# Concept of Proportion

“**A statement of equality of two ratios is called proportion.**”

Four numbers, a, b, c, d, are said to be in proportion when the ratio of the first two, a and b, is equal to the ratio of the last two, c and d.

i.e. or a : b = c : d

e.g. or 2 : 3 = 6 : 9

Some authors use the notation a : b :: c : d for proportion, but this notation is not preferred.

Here or a : b = c : d

If four numbers are in proportion, then we can also derive some other proportions from them.

Let be the given proportion, then

(1)

(2)

(3)

(4)

(5)

are called the Derived Proportions.

Here or a : b = c : d, then

The numbers a and d are called **extremes of proportion**, and the numbers b and c are called **means of proportion**.

Hence **Product of Extremes = Product of Means.**

To solve the proportion, we use the above principal, A single term in the proportion is called a proportional.

“**a**” is the 1st proportional.

“**b**” is the 2nd proportional.

“**c**” is the 3rd proportional.

“**d**” is the 4th proportional.

**Example:**

Find the 3rd proportional in 2 : 3 = : 15

**Solution:**

Let 2 : 3 = : 15

i.e.

3 x = 2 x 15 (by the principle of proportion)

3 = 30

**Example:**

Find the missing value in : 8 = 9 : 12

**Solution:**

Let : 8 = 9 : 12

12 = 9 x 8 (by the principle of proportion)

12 = 72

**Example:**

Find the 2nd proportional in 4, 20, 30.

**Solution:**

Let be the 2nd proportional

4 : =20 : 30

x 20 = 4 x 30

= = 6