How to Simplify Fractions

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Fractions are generally used to define any whole number into equal parts. While writing a fraction, there are two numbers involved. The number at the top is called the numerator, while that at the bottom is called a denominator. There are three types of fractions. They are:

Proper Fractions: In proper fractions, the denominator is greater than the numerator. For ex: \( \frac{3}{4} \ , \ \frac{1}{3} \)
Improper Fraction: As the name suggests, these fractions are “top-heavy” or the numerator is greater than the denominator. For ex: \( \frac{8}{7} \ , \ \frac{5}{2} \)
Mixed-Fraction: Mixed fractions are another type of improper fractions where there is a whole number as well as a fraction part. For ex: \( 1\frac{1}{3} \ , \ 2\frac{3}{7} \)

To simplify a fraction, we divide the numerator and the denominator with the same whole number. When the fraction can’t be divided by the same whole number except 1, then it is said to be in its simplest form.

Steps to simplify a fraction:

First, find a whole number that can completely divide the numerator and the denominator of the fraction (Greatest Common Factor). Once you get that number, divide the numerator and denominator and write the new fraction.
Now, follow this step until you can’t divide it by the same whole number. Once you see that the only number that can divide the numerator and denominator is 1, you have achieved the simplest form.

Example

Take the fraction \( \frac{9}{18} \)
Let’s divide the numerator and denominator by \( 3\), so the fraction becomes \( \frac{3}{6} \)
Next, let’s divide it by \( 3\) again, so the result is \( \frac{1}{2} \)
This is the simplest form.

WHAT IS THE GREATEST COMMON FACTOR OF 9 AND 18?

\( \frac{9}{18}=\frac{9 \div 3}{18 \div 3}=\frac{3 \div 3}{6 \div 3}=\frac{1}{2} \)
or
\( \frac{9}{18}=\frac{9 \div 9}{18 \div 9}=\frac{1}{2} \) , GCF(9,18) = 9

Free printable Worksheets

Exercises for Simplifying Fractions

1) \({40 \over 55} =\)

2) \({75 \over 90} = \)

3) \({33 \over 42} = \)

4) \({12 \over 21} = \)

5) \({20 \over 55} = \)

6) \({60 \over 95} = \)

7) \({15 \over 18} = \)

8) \({95 \over 130} = \)

9) \({24 \over 45} = \)

10) \({36 \over 39} = \)

Answers

1) \({40 \over 55} = \color{red}{{8 \over 11}}\)

Solution
To simplify \({40 \over 55}\) , you should first find a number that both 40 and 55 are divisible by. They both are divisible by 5, Therefore: \({40 \over 55} = {40 \div 5 \over 55 \div 5} = {8 \over 11}\)

2) \({75 \over 90} = \color{red}{{15 \over 18}}\)

Solution
To simplify \({75 \over 90}\) , you should first find a number that both 75 and 90 are divisible by. They both are divisible by 15, Therefore: \({75 \over 90} = {75 \div 15 \over 90 \div 15} = {5 \over 6}\)

3) \({33 \over 42} = \color{red}{{11 \over 14}}\)

Solution
To simplify \({33 \over 42}\) , you should first find a number that both 33 and 42 are divisible by. They both are divisible by 3, Therefore: \({33 \over 42} = {33 \div 3 \over 42 \div 3} = {11 \over 14}\)

4) \({12 \over 21} = \color{red}{{4 \over 7}}\)

Solution
To simplify \({12 \over 21}\) , you should first find a number that both 12 and 21 are divisible by. They both are divisible by 3, Therefore: \({12 \over 21} = {12 \div 3 \over 21 \div 3} = {4 \over 7}\)

5) \({20 \over 55} = \color{red}{{4 \over 11}}\)

Solution
To simplify \({20 \over 55}\) , you should first find a number that both 20 and 55 are divisible by. They both are divisible by 5, Therefore: \({20\over 55} = {20 \div 5 \over 55 \div 5} = {4 \over 11}\)

6) \({60 \over 95} = \color{red}{{12 \over 19}}\)

Solution
To simplify \({60\over 95}\) , you should first find a number that both 60 and 95 are divisible by. They both are divisible by 5, Therefore: \({60\over 95} = {60 \div 5 \over 95 \div 5} = {12 \over 19}\)

7) \({15 \over 18} = \color{red}{{5 \over 6}}\)

Solution
To simplify \({15\over 18}\) , you should first find a number that both 15 and 18 are divisible by. They both are divisible by 3, Therefore: \({15 \over 18} = {15\div 3 \over 18 \div 3} = {5 \over 6}\)

8) \({95 \over 130} = \color{red}{{19 \over 26}}\)

Solution
To simplify \({95\over 130}\) , you should first find a number that both 95 and 130 are divisible by. They both are divisible by 5, Therefore: \({95\over 130} = {95\div 5 \over 130 \div 5} = {19 \over 26}\)

9) \({24 \over 45} = \color{red}{{8 \over 15}}\)

Solution
To simplify \({24\over 45}\) , you should first find a number that both 24 and 45 are divisible by. They both are divisible by 3, Therefore: \({24\over 45} = {24\div 3\over 45\div 3} = {8\over 15}\)

10) \({36 \over 39} = \color{red}{{12 \over 13}}\)

Solution
To simplify \({36\over 39}\) , you should first find a number that both 36 and 39 are divisible by. They both are divisible by 3, Therefore: \({36\over 39} = {36\div 3\over 39\div 3} = {12 \over 13}\)

How to Simplify Fractions