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Ratio.

EXERCISE VII.

(Changing common fractions to decimals.) 1. Express the ratio of 3 to 4 (!), in hundredths. 2. Express the ratio of 20 to 50, in tenths. 3. Express the ratio of 30 to 80, in thousandths.

4. Express the ratio of 50 sq. rd. to 1 acre 40 rd., in hundredths.

5. Express the ratio of 4 ft. 6 in. to 5 yd., in tenths.

EXERCISE VIII.

(Finding what per cent one number is of another.)

1. Express the ratio of 15 to 20, in hundredths. 2. Express the ratio of 14 to 200, in hundredths. 3. Express the ratio of 17 to 25, in hundredths. 4. Express the ratio of 16 to 33}, in hundredths. 5. Express the ratio of 27 to 500, in hundredths.

EXERCISE IX.

(Changing “per cent” to a common fraction in its lowest terms, or to a whole or mixed number.)

1. A's money equals 40 % of B's money. (a) Express the ratio of A's money to B's money in the form of a fraction in its lowest terms. (b) Express the ratio of B's money to A's money in its simplest form.

2. One number is 50 % more than another number. (a) Express the ratio of the smaller to the larger number in the form of a fraction in its lowest terms. (b) Express the ratio of the larger to the smaller number in its simplest form.

Note.—Observe that the base in percentage corresponds to the consequent in ratio.

Ratio.

EXERCISE X. (The specific gravity of a liquid or solid is the ratio of its weight to the weight of the same bulk of water. See Book II., pp. 214 and 224.)

1. A cubic foot of water weighs 624 lbs. A cubic foot of cork weighs 15 lbs. Wliat is the ratio of the weight of the cork to the weight of the water? Express the ratio in hundredths. What is the specific gravity of cork ?

2. A certain piece of limestone weighs 37 ounces. Water equal in bulk to the piece of limestone weighs 15 ounces. What is the ratio of the weight of the limestone to the weight of the water? What is the specific gravity of the limestone?

3. A certain bottle holds 10 ounces of water or 94 ounces of oil. What is the ratio of the weight of the oil to the weight of the water ? Express the ratio in hundredths. What is the specific gravity of the oil ?

Note. Observe that the weight of water in specific gravity problems, corresponds to the consequent in ratio problems.

280. MISCELLANEOUS QUESTIONS. 1. What is the ratio of a unit of the first integral order to a unit of the first decimal order ?

2. What is the ratio of a unit of any order to a unit of the next lower order ?

3. What ratio corresponds to 6 per cent ?

4. What is the ratio of a dollar to a dime? Of a dime to a cent? Of a cent to a mill?

5. What is the ratio of a meter to a decimeter ? Of a decimeter to a centimeter ? *

6. What is the ratio of a rod to a yard? Of a yard to a foot? Of a foot to an inch?

*See Book II., p. 154.

Ratio.

281. SOME OLD PROBLEMS IN New Forms. *

1. What is the ratio of the area of a 2-inch square to the area of a 6-in, square? * Of a 6-in. square to a 2-in. square?

2. What is the ratio of the perimeter of a 2-in. square to the perimeter of a 6-in. square? Of the perimeter of a 6-in. square to the perimeter of a 2-in. square ?

3. What is the ratio of the area of a 3-cm. square to the area of a 6-cm. square? Of a 6-cm. square to a 3-cm. square? +

4. What is the ratio of the perimeter of a 3-cm. square to the perimeter of a 6-cm. square? Of the perimeter of a 6-cm. square to the perimeter of a 3-cm. square ?

5. What is the ratio of the solid content of a 2-inch cube to the solid content of a 6-in. cube? Of a 6-in. cube to a 2-in. cube?

6. What is the ratio of the surface of a 2-in. cube to the surface of a 6-in. cube? Of the surface of a 6-in. cube to the surface of a 3-in. cube?

7. What is the ratio of the solid content of a 3-cm. cube to the solid content of a 6-cm. cube? Of a 6-cm, cube to a 3-cm. cube?

8. What is the ratio of the surface of a 3-cm. cube to the surface of a 6-cm. cube? Of the surface of a 6-cm. cube to the surface of a 3-cm. cube?

9. What is the ratio of a square inch to a square foot? Of a cubic inch to a cubic foot ?

* If pupils image the magnitudes com pared, they will find no difficulty in the solution of these problems. † See Book II., pp. 151 and 164.

See Book II., p. 174.

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From the above learn that the antecedent is always equal to the product of the consequent and the ratio.

1. Consequent 75; ratio 11. Antecedent ?
2. Consequent 92; ratio 1. Antecedent ?
3. Consequent .56 ; ratio . Antecedent ?

EXAMPLE II. The antecedent is a; the ratio is r. What is the consequent ?

Let x = the consequent.

а
Then = r

х
and

a = Nx, or rx = a

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From the above learn that the consequent is always equal to the quotient of the antecedent divided by the ratio.

1. Antecedent 75 ; ratio 5. Consequent ?
2. Antecedent 96; ratio . Consequent ?
3. Antecedente; ratio . Consequent ?
4. Antecedent .25; ratio ]. Consequent ?

283. To FIND Two NUMBERS WHEN THEIR SUM AND

RATIO ARE GIVEN.

EXAMPLE.

The sum of two numbers is 36 and their ratio is 3. What are the numbers ?

Let
Then
and

the smaller number. 3 x = the larger number, x + 3 x = 36

36

9, the smaller number. 3 x = 27, the larger number.

4 x

X =

PROBLEMS.

1. The sum of two numbers is 196, and their ratio is 3. What are the numbers ?

2. The sum of two numbers is 294, and their ratio is 27. What are the numbers ?

3. The sum of two decimals is .42, and their ratio is 23. What are the decimals ?

4. The sum of two numbers is s, and the ratio of the larger to the smaller is r. What are the numbers?

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* Observe that any number you please may be put in the place of s, and any number greater than 1 in the place of r; so that when the sum of two numbers and the ratio of the larger to the smaller are given, the smaller number may be found by dividing the sum by the ratio plus 1.

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