Simplifying ratios

We can simplify ratios in the same way that we can simplify fractions.

How to simplify ratios

1. Find the highest common factor (HCF) of all the parts of the ratio.
2. Divide each part of the ratio by the HCF.
3. Write the new ratio.

Simplify 12:16

• The HCF of 12 and 16 is 4.
• We divide both parts of the ratio by 4:
  • 12 \div 4 = 3
  • 16 \div 4 = 4
• So, the simplified ratio is 3:4.

Simplify 18:24:30

• The HCF of 18, 24 and 30 is 6.
• We divide each part of the ratio by 6:
  • 18 \div 6 = 3
  • 24 \div 6 = 4
  • 30 \div 6 = 5
• So, the simplified ratio is 3:4:5.

Simplify 45:60

• The HCF of 45 and 60 is 15.
• We divide both parts of the ratio by 15:
  • 45 \div 15 = 3
  • 60 \div 15 = 4
• So, the simplified ratio is 3:4.

Simplify 100x:250x^2:400x

• The HCF of 100x, 250x^2 and 400x is 50x.
• We divide each part of the ratio by 50x:
  • 100x \div 50x = 2
  • 250x^2 \div 50x = 5x
  • 400x \div 50x = 8
• So, the simplified ratio is 2:5x:8.