19. If 95 cents be paid for 12 pounds of rice, what cost 1 pound?

20. If A can do of a piece of work in 1 day, and B can do of the same work in 1 day, what part of it will A and B together do in 1 day? In how many days will they perform the whole work?

21. If a man can do a piece of work in 5 days, what part will he do in 1 day? In 2 days? In 3 days? In 4 days?

22. A can build a wall in 10 days, and B can build the same wall in 12 days. In what time will A and B together do the work?

23. If C and D together can mow a field in 3 days, and D alone can mow the same field in 53 days, in what time can C alone mow the field?

24. If of of a barrel of flour cost $12, what cost 1 barrel? 1 barrels ?

25. Paid $3 for a City Directory, and 24 times as much for a Webster's Unabridged Dictionary; what did I pay for both?

26. A market woman bought eggs at 3 for 5 cents, and sold them at 4 for 7 cents. How much did she gain on each egg?

27. A confectioner bought oranges at 30 cents for 12, and sold them again at the rate of 8 for 21 cents; and then found that he had gained 64 cents. How many oranges did he buy?

28. After selling 200 bananas at a loss of 61 cents each, I found that I could purchase lemons at 3 for 7 cents and sell them at cents apiece. How many lemons must I buy and sell to make good my loss on the bananas?

29. How many pencils at 7c. must be paid for 150 pens, at the rate of 14 cents apiece?

Written Exercises

1. A bought a farm for $3250, and sold of it to B, and the remainder to C. What is the value of C's property? Ans. $2275.

2. A merchant bought 25 pieces of muslin at $3 per piece; 125 pieces prints at $23; 35 pieces ticking at $73. What was the amount of the bill?

3. A man owns a farm of 125 acre; another of 83 acres, worth much are both farms worth?

Ans. $716.25. acres, worth $625 per

$76 per acre. How Ans. $14240.14+.

4. A grocer bought 5 barrels of granulated sugar; the first barrel containing 225 pounds, the second 221 pounds, the third, 231 pounds, the fourth, 2294 pounds, and the fifth, 240 pounds, at 114 cents per pound. He sold of it at 123 cents per pound, and the remainder at 122 cents per pound. How much did he gain? Ans. $15.06+.

5. From 32 acres, I sell to A3 of an acre, to B, & of an acre, to C, of an acre, to D, § of an acre. How much is the remainder worth, at $2575 per acre? Ans. $2042o.

of an

6. Into how many house lots, each containing acre, can I divide 184 acres, and for how much apiece must I sell lots, to realize $95600? Ans. 150 lots; price, $6374.

7. A stove manufacturer purchased old metal at $ per hundred pounds, and makes out of it stoves weighing 350 pounds each, which he sells at $17 apiece. How much does he gain on each 100 pounds of old metal?

Ans. $4.13.

8. A man bought a farm for $17500, and sold of it to Mr. B for $4500; of the remainder to Mr. C for $4600;

and the remainder to Mr. L at a profit of $1250.

was his whole gain?

What

Ans. $5975. 9. A huckster bought 125 bushels of apples at $ per bushel; 35 bushels at $3 per bushel; and 25 bushels at $ per bushel. At what price per bushel must he sell them to gain $30.614? Ans. $.87.

10. A hunter in pursuit of a fox that was 3 miles ahead of him, ran 14 hours, at the rate of 5 miles an hour. The fox advanced at the rate of 3 miles per hour, for 14 hours. How far in advance of the hunter is the fox? Ans. 138 miles.

11. Henry, William, and Jacob can remove a pile of wood in 4 hours; and Henry and William together can remove it in 9 hours. In how many hours can Jacob alone remove it ? Ans. 61 hours.

12. Two men 115 miles apart start toward each other, and travel, one at the rate of 21 miles per hour, and the other at the rate of 3 miles per hour. In how many hours will they meet? Ans. 1834 hours.

It

13. L, M, and N bought a drove of cattle: L paid for 3. of the drove, M, for of it, and N, for the remainder. was found that L paid $640 more than N. pay, and what was the cost of the drove ?

What did each

Ans. L, $3840; M and N, each $3200; $10240. 14. How many barrels of apples at $9 per barrel will pay for 95 cords of wood at $51 per cord? Ans. 55.

15. A gentleman purchased a farm for $9000; he paid $95 for fencing and other improvements, and then sold it for $381 less than he had expended. What did he receive for it? Ans. $8713.75. of a barrel of flour

16. If a family of 5 persons consume

in one month, in how many months will they consume 9.1

barrels ?

Ans. 1318.

17. If a man earns $112 per month and spends $77 in the same time, how long will it take him to save $941 ? Ans. 263 months.

18. There are two outlets to a cistern; by one 15 gallons, and by the other 20 gallons, can be emptied in one minute. How many gallons may be emptied by both in 17 minutes?

19. The product of three numbers is 79. The first number is 7, the second is 93. What is the third? Ans. 1.

185. Converse Reductions.

We have already learned that Fractions with reference to the mode of expressing them are either called "Decimals" or "Fractions.”

In the decimal form, the denomination, or fractional unit, is indicated by the position of the decimal point (119); but, in the fractional form, the denomination, or fractional unit, is expressed by the denominator (152).

We shall now proceed to learn how to change Decimals to Fractions and Fractions to Decimals under the heading Converse Reduction.

EXAMPLE 1.-Reduce .875 to a common fraction.

EXPLANATION.-.875 is read 875 thousandths. Therefore our numerator is 875, and our denominator, 1000, and the fraction, 875, which reduced to its lowest terms by RULE (178) =},

unit by the known denominator 100, which gives us the complex frac

31 100'

tion which reduced to a simple fraction by Rule for Division of

Fractions = , required fractional form.

Hence, to reduce a decimal to a fraction, we have the following

RULE. Write the given number of decimal units. Omit the decimal point, and express the fractional unit by a denominator. Reduce the resulting fraction to its simplest form.

8

EXAMPLE 3.-Reduce to a decimal.

SOLUTION.

=

8)7.000

.875

1ST EXPLANATION.-Annexing three ciphers to 7, reduces it to thousandths, and of 7000 thousandths

= 875 thousandths or .875.

2D EXPLANATION.-Since expresses the quotient of 7 divided by 8, we annex decimal ciphers to 7, and divide by 8, as in Division of Decimals.

Hence, to reduce a fraction to a decimal, we have the following

RULE.-Annex a decimal cipher or ciphers to the numerator and divide by the denominator.

Sometimes the decimal is interminable, and in such cases a fraction may be written after the decimal figures, the quotient being carried to any desired number of decimal places; or the sign + may be written after the decimal figures, to show that the divisor is not exact.

Decimal figures which continually repeat, are called a Repetend.