Composition of ratios

Compounded ratio

If two or more ratios are multiplied term-wise, the ratio thus formed is called their compounded ratio.

Example:

The compounded ratio of 2:3 and 4:5 is 2 x 4:3 x 5 i.e. 8:15

Duplicate ratio

The compounded ratio of two equal ratios is called their duplicate ratio.

Example:

a) The compounded ratio of a:b, a:b is a²:b²

a²:b² is the duplicate ratio of a:b

b) The duplicate ratio of 2:3 is

2²:3² i.e. 4:9

Triplicate ratio

The compounded ratio of three equal ratios is called their triplicate ratio.

The triplicate ratio of a:b is a³:b³.

Example:

The triplicate ratio of 2:3 is 2³:3³=8:27.

Sub- Duplicate ratio

A ratio x:y is the sub-duplicate ratio of a:b. If a:b is the duplicate ratio of x:y.

a:b = duplicate ratio of x:y

a:b = x²:y²

Example:

Sub triplicate ratio

A ratio x:y is the sub triplicate ratio of a:b if a:b is the triplicate ratio of x:y.

a:b= Triplicate ratio of x:y

a:b= x³:y³

Example: