SUBTRACTION OF FRACTIONS.

160. 1. Jane earned of a dollar and spent of a dollar. How much had she left?

2. A man who owned of a factory sold of it. What part did he then own?

3. If I have of a dollar and give away of a dollar, what part of a dollar will I have left?

4. A boy sold a book for $ that cost $3. What part of a dollar did he lose?

5. A man who owned of an acre of land sold & of an acre. What part of an acre had he left?

6. What kind of fractions can be subtracted without changing their form?

7. What must be done to dissimilar fractions, before they can be subtracted?

161. PRINCIPLES.-1. Only similar fractions can be subtracted.

2. Dissimilar fractions must be reduced to similar fractions, before subtracting.

ORAL EXERCISES.

162. 1. A man who had of a bushel of peaches sold of a bushel. What part of a bushel had he remaining? 2. A boy paid of a dollar for an arithmetic and of a dollar for a grammar. How much more did he pay for

the one than the other?

3. If I have of a dollar and spend of a dollar, how much will I have left?

4. If I have of a dozen of marbles and lose of a dozen of them, what part of a dozen will I have left?

5. A lad hoed of a field of corn in a day. If he hoed in the forenoon, what part did he hoe in the afternoon?

6. James earns $3 per day, and Henry earns $3. How much more does James earn than Henry?

7. Jacob had $2, but spent $3. How much had he left? 8. Henry's father earned $3 per day, but paid $3 for his board. How much did he have left?

9. If I purchase a toy for $3, giving the merchant a two-dollar bill, how much should I receive in change? 10. William had $10. If he paid $2 for a hat and $31 for a pair of trousers, how much did he have left?

WRITTEN EXERCISES.

163. 1. What is the difference between and ?

PROCESS.

ANALYSIS. Since the fractions are not similar, they must be made similar be

16-8-38-18-30 fore subtracting.

The least common denominator of

the given fractions is 40, and 1=36 and 3=15. Hence the difference between the given fractions is the difference between 3 and 18, which is 1.

2. What is the difference between 6 and 25?

PROCESS.

ANALYSIS. Since the numbers are composed 61-63-515ed separately. of integers and fractions, each may be subtract

25=218-219 Reducing the fractions to similar fractions,

3 1/2

with 1 or

remainder of 312.

it is evident that can not be subtracted from hence 1, taken from 6, is united +12=11⁄2. Subtracting 212 from 511⁄2, there is a

RULE. Reduce the fractions to similar fractions, find the difference of the numerators, and write it over the common denominator.

When there are mixed numbers or integers, subtract the frac tions and integers separately.

34. A horse cost $147 and a carriage $1891. How much more did the carriage cost than the horse?

35. A man paid $219 for painting his house and $413 for other repairs. What was the difference between the cost of painting and other repairs?

36. The net profits of a grocer for the month of January were $3693; for the month of February his net profits were $2787. How much more did he gain in January than in February?

37. A woman having $25, paid $2 for a pair of gloves, $3 for silk, and $83 for a bonnet. How much money had she left?

38. The proceeds of a sale at auction were $317, of which $2124 was received in notes, $65 in bank-bills, and the rest in coin. How much was received in coin?

39. A clerk earned $60 per month. His expenses during that time were as follows: board $203, washing $5, other expenses $5. How much did he save per month?

40. The expenses of an office were as follows: for rent $183, for cleaning $34, for clerk hire $627, for stationery $276. If the income was $100, how much were the net proceeds?

MULTIPLICATION OF FRACTIONS.

164. To multiply a fraction by an integer.

1. At 2 fifths of a dollar per yard, what will 2 yards of cloth cost?

2. At of a dollar per pound, what will 2 pounds of tea cost?

10

3. If a man can eårn of a dollar per hour, how much can he earn in 2 hours? How much is 2 times ? 3

times?

10

4. How much is 5 times? 6 times? 7 times? 5. How, then, may a fraction be multiplied by any number?

6. How much is 4 times ? Express the result in smallest terms. How may this result be obtained from ?

7. How much is 5 times? Express the result in smallest terms. How may this result be obtained from ?

8. In what other way, besides by multiplying the numerator, may a fraction be multiplied?

165. PRINCIPLE.-Multiplying the numerator or dividing the denominator of a fraction by any number, multiplies the fraction by that number.

ORAL EXERCISES.

166. 1. If a man spends $2 per day, how much will he spend in 8 days?

2. At $5 each, how much will 7 baskets cost?

3. If paper is worth $3 per package, how much will 10 packages cost?

4. What will 9 yards of cloth cost at $11 per yard?

5. If a man can mow of an acre of grass in a day, how many acres can 12 men mow in the same time?

6. If molasses is selling at $ per gallon, how much must be paid-for 10 gallons?

7. If a man pays $1 for a book, how much will 20 such books cost?

8. When barley is worth $11 per bushel, how much will 24 bushels be worth?

9. If a man earns $1 per day, how much will he earn in 6 days?

10. If sugar is worth 8 cents per pound, how much are 5 pounds worth?

11. When oranges are selling at 12 cents per dozen, how much will 5 dozen cost?

12. At $63 per barrel, how much will 8 barrels of flour

cost?

13. What will 9 dozen of eggs cost at 10 cents per dozen? 14. What will 8 tons of hay cost at $85 per ton?

15. When hats sell at $3 apiece, how much will a hatter receive for 7 hats?

16. If a man walks 33 miles per hour, how far will he walk in 6 hours?

17. If shingles are worth $43 per thousand, how much will 8 thousand cost?

18. What will 31 pounds of rice cost at 9 cents per pound?