Simplifying Ratios

Simplifying Ratios

Learn how to simplify ratios in few simple and easy steps.

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.

Example 1:

Simplify. \(4:2=\)

Solution:

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

Example 2:

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

Solution:

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

Example 3:

Simplify. \(8:4=\)

Solution:

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

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

Reduce each ratio.

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

Download Simplifying Ratios Worksheet

Answers

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

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