How to Simplify Ratios? (+FREE Worksheet!)

Related Topics

• How to Find Similarity and Ratios
• How to Create a Proportion
• How to Find Proportional Ratios

Step by step guide to simplify ratios

• Ratios are used to make comparisons between two numbers.
• Ratios can be written as a fraction, using the word “to”, or with a colon.
• You can calculate equivalent ratios by multiplying or dividing both sides of the ratio by the same number.

Simplifying Ratios – Example 1:

Simplify. \(4:2=\)

Solution:

Both numbers \(4\) and \(2\) are divisible by \(2 , ⇒ 4 \ ÷ \ 2=2, 2 \ ÷ \ 2=1\),
Then: \(4:2=2:1\)

Simplifying Ratios – Example 2:

Simplify. \(\frac{14}{24}=\)

Solution:

Both numbers \(14\) and \(24\) are divisible by \(2, ⇒ 14 \ ÷ \ 2=7, 24 \ ÷ \ 2=12\),
Then: \(\frac{14}{24}=\frac{7}{12} \)

Simplifying Ratios – Example 3:

Simplify. \(8:4=\)

Solution:

Both numbers \(8\) and \(4\) are divisible by \(4 \), \(⇒ 8÷4=2, 4÷4=1\),
Then: \(8:4=2:1\)

Simplifying Ratios – Example 4:

Simplify. \(\frac{12}{36}=\)

Solution:

Both numbers \(12\) and \(36\) are divisible by \(12\), \(⇒ 12÷12=1, 36÷12=3\),
Then: \(\frac{12}{36}=\frac{1}{3 }\)

Exercises for Simplifying Ratios

Reduce each ratio.

• \(\color{blue}{21:49}\)
• \(\color{blue}{20:40}\)
• \(\color{blue}{10:50}\)
• \(\color{blue}{14:18}\)
• \(\color{blue}{45:27}\)
• \(\color{blue}{63:18}\)

Download Simplifying Ratios Worksheet

Answers

• \(\color{blue}{3:7}\)
• \(\color{blue}{1:2}\)
• \(\color{blue}{1:5}\)
• \(\color{blue}{7:9}\)
• \(\color{blue}{5:3}\)
• \(\color{blue}{7:2}\)