**Ratio**

- A ratio is the mathematical comparison of one number to another. Examples are as follows:

- 5 to 1 or 5:1
- 6 to 3 or 6:3 (Simplified – 2:1)
- 4 to 3 or 4:3
- 8 to 6 or 8:6 (Simplified – 4:3)

Ordinary fractions can be considered to be ratios.

- 3/4 or 3:4
- 5/4 or 5:4

**Proportion**

- A proportion is the statement that one ratio equals another ratio.

- 4 is to 6 as 2 is to 3 or 4:6 = 2:3
- To verify that this is correct, cross multply.numerator 1 with denominator 2 and denominator 1 with numerator 2. If the proportion be correct, the two products will be the same.

4 x 3 = 12

6 x 2 = 12 - Problem – 1: 4 is to what as 16 is to 25?
- Let the unknown number = Y. 4/Y = 16/24

4 x 24 = Y x 16

16Y = 96

16Y ÷ 16 = 96 ÷ 16

Y = 6 - Problem – You are 20 years old and are 2/3 the age of your sister, how old is your sister?
- Let your sister’s age = Y.

20/Y = 2/3

2Y = 60

2Y ÷ 2 = 60 ÷ 2

Y = 30

Your sister’s age = 30.