Ratio and Proportion

Ratio is the spoken language of arithmetic. It is a way of comparing two or more quantities having the same units. A ratio can be written as a is to b or a : b or by giving the value of their quotient 𝑎 �

Proportion is an equality between two ratios or fractions. A proportion can be written in two ways: as two equal fractions 𝑎 𝑏 = 𝑐 𝑑 or using a colon a : b = c : d → read as a is to b as c is d

There are two circles and three triangles in a box. Express the number of circles to the number of triangles and vice versa.

Solutions:

a. Draw the figures in the given problem like this.

b. Express the ratio of the two quantities

(circles and triangles) in three different ways.

 Word form → 2 is to 3

 Colon form → 2:3

 Fraction form → 2 3 ⁄

Means it refers to the inner numbers of the proportion.

Extremes it refers to the outside numbers of the proportion.

means a : b = c : d extremes

A proportion is said to be equal if the product of the means is equal to the product of the extremes.

Example: 18 Means Extremes 2:3 = 6:9 or 3 x 6 = 2 x 9 18 = 18 18 10