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
(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.
(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.
(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
(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.
(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.
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
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
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
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
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.
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