APPLICATIONS.

1. If 4 pounds of sugar cost of a dollar, how much will a pound cost? Ans. of a dollar.

2. If a horse consume 13 of a ton of hay in 5 months, how much will he consume in one month? Ans. of a ton.

3. If 10 bushels of wheat cost $13, how much is it a bushel? Ans. $13. 4. If $250% are divided equally among 19 men, how much will each man receive? Ans. $13.

5. If g of a barrel of flour cost $9, how much will a whole barrel cost?

SOLUTION. If of a barrel of flour cost $9, of a barrel must cost of $9, or $3; and §, or a whole barrel, must cost 5 times $3, which are $15. Therefore, etc.

6. When $43 is paid for of a cord of wood, how much is it a cord? Ans. $6%. 7. If 104 yards of cloth can be bought for $87, how much is the cloth a yard? Ans. of a dollar 8. At of a dollar a pound, how many pounds of coffer can be bought for 1 of a dollar ?

SOLUTION. At of a dollar a pound, as many pounds of coffee can be bought for 15 of a dollar as = of a dollar are contained times in 1 of a dollar, which are 23. Therefore, etc.

9. At $9 a barrel, how much flour can be bought for $31? Ans. of a barrel. 10. At of a dollar a bushel, how many bushels of corn can be bought for $87?

11. At the rate of 171⁄2 miles an hour, how long will it take a train of cars to run 18063 miles? Ans. 1034 hours.

REVIEW QUESTIONS. What is Reduction of Fractions? (142) When is a fraction expressed in its smallest terms? (143) When have fractions a Common Denominator? (147) When, only, can fractions be added? (152) When, only, can fractions be subtracted? (155) What is multiplying a number by a fraction equivalent to? (160)

RELATIONS OF NUMBERS.

172. The Relation of Numbers is the number of times one number contains another with which it is compared, or the part the latter is of the former.

173. Numbers can only be compared, and their relations expressed, when they represent units of the same name or kind.

174. To find the relation of numbers, or the part that one number is of another.

4. What part of 2 is 3? Of 1 is ? Of 3 is ?

or 1, is of 2, and 3

7. What part of is ?

OPERATION.

2x45, Ans.

X 3

Or, =,= 18; & ÷ 18 = √, Ans. is of of, or

15. 8

209

159

of 3.

What is the Relation of Numbers? When can numbers be compared and their relations expressed?

Or, is 1 and 3 is, and is the same part of 15, as 8 is of 15, or; hence, is of

8

15

8. What part of is? Of is ? Of is fo ?

RULE. Divide the number denoting the part, by that with which it is compared.

Ans. .

18. What is the relation of 125 to 1000?

APPLICATIONS.

1. A liberty pole, whose hight was 75 feet, was broken off by the wind 45 feet from the ground; what part of it was left standing? Ans. of it.

2. If I perform a piece of work in 6 days, what part of it can I perform in 14 days?

3. When 24 pairs of boots cost $156, what will 20 pairs cost?

4. A and B mowed a field for a certain sum of money, A mowing 12 acres, and B 182 acres. What should be A's share of the money, if B's is $30? Ans. $20.

5. If a boy has spent of of his money, what part of f of his money has he left?

6. A farmer owns 320 acres of land, and his son as many.

What is the Rule?

Should the son add 40 acres to his land, how would his number of acres compare with the number his father has?

Ans. It would be as many.

REVIEW EXERCISES.

1. Reduce 1 to its smallest terms.

Ans. H

2. Change to an equivalent fraction having 671 for its denominator.

3. Change 100188 to an improper fraction.

Ans.
Ans. 299.

4. Reduce,,&, and to equivalent fractions, having 30 for their denominator.

5. If I should receive from one person $19, and from another $518, and then pay away $633, how much should I have remaining? Ans. $75%.

59

6. Joseph has $133, Andrew has $7% more than Joseph, and Henry has as much as both of them; how many dollars each have Andrew and Henry?

Ans. Andrew, $203; Henry, $33. 7. If be a minuend, and a remainder, what is the subtrahend?

8. A merchant owned 1 of a ship, and sold } of his share; what part of the whole ship did he sell?

Ans.

9. If a product be 12, and the multiplicand 33, what is the multiplier?

Ans. 3. of 2

10. How many oranges can be bought for 24 times cents, when they are of 1 of 2 cents apiece? 11. A has $3240, and B has as much, lacking $500; how much has B? Ans. $2092. 12. If there leaks out from a cask containing 31 gallons of cider, of a gallon each week, in how many weeks will the whole have leaked out? Ans. 474 weeks.

REVIEW QUESTIONS. What is the unit of a fraction? (131) What is a fractional unit? (131)

13. If the divisor is and the quotient only as large, what

15. If 3 be added to each term of the fraction, how much will the value expressed be increased or diminished?

Ans. Increased.

16. If 3 be added to each term of the fraction 3, how much will the value expressed be increased or diminished?

Ans. Diminished 1.

17. What number must be multiplied by 13, that the product may be 100 ? Ans. 1111.

18. If I pay away of my money, then of what remains, and then of what still remains, what fraction of the whole will be left?

Ans. 1.

19. A farmer, having a flock of 120 sheep, sold 30, and the dogs killed of the remainder. What part of the original

number then remained?

Ans..

20. If 8 horses eat in a certain time 13 tons of hay, how much will one horse eat in the same time?

21. At $83 a ton, how many tons of coal can be purchased for $413? Ans. 5 tons.

22. Bought 4 casks of molasses, containing 31 gallons each. What part of the whole is 100 gallons? Ans. 18.

23. A man owning of a steamboat, said that his part was 10 times as large as that of another man, who owned 3 4; but not being a good arithmetician, he had made a wrong calculation. How many times as large, in fact, was his part?

Ans. 8 times.

REVIEW QUESTIONS. How may a fractional expression be explained? (140) How may a fraction be regarded? (141) What is the value expressed by a fraction? (141) How is a fraction reduced to its smallest terms? (143) How is a mixed number reduced to an equivalent improper fraction? (145)