15. At of a dollar a gallon, how many gallons of kerosene can be bought for $51?

16. How many bottles, of 11 pints each, can be filled with 27 gallons of wine? Ans. 148 bottles.

REVIEW EXERCISES.

1. Reduce 1 to its lowest terms.

2. Reduce

to its lowest terms.

3. Change $31 to sixths of a dollar.

4. Reduce 19 to an improper fraction.

5. Change 22 to a fractional form.

Ans. .

Ans. $186.

Ans. 136.

Ans. 22.

6. Change 22 to a fraction whose denominator is 3.

7. Reduce and to fractions having a common de

(139.) A Common Fraction? (142.) The Terms of a Fraction?

Aus. 1.

What is a Fraction?

23. A merchant owning

of a ship, bought more;

how much did he then own of it?

Ans.

24. A farmer divided some hay into 20 equal parts, and gave 16 parts to his cows, and the rest to his sheep; what fraction of the whole did the sheep get? Ans..

25. What number is that to which if you add 35, the sum will be 161⁄2? Ans. 12. 26. If of a mill is worth $3740, what is the value of the whole? 27. When 13 tons of coal are sold for $71, what is the price per ton?

28. Paid $10 for tea, at the rate of pound; how many pounds did I buy?

Ans. 99731.

Ans. 51.

of a dollar a

29. If the divisor is, and the quotient 21, what is

the dividend?

30. How many bushels of corn, at

Ans. . of a dollar a

bushel, must be given for 13 of a ton of coal, at $4 a ton?

Ans. 8.

31. When broadcloth is 43 dollars a yard, how many yards can be bought for 3 cords of wood, at 7 dollars a cord? Ans. 4 yards.

QUESTIONS FOR ANALYSIS.

1. If 1 barrel of flour cost $9, how much will of a barrel cost?

SOLUTION.

If 1 barrel cost $9, of a barrel will cost of $9, or $2.25; and will cost 3 times $2.25, or $6.75. Therefore, if 1 barrel of flour cost $9, of a barrel will cost $6.75.

2. If 1 ton of coal be worth $5.25, what is of a ton worth? Ans. $4.20.

3. When $8.80 is paid for doing a certain amount of work, how much must be paid for doing as much?

4. If an acre of land produce 1 T. 16 cwt. 18 lb. of hay, how much will of an acre produce?

5. If in a lot there are 15 A. 3 R. 28 P., what is the extent of of it? Ans. 11 A. 1 R. 20 P. 6. If of a barrel of flour cost $6.75, what will 1 barrel cost?

SOLUTION. - If of a barrel cost $6.75, 4 of a barrel will cost of $6.75, or $2.25, and 4, or 1 barrel, will cost 4 times $2.25, or $9. Therefore, if of a barrel of flour cost $6.75, 1 barrel will cost $9.

7. If of a yard of cloth cost $3.78, what will a whole yard cost? Ans. $4.32. 8. Paid $156 for a horse, which was as much as I paid for a wagon; how much did I pay for the wagon? Ans. $180.

9. A farmer sold 31 bu. 3 pk. 6 qt. of grain, which was of all he had; how much had he?

Ans. 36 bu. 2 pk.

10. If 11 A. 1 R. 15 P. is of a certain field, what is Ans. 15 A. 3 R. 21 P.

its entire extent?
11. If 4 tons of hay cost $52, what will 3

SOLUTION.

tons cost?

- If 4 tons cost $52, 1 ton will cost of $52, or $13. 3 tons are {} tons; and if 1 ton cost $13,will cost of $13, or $1, and will cost 41 times $1, or $41. Therefore, if 4 tons of hay cost $52, 3 tons will cost $41.

12. When $60 are paid for 12 yards of broadcloth, how much must be paid for 9 yards? Ans. $49.37.

13. If 3 tons of hay cost $41, what will 4 tons cost?

14. If 9 bushels of wheat are worth $19.35, what are 10g bushels worth? Ans. $22.79.

15. If 17 bushels of corn cost $16.32, what will 152 bushels cost? Ans. $15.12. 16. If of an acre of land is worth $60, what is of an acre worth?

SOLUTION. - If of an acre is worth $60, is worth or $30, and §, or 1 acre, is worth 3 times $30, or $90; acre is worth $90, 1 of an acre is worth is worth 5 times $15, or $75. $60, of an acre is worth $75.

Therefore, if

of $60,

and if 1

of $90, or $15, and § of an acre is worth

17. If of a cord of wood cost $2.85, what will of a cord cost? Ans. $5.70.

18. When of a pound of tea can be bought for $0.54, what will 43 pounds cost?

Ans. $3.12.

19. If 4 pounds of butter are worth $1.44, what are 11 pounds worth?

Ans. 3.66.

DECIMAL FRACTIONS.

171. If a unit be divided into ten equal parts, each of these parts will be 1 tenth.

If each tenth be divided into ten equal parts, each part will be of, or 1 hundredth.

If each hundredth be divided into ten equal parts, each part will be of 7, or 1 thousandth.

In like manner, we may, by dividing by ten, continue to obtain fractions, each of whose values is one tenth of the fraction preceding it.

172. A Decimal Fraction, or a Decimal, is a fraction whose unit is divided into tenths, hundredths, thousandths, etc.

ΝΟΤΑΤΙΟΝ AND NUMERATION.

173. A decimal fraction, by means of the decimal point (.), is written without the denominator, and the value of the decimal figures determined by the place of each with reference to the decimal point.

The first order to the right of the decimal point is that of tenths. Thus,

The second order to the right of the decimal point is that of hundredths.

Thus,

To may be written .01, and read 1 hundredth ;

The third order to the right of the decimal point is that of thousandths.

Thus,

Too may be written .001, and read 1 thousandth;

first order to the right of the point? The second? The third?