- Write in its simplest form.[1]
Loading...
A recipe needs flour and sugar in the ratio . A map uses a scale of . Two friends split a prize . A ratio compares quantities by their relative size, and nearly every ratio problem comes down to one step: find the value of .
The big picture
A ratio says that for every of one thing there are of the other, so the whole is made of equal parts. Once you know what one part is worth — from the total, from one share, or from the difference between shares — every other quantity follows.
Edexcel likes ratio problems that give information indirectly: "Sam gets £36 more than Tia", or a ratio that changes after something is added. Drawing the parts as bars keeps these clear.
What you'll learn
Divide all parts by their highest common factor: .
Convert to the same units first: 45 cm to 2 m is .
To write a ratio in the form , divide both parts by the first: .
Write kg g in its simplest form.
Type it like 3:5.
Tip — A ratio has no units once simplified, but the parts must be measured in the same units before you simplify.
Add the parts to find the total number of shares, divide the amount by that total to find one part, then multiply.
Check that the shares add up to the original amount.
Share £360 in the ratio . How much is the larger share, in pounds?
If you know the difference between two shares, that difference corresponds to the difference in parts.
If you know one share, divide it by its number of parts to find one part.
Two amounts are in the ratio . The larger is 45 more than the smaller. What is the total?
The difference of £36 is not a share of anything on its own — it is the value of the three extra parts Bea has. Matching money to parts, not to people, is the key move.
To combine and , make the shared quantity match. is 3 in one and 4 in the other; the LCM is 12, so scale to and , giving .
A ratio converts to fractions of the whole: in , the first quantity is of the total.
In a club, boys : girls . When 12 more girls join, the ratio becomes . How many members were there originally?
Tip — When a ratio changes, use a letter for one part and write both quantities in terms of it. The number of blue counters did not change, which gives the equation.
Think like an examiner
Ratio
Watch out for these
Stretch yourself
Three sisters share an inheritance in the ratio of their ages, . The eldest receives £4200 more than the youngest. How much is the inheritance, and what does the middle sister receive?
Hint — Find the difference in parts between the eldest and the youngest.
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
Orange paint is made by mixing red and yellow paint in the ratio . Ali has 12 litres of red and 15 litres of yellow.
Unlimited practice
A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.
Generating a question…
Test yourself
Ready to practise Ratio? Pick a mode and earn XP & Dobloons.
Real past-paper questions on Ratio, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.