CASE II.

101. To divide an integer by a fraction.

1. At of a dollar a yard, how many yards of ribbon can be bought for 2 dollars?

ANALYSIS. As many yards as of a dollar, the price of 1 yard, is contained times in 2 dollars. Since in 1 dollar there are 3 thirds of a dollar, in two dollars, there are 2 times 3 thirds, or 6 thirds; and 1 third is contained in 6 thirds, 6 times. Therefore 6 yards of ribbon can be bought for 2 dollars.

2. When potatoes are of a dollar a bushel, how many bushels can be bought for 2 dollars? for 4 dollars? for 6 dollars?

3. If a man spend of a dollar a day for cigars, how long will it take him to spend 3 dollars? 5 dollars? 6 dollars" 4. At of a dollar a bushel, how many bushels of corn can be bought for 16 dollars?

and multiply the quotient by the denominator, which produces the same result as in the first operation. Hence

Dividing by a fraction consists in multiplying by the denominator, and dividing the product by the numerator of the divisor.

19. When potatoes are of a dollar a bushel, how many bushels can be bought for 10 dollars? Ans. 129 bush.

20. Divide 9 bushels of corn among some persons, giving them of a bushel each; how many persons will receive a share? Ans. 48.

Ans. 9

cords.

21. At 2 dollars a cord, how many cords of wood can be bought for 27 dollars? 22. If a horse eat of a bushel of oats in a day, in

how many days will he eat 20 bushels?

23. If a man walk 2 miles an hour,

will he require to walk 48 miles?

Ans. 36 days.

how many hours Ans. 1616 hours.

24. At of a dollar a pound, how many pounds of rice

can be bought for 3 dollars?

Ans. 48 pounds.

102. To divide a fraction by a fraction.

1. At of a dollar a pound, how many pounds of tea can be bought for of a dollar?

ANALYSIS. As many pounds as of a dollar, the price of 1 pound, is contained times in of a dollar; 2 fifths are contained in 4 fifths, 2 times. Therefore 2 pounds can be bought for of a dollar.

Hence we see, that when fractions have a common denominator, division may be performed by dividing the numerator of the dividend by the numerator of the divisor.

2. How many pine-apples at of a dollar each, can be bought for of a dollar? for? for 1?

3. If a horse eat

of a bushel of oats in 1 day, in how many days will he eat of a bushel?? 10? 14?

4. At of a dollar a bushel, how many bushels of apples can be bought for of a dollar? for? for §?

5. At of a dollar a pound, how many pounds of tea can be bought for of a dollar?

FIRST OPERATION.

ANALYSIS. As many pounds

SECOND OPERATION

of a dollar, the price of 1 pound, is contained times

in

of a dollar. equal 1+1=1X=V=-17 Ans. equal, and 8 twenti

8

eths are contained in 15 twen

tieths 17 times. Or, as in the second operation, we have multiplied the dividend, by the denominator 5, of the divisor, and divided the result by the numerator 2, of the divisor. Hence, by inverting the terms of the divisor the two fractions will stand in such relation to each other, that we can multiply together the two upper numbers for the numerator of the quotient, and the two lower numbers for the denominator, as shown in the second operation. Hence

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

II. Invert the terms of the divisor, and proceed as in mul tiplication.

16. Divide of by 2 of 7.

17. At of a dollar a pound, how many pounds of su

gar can be bought for 4 of a dollar ?

18. At

bought for

Ans. 5 pounds.

of a dollar a pint, how much wine can be

of a dollar?

19. At of of a dollar a yard, how 18

bon can be bought for of a dollar?

Ans. of a pint.

20. At of a dollar a yard, how many

be bought for of a dollar?

many yards of rib

Ans. 2ğ yards.

yards of silk can Ans. 24 yards.

21. A man owning of a copper mine, divided his share equally among his sons, giving them each; how many sons had he?

Ans. 2.

22. If § of a bushel of pears cost of a dollar, how much will 1 bushel cost? Ans. of a dollar. 23. How much corn at of a dollar a bushel, can be bought for of a dollar. Ans. of a bushel.

PROMISCUOUS EXAMPLES.

1. In 25 pounds how many 16ths of a pound?

2. Reduce 421 to a mixed number.

36

3. Reduce 15 to its lowest terms.

4. In 7859 of a day how many days?

Ans. 113.

5. Change 42 pounds to sevenths of a pound.

6. Reduce 21 to an improper fraction.

7. Reduce 126 to thirds.

Ans. 4.

Ans. 109.

Ans. 380.

Ans. t.

9. Reduce and to a common denominator.

10. Reduce 36 to a fraction whose denominator is 12.

11. What is the sum of 2, § and 1⁄2?

12. Add together, and 31.

13. What is the difference between ? and ??

Ans. 17.

Ans. 43.

14. Reduce, and to a common denominator.

15. Sold 9 cords of wood to one man, and 12 to another; how much did I sell to both?

16. Paid 87% dollars for a horse, and 62 dollars for a wagon; how much more was paid for the horse than the wagon? Ans. 25 dollars.

17. A farmer having 23415 acres of land, sells at one time 42 acres, at another time 613, and at another 701 acres; how many acres has he left? Ans. 605 acres.

18. A speculator bought 120 bushels of wheat, for 1363 dollars, and sold it for 197§ dollars; how much did he gain?

19. Bought 12 pounds of coffee at of a dollar a pound, and 9 pounds of tea at of a dollar a pound; what was the cost of the whole ? Ans. 87 dollars. 20. Bought 10 bushels of wheat, at 11 dollars a bushel, and 14 bushels of corn, at of a dollar a bushel; which cost the more, and how much?

Ans. the corn, 34 dollars.