Ratio and Proportion: Basic Concepts, Formulas

What do you mean by Ratio?

Let say ‘a’ and ‘b’ are two quantities; then the fraction of these two quantities is called ratio. Remember the quantities in ratio must have the same unit.

In a ratio of a:b, ‘a’ is called the first term or antecedent, and ‘b’ is called the second term or consequent.

Note- The multiplication or division of each term of the ratio with the same non-zero number does not affect the ratio.

Algebraic Identities

What do you mean by Proportion?

When we equate the two ratios, it is called proportion.

If a:b = c:d then in ratio we write as a:b :: c:d and we read it as a,b,c and d are in proportions.

Note- Here ‘a‘ and ‘d‘ are called extremes & ‘b‘ and ‘c‘ are called mean terms.

The product of means = Product of extremes

i.e., a × d = b × c

Important Results

Duplicate Ratio of  a:b is a² : b²

Triplicate Ratio of  a:b is a³ : b³

Sub-Duplicate Ratio of  a:b is √a : √b

Sub-Triplicate Ratio of  a:b is ∛a : ∛b

Inverse Ratio of a:b is 1/a : 1/b

Mean Proportion of two numbers a and b is √(ab)

Third Proportion of two numbers a and b is b²/a

Fourth Proportion of three numbers a, b and c is bc/a 

In a 2-D geometrical figure if the two corresponding sides are in the ratio a:b then their Areas are in the ratio of a² : b²

In a 3-D geometrical figure if the two corresponding sides are in the ratio a:b then their Volumes are in the ratio of a³ : b³

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