Ratio and Proportion Example

This illustrated example shows the link between ratios and fractions. There are four ratios depicted with the use of coloured balls and the fraction of each colour.

Understanding Ratio and Proportion: A Complete Guide with Examples

Ratios and proportions are two core concepts in maths. Understanding them will help your students compare quantities and explore the relationships between values. These concepts are key in the KS2 and KS3 curriculum.

Whether you’re a student learning ratio examples or a teacher teaching number skills, this guide will help you master the topic.

What is a Ratio?

A ratio compares two or more quantities. For example:

If a bag contains 2 red balls and 3 green balls, the ratio of red to green is 2 : 3.

This means: for every 2 red balls, there are 3 green balls.

Key Points About Ratios:

• Written as a colon: 2 : 3
• Written as a fraction: \( \frac{2}{3} \)
• Written in words: “2 to 3”
• Ratios can be simplified: \( 4 : 6 = 2 : 3 \)
• Order matters: \( 2 : 3 \neq 3 : 2 \)

What is Proportion?

A proportion shows that two ratios are equal. It helps solve problems by comparing equivalent relationships.

Example: If the ratio of boys to girls is 3 : 2 and there are 12 boys, how many girls are there?

\[
\frac{12}{x} = \frac{3}{2} \Rightarrow 3x = 24 \Rightarrow x = 8
\]

There are 8 girls.