RATIO

ORAL EXERCISES.

741. 1. A father is 30 years old, and his son 6; how many times as old as the son is the father?

2. 30 are how many times 6?
3. What part of $30 are $6?
4. What is the relation of 8 to
5. What relation has 12 to 3 ?

30 ÷ 6 =

?

Of 20 cents are 5 cents? 2? Of 40 rd. to 4 rd.? 60 lb. to 20 lb.?

Compare the following, and give their relative values.

742. Ratio is the relation between two numbers of the same unit value, expressed by the quotient of the first divided by the second. Thus the ratio of 12 to 4 is 1243.

743. The Sign of ratio is the colon (:), or the sign of division with the line omitted.

Thus, the ratio of 9 to 3 is expressed 9: 3, or 9÷3, or in the form of a fraction, and is read, the ratio of 9 to 3, or 9 divided by 3.

744. The Terms of a ratio are the two numbers compared.

745. The Antecedent is the first term, or dividend. 746. The Consequent is the second term, or divisor.

747. The Value of a ratio is the quotient of the antecedent divided by the consequent, and is an abstract number.

Thus, in the ratio $18 : $6, $18 and $6 are the terms of the ratio; $18 is the antecedent; $6 is the consequent; and 3, the quotient of $18 $6, is the value of the ratio.,

748. A Simple Ratio is the ratio of two numbers; as 10: 5.

749. A Compound Ratio is the ratio of the products of the corresponding terms of two or more sim ple ratios.

Thus the ratio compounded of the simple ratios,

8: 4)

9: 12 may be expressed {

Or,

(8: 4) × (9: 12) } =72: 48;

or, 8×9: 4 × 12

4× == 3: 2.

When the multiplication is performed the result is a simple ratio.

750. The Reciprocal of a ratio is 1 divided by the ratio (196), or it is the consequent divided by the ante cedent. Thus the ratio of 8 to 9 is 8: 9, or §, and its reciprocal is .

The ratio of two fractions is obtained by reducing them to a common denominator, when they are to each other as their numerators (241).

If the terms of a ratio are denominate numbers, they must be reduced to the same unit value.

751. From the preceding definitions and illustrations are deduced the following

FORMULAS.-1. The Ratio

Antecedent÷Consequent. Antecedent Ratio. 3. The Antecedent Consequent × Ratio.

2. The Consequent

=

752. Since the antecedent is a dividend, and the consequent a divisor, any change in either or both of the terms of a ratio will affect its value according to the laws of division or of fractions (200), which laws become the

GENERAL PRINCIPLES OF RATIO.

1. Multiplying the antecedent, or

Dividing the consequent,

2. Dividing the antecedent, or Multiplying the consequent,

3. Multiplying or dividing both) antecedent and consequent by

the same number,

} Multiplies the ratio.

Divides the ratio.

Does not change the

ratio.

753. These principles may be embraced in one

GENERAL LAW.

A change in the antecedent produces a LIKE change in the ratio; but a change in the consequent produces an OPPOSITE change in the ratio.

EXERCISES.

754. 1. Express the ratio of 11 to 4; of 16 to 2; of 20 to 63; of $36 to $12; of 9 lb. to 27 lb. ; of 44 bu. to 9 bu. 2. Can you express the ratio between $15 and 5 lb. ? Why not?

3. Indicate the ratio of 18 to 20 in two forms. What are the terms of the ratio? The antecedent? The consequent? The kind of ratio? The value of the ratio. In like manner express, analyze,

4. Of 80 to 120; of 12 to 37;

and give the value, of 161 to 3.

2 × 27 × 42

5. Of 5.2 to 1.3; of

to; of

12 × 4 × 126*

6. The antecedents of a ratio are 7 and 10, and the consequents, 5 and 4. What is the value of the ratio?

7. The first terms of a ratio are 18, 12, and 30, the second, 54, 6, and 15. What is the kind of ratio? Express in three forms. Find its value in the lowest terms. Solve, and state the formula applied to the following: 8. The consequent is 34, the antecedent; what is the ratio?

9. The antecedent is 60, the ratio 7; what is the consequent ?

10. The consequent is $6.12, the ratio ; what is the antecedent?

11. The ratio is 2, the antecedent of; what is the consequent ?

12. The ratio is 6, the consequent 1 wk. 3 da. 12 hr. ; what is the antecedent?

13. Express the ratio of 120 to 80, and give its value in the lowest terms.

14. Make such changes in the last example as will illustrate PRIN. 1.

15. With the same example, illustrate PRIN. 2.

16. Illustrate by the same example PRIN. 3.

17. Find the reciprocal of the ratio of 75 to 15.

18. Find the reciprocal of the ratio of 2 qt. 1 pt. to 4 gal. 1 qt. 1 pt.

What is the ratio

19. Of 40 bu. 4.5 pk. to 25 bu. 2 pk. 1 qt.

20. Of 6 A. 110 P. to 10 A. 60 P.

21. Of 25 lb. 11 oz. 4 pwt. to 19 lb. 5 oz. 8 pwt.

755. 1. What is the ratio of 4 to 2? Of 6 to 1? Of 14 to 7? Of 21 to 3?

2. Find two numbers that have the same quotient as 82. As 273. As 164. As 306. As 4. 3. Express in the form of a fraction the ratio of 26 to Of 32 to 8.

13.

4. Express in both forms the ratio of two other numbers equal to the ratio of 10 to 2. Of 15 to 5. Of 12 to 3. 5. If 4 stamps cost 12 cents, what will 20 stamps cost at the same rate?

6. What number divided by 12, gives the same quotient as 20÷4?

7. What number has the same ratio to 12, that 20 has to 4?

8. To what number has 48 the same ratio that 80 has to 5? That 24 has to 3?

9. The ratio of 20 to 5 is the same as the ratio of what

number to 4? To 6? To 5? To 61?

10. The ratio of 45 to 9 is the same as the ratio of 15 to what number? Of 30 to what number?

11. 28 is to 7 as 8 is to what number?

12. 56 is to 8 as what number is to 5?

13. 63 what number equals the ratio of 36 to 4?