45. How many yards of cloth in four pieces containing 137 yards, 21 yards, 31 yards, and 45ğ yards?

46. John lives 24 rods from school, Harry 63 rods farther than John, and Thomas 1018 rods farther than Harry. How far does Thomas live from school?

109

47. A farmer sold hay for $ 457, oats for $15,3%, corn for $203, and potatoes for $35. What was the amount of

his sales?

48. I paid $2 for car-fare, $ 47 for cotton cloth, $ 5% for shoes, $25 for a suit of clothes, and had $17 left. How much money did I have at first?

49. A boy was absent from school the first week of the term 12 hours, the second week 163 hours, the third week 87 hours, and the fourth week 75 hours. How many hours was he absent during the four weeks?

50. I bought 31⁄2 tons of coal in January for $191, 27 tons in February for $153, and 5,7 tons in March for $30. How much coal did I buy in all, and what was the cost?

51. James weighs 58 pounds, William 65 pounds, Charles 67 pounds, and their father as much as all three of them. How much does their father weigh?

20

52. I bought of A 10,3 tons of hay, of B 18 tons, and of C 163 tons. How many tons did I buy in all?

53. Four piles of wood contain respectively 243 cords, 18 cords, 27 cords, and 30 cords. How many cords in all?

SUBTRACTION.

Oral.

133. 1. From take. How much is less ? less ? 11 less?

2. From take. How much is minus ? § minus 1? -16? # 10

3. A boy had $ and spent $1. What part of a dollar had he left?

4. A owns of a store, and B 4. How much of the store does A own more than B?

5. John runs of a mile, and Jerry of a mile. Which runs farther, and what part of a mile?

6. Mr. Ames owned of a farm, and sold of it. What part remained?

7. What is the difference between of anything and of it? Which is greater?

8. Lucy has $}, and Alice $ 4. Which has the more, and how much?

PRINCIPLE. — Only like fractions can be subtracted.

111 = 10% 48 = 48

6

Their difference

SOLUTION. We subtract the fractions and integers separately. After changing the fractions to their least common denominator, we have 11 - 48. cannot be subtracted from 3, hence we take 1 of the 11 units, change it to sixths, and add the 3, making 10%. 1084 = 6 = 61. Ans.

Rule. If the fractions are not like fractions, reduce them to

a common denominator, and write the difference of their numerators over the common denominator.

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

NOTE. Mixed numbers may be changed to improper fractions, and subtracted as fractions.

55. From a cask of oil containing 42 gallons I sell 81 gallons, 174 gallons, and 5 gallons. How much oil remains in the cask?

56. A rod is 16 feet.

Take 124 feet from a rod.

57. From a cask of vinegar containing 43 gallons 17 gallons were drawn. How many gallons remained?

58. A farmer having 217 bushels of wheat, scld 9511 bushels. How many bushels had he left?

59. The minuend is 1231, and the remainder 3811 What is the subtrahend?

6

60. From a piece of cloth containing 54 yards, 15,5% yards were sold at one time and 217 yards at another. How many yards were left?

61. If a grocer gained $13 by selling a barrel of flour for $63, what did it cost him?

62. A lady bought a hat for $43, shoes for $53, and some cotton cloth for $37, and gave in payment a twentydollar bill. How much change should she receive?

MULTIPLICATION.

Oral.

134. 1. 4 times 1 apple are how many apples? 7 times 1 apple? 4 times 6 apples?

2. 5 times 1-ninth are how many ninths? 6 times oneninth? 3 times ?

=

6. 3×? 8x=? 4x1=? 3×{=?

11. At $ each what will 8 books cost?

12. If a horse eat of a bushel of grain in a week, how much will 5 horses eat?

13. If a pound of tea costs 48 cents, what will of a What will of a pound cost?

pound cost?

14. A owned of a ship, and sold of his share. part of the ship did he sell?

What part was left?

What

15. What will yard of ribbon cost at 16 cents a yard? of a yard? of a yard?

16. 8 boys earn $4 each.

What do all earn?

17. John earns $3, Henry as much, and Edward as much. What do Henry and Edward earn?

18. John earns $ 3, and Henry as much. How much does Henry earn?

415

or,

of? Since of, will be 2 times or = 1.

Written.

19. Multiply by 4.

43

=

SOLUTION.

=

Ans.

multiplied by is the same as

of . of , and is 3 times, or . This solution, in effect, is the same as multiplying the numerators together for a new numerator, and the denominators for a new denominator.

Cancellation shortens the process.

Rule. Reduce integers and mixed numbers to improper fractions.

Multiply the numerators together for the numerator of the product, and the denominators for the denominator of the product.

Cancel when possible.

Two or more fractions joined by of form a Compound Fraction. The word of between two fractions is equivalent to the sign of multiplication.

To change a compound to a simple fraction, multiply the fractions together.

Thus, & of of = 2 × 3 × = Z.