How to Simplify Fractions
Support Page

To simplify a fraction, you need to follow the 2 steps below:

Step 1

Look for a common factor of both the numerator and denominator.

• If there are no common factors (other than 1) then the fraction is already in its simplest form and you have finished.
• Try to find the highest factor of both numbers (highest common factor) that you can!

Step 2

Reduce the numerator and denominator by dividing them both by the common factor. Now go back to Step 1.

Your fraction should now be in its simplest form.

Example 1) Convert into simplest form the fraction \[ {35 \over 45} \]

A common factor of both numbers is 5, so we need to divide the numerator and denominator by 5.

This gives us \[ {35 \over 45} \; = \; {35 ÷ 5 \over 45 ÷ 5 } \; = \; {7 \over 9} \]

There are no more common factors (except 1) and so this fraction is now in simplest form.

Final answer \[ {35 \over 45} \; = \; {7 \over 9} \]

Example 2) Convert into simplest form the fraction \[ {68 \over 220} \]

A common factor of both numbers is 2, so we need to divide the numerator and denominator by 2.

This gives us \[ {68 \over 220} \; = \; {68 ÷ 2 \over 220 ÷ 2 } \; = \; {34 \over 110} \]

We are not finished yet, because 2 is still a common factor of both numbers.

Canceling the common factor of 2 gives us \[ {34 \over 110} \; = \; {34 ÷ 2 \over 110 ÷ 2 } \; = \; {17 \over 55} \]

There are no more common factors (except 1) and so this fraction is now in simplest form.

Final answer \[ {68 \over 220} \; = \; {17 \over 55} \]

Note - a quicker way to simplify this fraction would be to have divided the numerator and denominator by 4 as this is a higher common factor than 2.

Example 3) Convert into simplest form the fraction \[ {120 \over 75} \]

A common factor of both numbers is 5, so we need to divide the numerator and denominator by 5.

This gives us \[ {120 \over 75} \; = \; {120 ÷ 5 \over 75 ÷ 5 } \; = \; {24 \over 15} \]

We are not finished yet, because 3 is a common factor of both numbers.

Canceling the common factor of 3 gives us \[ {24 \over 15} \; = \; {24 ÷ 3 \over 15 ÷ 3 } \; = \; {8 \over 5} \]

There are no more common factors (except 1) and so this fraction is now in simplest form.

Final answer \[ {120 \over 75} \; = \; {8 \over 5} \]

Note - we could have simplified this fraction more quickly by seeing that the highest common factor was 15, and divided the numerator and denominator by this number first.