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KATIO AND PROPORTION.

1. One fifth of 25 is . 25 is \ of .

2. One fourth of 21 is . 21 is \ of .

3. One third of 22 is . 22 is \ of .

4. One half of 45 is . 45 is £ of .

5. Three fourths of 24 are . 24 is J of .

6. Three fourths of 36 are . 36 is £ of .

(a) Find £ of 96. (b) 96 is -| of what number?

(c) Find | of 96. (d) 96 is f of what number?

(e) Find £ of 96. (f) 96 is I of what number?

7. 12 is of 18. 18 is of 12.

8. 18 is of 24. 24 is of 18.

9. 24 is of 30. 30 is of 24.

10. Two thirds of 18 are 1 half of .

11. Three fourths of 24 are 2 thirds of .

12. Two thirds of 30 are 1 half of .

(g) One third of 132 is 1 half of what number?

(h) Two thirds of 252 are 1 half of what number?

(i) Three fourths of 96 are 2 thirds of what number?

(j) Two thirds of 96 are 3 fourths of what number?

13. Nine is of 12. A man can earn

as much in 9 days as he can earn in 12 days. If he

can earn $40 in 12 days, in 9 days he can earn dollars.

(k) If a man can earn $896 in 12 months, how many dollars can he earn in 9 months?

(1) If Mr. Conrad's horses consume 726 bushels of oats in a year, how many bushels will be required to feed them 8 months?

PERCENTAGE.

16| per cent = .16| = -J.
14f per cent = .14 $ = 4.
121-per cent = .121-=:^.

(1) (2)

1. 16f per cent of 12 = 12 is 16|% of —

2. 14} per cent of 21 = 21 is 14f % of —

3. 12£ per cent of 16 = 16 is 12£% of —

4. 16| per cent of 18 = 18 is 16|% of —

5. 14} per cent of 28 = 28 is 14$% of —

6. 12£ per cent of 24 = 24 is 12£% of

7. 50 per cent of 12 = 12 is 50% of —.

8. 25 per cent of 16 = 16 is 25% of .

9. 20 per cent of 25 = 25 is 20% of .

10. 33} per cent of 18 = 18 is 33}% of .

(5) (3)

11. 2 is per cent of 6. 2 is % of 4.

12. 2 is per cent of 8. 2 is % of 14.

13. 2 is per cent of 12. 2 is % of 10.

14. 2 is per cent of 16. 1 is % of 2.

15. There were 40 pears on a tree; 25% of them fell off; pears remained on the tree.

16. William sold 7 melons; these were 12£% of all the melons he raised; he raised melons.

17. Mary had 30 little chickens; a hawk killed five of them; the hawk killed per cent of her chickens.

18. Twelve and one half per cent of $48 is dollars

(a) Find 12* per cent of $992.

(b) Find 16| per cent of $852.

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REVIEW.

1. Two is an exact divisor of 28, 274, , .

2. Five is an exact divisor of 75, 230, , .

3. Ten is an exact divisor of 80, , ——, .

4. Twenty is an integral number. J and .5 are

numbers. 5^ and 3.2 are numbers.

5. The fractions -fa, ¥»T, , , have a common

denominator. f and do not have a common denominator.

6. The sum of .135 and .6 is . .135 - .06 =

7. Divide .045 by .009. (This means 4* .)

(a) Find the quotient of .875 divided by .005.

8. Divide .045 by 9. (This means . 5* .)

(b) Find the quotient of 54.063 divided by 9.

9. When hay is $8 a ton, 2500 lb. cost .

10. Five bushels of wheat weigh pounds.

(c) Sixty-five bushels of wheat weigh how much more than 65 bushels of oats?

11. The area of a 10-inch square is square inches.

(d) How many square feet in a 15-foot square?

(e) How many square yards in a 15-foot square?

12. The solid content of a 10-inch cube is . cu. in.

(f) How many cubic feet in a 15-foot cube?

(g) How many cubic yards in a 15-foot cube?

13. Three fourths of 60 are . 60 is £ of .

(h) Find £ of 132. (i) 132 is £ of what number?

14. Two thirds of 27 are 1 half of -—.

(j) Two thirds of 132 are 1 half of what number? * These figures refer to notes on page 8.

MISCELLANEOUS PROBLEMS.

1. Byron bought 6 melons for 540; he sold them at 150 each; on each melon he gained cents.

(a) A merchant bought 6 barrels of apples for $13.50, and sold them at $2.75 a barrel. How much did he gain on each barrel?

2. James carried 4 dozen eggs to market; he sold them for 120 a dozen; the dealer paid James for the eggs with

sugar at 50 a lb.; James should receive and

pounds of sugar.

(b) A farmer took four cords of wood to market; he sold it for $6.75 a cord and took its value in coal at $6 a ton. How many tons of coal should he receive?

3. At 50 a quart, 1 gallon of milk is worth cents.

2£ gallons are worth cents.

(c) At 50 a quart, how much are 45^- gallons of milk worth?

4. Two and 1 half feet are inches. 4 weeks are

days.

(d) Forty-six and 1 half feet are how many inches?

(e) Fifty-two weeks are how many days ?*

(f) Seventy-five gallons are how many quarts?

5. William had 300; he spent £ of his money for ink and pencils and the remainder for paper; the paper cost cents.

(g) William's father had $585; he spent f of his money for a carriage and harness and the remainder for horses. How much did the horses cost?

* The pupil should see that in the solution of this problem he may take fifty-two 7's or seven 62's. If he adopts the latter method his thought may be— One day in each week would make 52 days, and seven days in each week would make 7 times 52 days; or he may think that fifty-two 7's are equal to seven 52's, and that, as a matter of convenience, he finds seven 52's.

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