**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

*, and ‘b’ is called the*

**antecedent***or*

**second term**

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

**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**