GCSE maths · Ratio, proportion and rates of change
Ratio: simplifying and sharing
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.
1Simplify using HCF
Divide both parts of a ratio by their highest common factor until you cannot divide further.
Think of it like
Think of a ratio as two piles of counters shrinking together, both split into the same size groups.
Worked example
Simplify the ratio 32:48 into the form x:3.
- HCF of 32 and 48 = 16find biggest shared factor
- divide both parts by it
- Answer
TrapIf you divide the two parts by different numbers, the ratio changes value.
Explain it back
Why must you divide both parts by the same number?
Say it out loud in two or three sentences. Where you get stuck is what to revise.
2Share using one part
Add the parts, divide the total by that sum, then multiply to find each share.
Think of it like
Cut a cake into equal slices first, then hand out groups of slices to match the ratio.
Worked example
Share £220 in the ratio 4:7. How much is the larger share?
- add the parts
- find value of one part
- multiply for larger share
- Answer£140
TrapIf you divide the total by one of the ratio numbers instead of their sum, shares are wrong.
Explain it back
Why do you add the parts before dividing the total?
3Ratio to fraction
Add the parts for the whole, then put each part over that total as a fraction.
Think of it like
Picture the ratio as slices of one pizza; the total slices make the whole pizza.
Worked example
The ratio of cats to dogs at a shelter is 4:9. Write the fraction of animals that are dogs, in simplest form.
- add parts for whole
- Answerpart over the total
TrapIf you write the fraction over one part instead of the total, it is too big.
Explain it back
Why does the total number of parts become the denominator?
Practise with Mathable
Practise ratio with a tutor that checks every line
- ›Ten questions on ratio, 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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