How to Simplify Fractions? (+FREE Worksheet!)

First of all, it is good to know that in simplifying fractions, the actual value of the fraction will not change.

Each fraction consists of two numbers. The number at the top of the fraction is called the numerator, and the number at the bottom of the fraction is called the denominator.

But how can you know if the fraction is as simple as possible? When a fraction is in its simplest form, its numerator and denominator can no longer be divided by the same whole number except \(1\).

Related Topics

• How to Add and Subtract Fractions
• How to Multiply and Divide Fractions
• How to Add Mixed Numbers
• How to Multiply Mixed Numbers
• How to Divide Mixed Numbers

Step by step guide to Simplify Fractions

• Step 1: First, find the common factors of the numerator and denominator. Evenly divide both the top and bottom of the fraction by the common factors \(2, 3, 5, 7\), … etc.
• Step 2: You should divide the numerator and denominator by the common factors until they no longer be divided by the same whole number except \(1\). In this case, the fraction is as simple as possible.

Simplifying Fractions – Example 1:

Simplify . \( \frac{18}{24} \)

Solution:

To simplify \(\frac{18}{24}\) , find a number that both \(18\) and \(24\) are divisible by. Both are divisible by \( 6\) . Then: \(\frac{18}{24}=\frac{18 \ \div \ 6 }{24 \ \div \ 6 }=\frac{3}{4}\)

Simplifying Fractions – Example 2:

Simplify . \( \frac{72}{90} \)

Solution:

To simplify \(\frac{72}{90}\), find a number that both \(72\) and \(90\) are divisible by. Both are divisible by \(9\) and \( 18\). Then: \(\frac{72}{90}=\frac{72 \ \div 9}{ 90 \ \div \ 9 } =\frac{8}{10}\), \(8\) and \(10\) are divisible by \(2\), Then: \(\frac{8}{10}= \frac{8\ \div 2}{ 10 \ \div \ 2 }= \frac{4}{5}\)
or \(\frac{72}{90}=\frac{72 \ \div 18 }{90 \ \div 18}=\frac{4}{5}\)

Simplifying Fractions – Example 3:

Simplify . \( \frac{12}{20} \)

Solution:

To simplify \(\frac{12}{20}\), find a number that both \(12\) and \(20\) are divisible by. Both are divisible by \(4\). Then: \(\frac{12}{20}=\frac{12÷4}{20÷4}=\frac{3}{5}\)

Simplifying Fractions – Example 4:

Simplify . \( \frac{64}{80} \)

Solution:

To simplify \(\frac{64}{80}\), find a number that both \(64\) and \(80\) are divisible by. Both are divisible by \(8\) and \(16\). Then: \(\frac{64}{80}=\frac{64÷8}{80÷8}=\frac{8}{10}\) , \(8\) and \(10\) are divisible by \(2\), then: \(\frac{8}{10}= \frac{8\ \div 2}{ 10 \ \div \ 2 } =\frac{4}{5}\)
or \(\frac{64}{80}=\frac{64÷16}{80÷16}=\frac{4}{5}\)

Exercises for Simplifying Fractions

Simplify the fractions.

1. \(\color{blue}{\frac{22}{36}}\)
2. \(\color{blue}{\frac{8}{10}}\)
3. \(\color{blue}{\frac{12}{18}}\)
4. \(\color{blue}{\frac{6}{8}}\)
5. \(\color{blue}{\frac{13}{39}}\)
6. \(\color{blue}{\frac{5}{20}}\)

Download Simplifying Fractions Worksheet

1. \(\color{blue}{\frac{11}{18}}\)
2. \(\color{blue}{\frac{4}{5}}\)
3. \(\color{blue}{\frac{2}{3}}\)
4. \(\color{blue}{\frac{3}{4}}\)
5. \(\color{blue}{\frac{1}{3}}\)
6. \(\color{blue}{\frac{1}{4}}\)