Simplifying fractions

When we have a fraction, such as , we often want to write it as simply as we can.

Fraction equivalence

To simplify fractions, we need to understand one simple rule: if we multiply or divide both the top and bottom of a fraction by the same number, we get an equivalent fraction. In other words, the value of the fraction does not change.

For example, if we have the fraction , we can divide both the top and bottom by 2 to get:

This fraction is equivalent to , but it is in a simpler form.

Simplifying fractions

To simplify a fraction, we need to find the highest number that goes into both the numerator (top) and denominator (bottom) of the fraction.

This is called the highest common factor (HCF) - see here for more details on how to find it.

Example: Simplify

• The HCF of 18 and 24 is 6.
• We can divide both the top and bottom of the fraction by 6:
• Answer:

Example: Simplify

• The HCF of 45 and 60 is 15.
• We can divide both the top and bottom of the fraction by 15:
• Answer:

Example: Simplify

• The HCF of 56 and 98 is 14.
• We can divide both the top and bottom of the fraction by 14:
• Answer:

Example: Simplify

• The HCF of 81x and 108x is 27x.
• We can divide both the top and bottom of the fraction by 27x:
• Answer:

Example: Simplify

• The HCF of and is .
• We can divide both the top and bottom of the fraction by :
• Answer: