 18% cents a bushel ?

36. At 7 shillings a yard, what cost 8} yards of silk ?

37. At s of a dollar a bushel, what cost 474 bushels of peaches ?

38. What cost 634 pounds of sugar, at 93 cents per pound?

39. What cost 25 yards of velvet, at 3. dollars a yard ? 40. What cost 98 yards of calico, at is shillings a yard ? 41. What cost 254 pounds of figs, at 15} cents a pound ?

42. What cost 35% cords of wood, at 18} shillings per cord ?

43. What cost 1751 bushels of corn, at g of a dollar a bushel ?

44. What cost 84 tons of hay, at 153 dollars a ton?

45. If a man travel 42 } miles in one day, how far will he travel in 17} days ?

DIVISION OF FRACTIONS.

MENTAL EXERCISES.

Ex. 1. A man divided of a pound of honey equally among his 3 children: what part of a pound did each receive ?

Suggestion. l is 1 third of 3; therefore 1 child must have received 1 third of 6 sevenths. I third of 6 sevenths is 2 sevenths. Ans. Each child received of a pound.

2. If 4 pounds of loaf sugar cost g of a dollar, how much will 1 pound cost ? 3. A father

gave his two sons 19 of a dollar: how many twelfths did each receive ?

4. A little girl bought 5 lead pencils for 1: of a shilling: how much did she give apiece for them?

5. A father gave 3. parts of a vessel to his 6 sons : what part of the vessel did each receive ?

6. At į dollar a yard, how many yards of French muslin can you buy for 4 dollars ?

Suggestion. 4 dollars will buy as many yards as 1 half is contained times in 4, or as there are halves in 4 dollars. Now since there are 2 halves in a whole dollar, in 4 dollars there will be 4 times 2; and 4 times 2 halves are 8 halves. Ans. 4 dollars will buy 8 yards.

7. At } cent apiece, how many apples can I buy for 6 cents ?

8. At $ dollar a pound, how many pounds of almonds can you buy for 12 dollars ?

9. How many quills, at of a penny apiece, can you buy for of a penny ?

Suggestion. of a penny will buy as many as į is contained times in S, and in S, 3 times. Ans. 3 quills.

10. How many yards of cloth can a farmer buy for of a cord of wood, if he gives of a cord for a yard of cloth ?

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