**Types of ratios in math :**

Students who would like to learn ratio must be aware of the different kinds of ratios.

Because, without knowing the kinds of ratios, always it is difficult to solve problems using ratios.

Let us come to know the different types of ratios.

**Compound ratio : **

The ratio compounded of the two ratios a : b and c : d is

ac : bd

For example,

(i) Compound ratio of 3 : 4 and 5 : 7 is 15 : 28

(ii) Compound ratio of 2 : 3, 5 : 7 and 4 : 9 is 40 : 189

**Duplicate ratio : **

A ratio compounded of itself is called its duplicate ratio.

Thus a² : b² is the duplicate ratio of a : b. Similarly, the triplicate ratio of a : b is a³ : b³.

For example,

(i) Duplicate ratio of 2 : 3 is 4 : 9.

(ii) Duplicate ratio of 4 : 5 is 16 : 25

**Triplicate ratio : **

A ratio compounded of itself twice is called its triplicate ratio.

Thus a³ : b³ is the duplicate ratio of a : b.

For example,

(i) Triplicate ratio of 2 : 3 is 8 : 27.

(ii) Duplicate ratio of 4 : 5 is 64 : 125

**Sub-duplicate ratio : **

The sub–duplicate ratio of a : b is √a : √b

For example,

(i) Sub-duplicate ratio of 4 : 9 is √4 : √9 = 2 : 3

(ii) Sub-duplicate ratio of 16 : 25 is √16 : √25 = 4 : 5

**Sub-triplicate ratio : **

The sub–triplicate ratio of a : b is ³√a : ³√b.

For example,

(i) Sub-triplicate ratio of 8 : 27 is ³√8 : ³√27 = 2 : 3

(ii) Sub-triplicate ratio of 64 : 125 is

³√64 : ³√125 = 4 : 5

**Inverse ratio :**

One ratio is the inverse of another, if their product is 1. Thus a : b is the inverse of b : a and vice–versa.

For example,

3 : 4 is the inverse of 4 : 3

4 : 3 is the inverse of 3 : 4

Therefore, 3 : 4 and 4 : 3 are inverse to each other.

And also, (3:4) x (4:3) = (3/4) x (4/3) = 1

**Ratio of equality :**

A ratio a : b is said to be of equality if a = b

For example,

7 : 7 is a ratio of equality. Because 7 = 7

**Ratio of inequality :**

A ratio a : b is said to be of inequality if a ≠ b

For example,

5 : 7 is a ratio of inequality. Because 5 ≠ 7

**Ratio of greater inequality :**

A ratio a : b is said to be of greater inequality if a > b

For example,

17 : 9 is a ratio of greater inequality. Because 17 > 9

**Ratio of lesser inequality :**

A ratio a : b is said to be of lesser inequality if a < b

For example,

9 : 17 is a ratio of lesser inequality. Because 9 < 17

**Continued ratio :**

Continued Ratio is the relation (or compassion) between the magnitudes of three or more quantities of the same kind.

The continued ratio of three similar quantities a, b, c is written as a: b: c.

**Ratio of in-commensurable quantities : **

If the ratio of two similar quantities can be expressed as a ratio of two integers, the quantities are said to be commensurable; otherwise, they are said to be in-commensurable.

√3 : √2 cannot be expressed as the ratio of two integers and therefore, √3 and √2 are in-commensurable quantities.

Hence, √3 : √2 is the ratio of in-commensurable quantities.

**Related topics : **

Ratio and proportion word problems

Ratio and proportion worksheets with answers

Ratio and proportion aptitude shortcuts pdf

Ratio and proportion problems and solutions for class 7

Ratio and proportion problems and solutions for class 6

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