Ratio and Proportion

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

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

Ordinary fractions can be considered to be ratios.

1. 3/4 or 3:4
2. 5/4 or 5:4

Proportion

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

1. 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
2. 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
3. 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.