## Proportion

The equality of two ratios is called proportion.

In other words, If two ratios are equal then the two ratios or the quality of two ratios make a proportion.

### Example

Since 2:5 = 4:10 and say that 2, 5, 4, 10 are in proportion.

## Properties of Proportion

If the proportion is a:b::c:d , then the quantities a and b must be of the same kind, c and d may be of the same kind or of different kind.

The quantities of proportion are called sequentially as 1st, 2nd, 3rd, 4th term.

### Example

Let 2:3 = 10:15 as a proportion.

So, 1st term=2, 2nd term=3, 3rd term=10, 4th term=15.

The multiplication of 1st and 4th term will be equal to the multiplication of 2nd and 3rd term.

### Example

Let 3:5 = 9:15 as a proportion.

Here, 1st term=3, 2nd term =5, 3rd term =9, 4th term =15

So, 1st x 4th = 3 x 15 = 45

2nd x 3rd = 5 x 9 = 45

So, it can be say that if a:b = c:d, then ad = bc

Note: Proportion can be restated as “two sets of numbers are in proportion to one another when one set is a constant times the other”

## Continued Proportion

If the price of 3 kg and 6 kg rice is 6 dollar and 12 dollar respectively then;

3:6 = 6:12 | or | 3 | = | 6 | |||||||

6 | 12 |

So, here we can see the Consequent of the 1st ratio is equal to the Antecedent of the 2nd ratio.

Now we can say that 3, 6, 12 are in Continued proportion.