How to Simplify Ratios? (+FREE Worksheet!)
In this post, you learn how to simplify ratios in a few simple and easy steps.
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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.
For education statistics and research, visit the National Center for Education Statistics.
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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: \(8:4=2:1\)
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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
- \(\color{blue}{3:7}\)
- \(\color{blue}{1:2}\)
- \(\color{blue}{1:5}\)
- \(\color{blue}{7:9}\)
- \(\color{blue}{5:3}\)
- \(\color{blue}{7:2}\)
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