10. When $8 will buy 40 rakes, how many can be bought for $11?

11. If 12 men can do a piece of work in 6 days, how many days will it take 9 men to do the same?

SOLUTION. - If 12 men can do the work in 6 days, it will take 1 man 12 times 6 days, or 72 days, to do it, and 9 men 1 ninth of 72 days, or 8 days.

12. If 7 men can dig a ditch in 8 days, how many days will be required for 14 men to dig it?

13. If 6 horses eat a bag of oats in 10 days, how many horses will eat the same quantity in 15 days?

14. How long will it take 5 men to reap a field, if it take 15 men 3 days to reap it?

15. How long will it take 9 men to build a wall, if it take 6 men 6 days to build it?

16. If 7 books cost $21, what will 11 books cost?

17. When 8 barrels of flour will pay for 12 yards of broadcloth, at $6 a yard, how much is the flour per barrel?

18. If 5 men can hoe a field of corn in 9 days, in what time can 15 men hoe it?

19. When 10 oranges will pay for 20 apples, at 2 cents each, what is the price of each orange?

20. When 10 bushels of wheat will pay for 5 cords of wood, at 4 dollars per cord, how much is the wheat per bushel?

21. If 9 pencils cost 54 cents, what will 12 pencils cost, at the same rate?

REVIEW.-What is an Integer? (84.) A Prime Number? (85.) A Composite Number? (86.) A Factor? (87.)

WRITTEN EXERCISES.

1. If 9 acres of land produce 315 bushels of wheat, many bushels will 7 acres produce?

how

2. If 10 yards of cloth cost $15, what will 8 yards cost? Ans. $12. 3. If 5 pounds of cheese cost 45 cents, what will 18 pounds cost? Ans. $1.62. 4. If 26 yards of cloth cost $78, what will 17 yards cost?

5. If 72 bushels of apples cost $36, what will 84 bushels cost? Ans. $42.

6. If 8 bushels of wheat cost 12 dollars, what will 20 bushels cost? Ans. $30.

7. If a man can earn in 5 months $176.25, how much can he earn in 12 months, or 1 year?

Ans. $423.

8. When 3 books cost $1.14, what will 3 dozen cost?

Ans. $13.68.

9. If 3 dozen books cost $13.68, what will 3 books cost?

10. When $12.75 will purchase 17 yards of cloth, how many yards will $2.25 purchase?

11. How far can a man travel in 7 days, at the rate of 244 miles in 4 days? Ans. 427 miles.

Factoring? (88.)

REVIEW. What is a Prime Factor? (87.) What is Cancellation? (92.) Upon what principle does it depend?

12. If 14 horses eat a load of hay in 14 days, how many horses would be required to eat the hay in 7 weeks? Ans. 4 horses.

13. Bought 72 yards of broadcloth for 160 bushels of wheat, at $1.80 per bushel; how much was the broadcloth a yard? Ans. $4. 14. If I give $1887 for 148 barrels of flour, how many barrels can I buy for $63.75? Ans. 5 barrels. 15. If 7 men can build a house in 84 days, how many men could build it in 21 days? Ans. 28 men.

16. When $30 is paid for 25 pounds of tea, how much must be paid for 40 pounds?

17. A drover exchanged 25 horses for 550 sheep, at $5.50 each; how much did he get for each of his horses? Ans. $121.

18. If 5 tons of hay cost $106.25, what will 13 tons cost? Ans. $276.25. 19. In what time will 48 men do a piece of work that 12 men can do in 24 days? Ans. 6 days. 20. When 15 pounds of sugar can be bought for $1.80, what will 18 pounds cost?

21. How far can a man travel in 18 days, at the rate of 378 miles in 6 days? Ans. 1134 miles.

22. If a man travel 1134 miles in 18 days, how many miles will he travel in 6 days?

23. How many pounds of coffee can be bought for $21, if 30 pounds cost $6? Ans. 105 pounds.

24. When 18 pounds of sugar can be bought for $2.16, what will 15 pounds cost? Ans. $1.80.

REVIEW. - What is Analysis in Arithmetic? (94.) What is Arithmetic? (15.) Addition? (39.) Subtraction? (44.) Multiplication? (49.) Division? (59.)

COMMON FRACTIONS.

If a unit, as one apple, be divided into two equal parts, each of these parts is one half.

If a unit be divided into three equal parts, one of these

parts is one third; two of them, two thirds, etc.

If a unit be divided into four equal parts, one of these parts is one fourth; two of them, two fourths; three of them, three fourths; etc.

In like manner, if a unit be divided into five equal parts, the parts are fifths; if into six equal parts, sixths; and

so on.

* 96.

A Fraction is one or more equal parts of a unit. Thus, one half, two thirds, are fractions.

97. The Denominator of a fraction is the number which shows into how many equal parts the unit is divided. Thus,

Three is the denominator of two thirds.

If a unit be divided into two equal parts, what is one of the equal parts called? Into three equal parts? Into four? Into five? What is a Fraction? The Denominator?

98. The Numerator of a fraction is the number which shows how many of the equal parts of the unit are taken.

Thus,

Two is the numerator of two thirds.

× 99.

A Common Fraction is a fraction expressed by writing the numerator above, and the denominator below,

100. The Terms of a fraction are the numerator and denominator.

The Unit of a fraction is the unit, or single thing, divided into equal parts.

A Fractional Unit is one of the equal parts into which the unit of a fraction is divided.

101.

An Integer may be expressed in a fractional form, by writing 1 under it, for a denominator. Thus,

What is the Numerator of a fraction? What is a Common Fraction? What are the Terms of a fraction? What is the Unit of a fraction? A Fractional Unit? How may an Integer be expressed in a fractional form?