GCSE maths · Number
Adding, multiplying and dividing fractions
Revision notes for Foundation and Higher. Three ideas, each with a worked example, the reason for every line, and the trap to avoid.
Every worked example was checked by the code that marks Mathable’s tests.
1Find a common denominator
Fractions need the same denominator before you can add or subtract the numerators.
Think of it like
You can't add 3 apples and 2 oranges; rename both as pieces of the same size first.
Worked example
Work out 1/6 + 3/8, giving your answer as a fraction in its simplest form.
- LCM of 6 and 8 = 24find common denominator
- rewrite both fractions
- Answeradd numerators only
TrapIf you add numerators and denominators straight away, you get 4/14 which is wrong.
Explain it back
Why must fractions have the same denominator before adding?
Say it out loud in two or three sentences. Where you get stuck is what to revise.
2Multiply, or flip to divide
Multiply straight across; to divide, flip the second fraction and multiply instead.
Think of it like
Dividing by a fraction is like asking how many of it fit, so flip and multiply.
Worked example
Work out 3/5 divided by 7/10, giving your answer as a fraction in its simplest form.
- flip second fraction
- multiply numerators denominators
- Answerdivide top bottom by 5
TrapIf you flip the first fraction instead of the second, your answer is upside down.
Explain it back
Why does dividing by a fraction mean multiplying by its reciprocal?
3Simplify the final fraction
Divide the top and bottom by their highest common factor until no number divides both.
Think of it like
Think of cutting a pizza into fewer, bigger slices that cover the exact same amount.
Worked example
Work out 8/9 × 3/4, giving your answer as a fraction in its simplest form.
- multiply across first
- HCF of 24 and 36 = 12find highest common factor
- Answerdivide top and bottom
TrapIf you leave the answer as 24/36, you lose marks for not simplifying fully.
Explain it back
Why does dividing top and bottom by the same number keep the value?
Practise with Mathable
Practise fractions with a tutor that checks every line
- ›Ten questions on fractions, marked for you.
- ›It points at the first mistake in your working.
- ›One hint at a time, so you work out the fix yourself.
- ›Explain an idea back, and it tells you the one gap.
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