Year 8: Simplify fractions

Simplifying fractions means reducing a fraction to its simplest form. This means the numerator (top number) and the denominator (bottom number) have no common factors other than 1.

What is a Common Factor?

A common factor is a number that divides evenly into both the numerator and denominator.

How to Simplify Fractions

1. Find the greatest common factor (GCF), also known as the highest common factor (HCF): Find the largest number that divides evenly into both the numerator and denominator.
2. Divide: Divide both the numerator and denominator by the HCF.

Example

Let's simplify 6/8:

1. The factors of 6 are: 1, 2, 3, 6
2. The factors of 8 are: 1, 2, 4, 8
3. The highest common factor (HCF) is 2.
4. Divide both by 2: 6 ÷ 2 = 3 and 8 ÷ 2 = 4.
5. Therefore, the simplified fraction is 3/4.

Tips

Always look for common factors.

It’s okay to use a factor tree to find the prime factors.

Make sure your final answer is in its simplest form – check if the numerator and denominator share any more common factors.