Equivalent fractions
Two fractions are equivalent when they represent the same proportion: ½ = &frac24; = &frac{50}{100}.
Year 3 introduces equivalent fractions visually (a half is the same as two quarters). By Year 5 children find equivalents algebraically: multiply or divide both numerator and denominator by the same non-zero number.
Worked examples
½ = &frac24; = &frac36; = &frac48;. Multiply top and bottom by 2, 3, 4 ...
&frac{12}{18} = &frac23. Divide top and bottom by 6 (the HCF).
Simplest form: &frac{15}{20} = ¾. Divide both by 5.
Frequently asked questions
How do I know it's in simplest form?
When the HCF (highest common factor) of numerator and denominator is 1. The fraction simplifier above does it for you.
Are these the same as ‘cancelling’?
Yes — cancelling means dividing top and bottom by their HCF. Same operation, different name.