WRITTEN

EXERCISES.

232. 1. Multiply by J.

OPERATION.

ANALYSIS.-To multiply by is to find of, which is 7 times of, and is

>=1=16 found by multiplying the denominator (200, 1.) Hence of is, and of is 7 times, or fa , the required product.

2

In like manner multiply

=

8. Find the product of,, 5, and 2.

16

RULE.-I. Reduce all integers and mixed numbers to improper fractions.

II. Multiply together the numerators, for the numeraor; and the denominators, for the denominator of the product. Or,

I. Multiply by the numerator of the fractional multiplier and divide by the denominator.

II. When the multiplier is a mixed number, multiply by the fractional and integral parts separately and add their products.

Cancel all factors common to numerators and denominators before multiplying, thus shortening the operation, and obtaining the answer in its lowest terms.

Find the cost

a yard.

17. Of 15 cords of bark, at $4§ a cord.
18. Of 24 pounds of tea, at $3 á pound.
19. Of 80 yards of cloth, at $4
20. Of 21 bushels of corn, at $ a bushel.
21. Of of 51 tons of hay, at $15 a ton.
22. Of 18 barrels of crude oil, at $7 a barrel.
23. Of of 18 yards of silk, at of $5 a yard.
24. Of 126 pounds of beef, at 94 cents a pound.
25. Of 36 tons of railroad iron, at $624 a ton.
26. Of 35 horses, at $2053 each.

27. Of 4 of 156 acres of land, at 4 of 854 an acre. 28. Of 28 bushels of sweet potatoes, at $1 a bushel. 29. Of of a yard of satin, at $18 a yard.

30. Of of an acre of land, at $125 an acre.

31. Of

tons of middlings, at $264 a ton?

32. Paid $365 for a horse, and sold him for 4 of what he cost. What was the loss?

33. When peaches are worth $3 a basket, what are 126 baskets worth?

34. Find the value of (129768) × of 121 −2} + 21×61.

DIVISION.

233. When the divisor is an integral number.

ORAL

EXERCISES.

1. If of an acre of land is divided into 3 equal lots, what part of an acre does each lot contain?

2. of is what part of 1?

of? of? of?

3. Dividing by 3, 4, and 5 is the same as multiplying

by what fractions?

4. How much is

×?÷3?

×? ÷4?

5. If 4 slates cost $8, what will 1 slate cost?

6. If 5 boxes of figs cost $3, what will 1 box cost?

7. Divide of a barrel of flour equally among 3 families.

What part of a barrel will each family receive?

8. What is of? divided by 8?

9. What is the quotient of

divided by 2? by 3?

10. Show that dividing the numerator of by 3 divides the fraction by 3.

11. Show that multiplying the denominator of by 3 divides the fraction by 3.

How many ways to divide a fraction by an integer?

12. Divide by 4; f by 5; ♬ by 7; § by 9.

13. If 6 pounds of sugar cost $3, what will 1 pound cost? 14. Divide § by 3⁄4 of 20; 14 by ₺ of 15; 7 by 1 of 40. 15. At $4 a yard, how many yards of silk can be bought for $214?

ANALYSIS.-As many yards as $4 is contained times in $215, or 1 of 215 = 4 of 152, or 38 – 5% times.

Or, 4 is contained in 214, 5 times and 14 or 12 remainder; of is, which added to 5 makes 53. Hence, etc.

16. If a man walks 18 miles in 4 hours, how far does he walk in 1 hour? In 3 hours? In 5 hours?

17. How many times will 16 gallons of cider fill a vessel that holds 3 gallons?

18. What cost 1 pound of sugar, if 6 pounds cost $14? 19. If a boy earn $123 in 10 days, how much does he earn in 1 day? In 4 days? 1n 5 days? In 7 days? 20. Divide 8 by 5; 10% by 7; 181 by 12; 42 by 8. 21. Divide & of 21, by % of 10; 3 of 29, by † of 63.

234. PRINCIPLE.-Dividing the numerator or multiplying the denominator divides the fraction. (200, 2.)

Always divide the numerator when it is a multiple of the divisor; otherwise multiply the denominator.

fraction by 6, which gives the same result.

In the first operation, the number of parts or of fractional units is diminished, while their size or value remains the same; in the second operation, the number of the parts remains unchanged, while their size is diminished.

equal, which divided by 8 gives 8 or, which added to the partial quotient 6 gives 63, the required quotient.

16. The product of two numbers is 72, and one of them is 14; what is the other?

17. If of an acre produce 25 bushels of wheat, what part of an acre will produce 1 bushel?

18. If 12 ploughs cost $124, what is the cost of each? 19. What number multiplied by 48 produces 694% ? 20. If 54 horses cost $4622, what is the cost of each ? 21. The product of two numbers is 12487, and one of the numbers is 32; what is the other?

22. If f1 men consume of 100 pounds of meat in 1 week, how much does 1 man consume in the same time? 23. What is the weight of 4 tubs of lard, if 12 tubs weigh 5281 pounds?