Study Tips
How to Understand Ratio and Proportion
By Sana Iqbal · · 4 min read
Quick answer
A ratio compares two or more quantities, like 2:3. To share an amount in a ratio, add the parts to find how many shares there are, divide the total by that, then multiply out. Proportion problems keep quantities in the same relationship as one scales — recipes, maps and speeds are all proportion.
What a ratio says
A ratio like 2:3 says that for every 2 of one thing there are 3 of another. It is a comparison, not a total — 2:3 could mean 2 and 3, or 20 and 30, or 200 and 300.
That relative nature is the key idea. A ratio fixes the relationship between quantities without fixing their actual size.
Sharing in a ratio
To split 40 sweets in the ratio 3:5, add the parts (3 + 5 = 8 shares), divide the total by the number of shares (40 ÷ 8 = 5 per share), then multiply out (15 and 25).
This three-step method — total the parts, find one share, scale up — solves every 'share in a ratio' question. Skipping the first step is the usual error.
Simplifying and equivalent ratios
Ratios simplify like fractions: 20:30 divides down to 2:3. Equivalent ratios describe the same relationship at different scales, which is exactly what you use when scaling a recipe up or down.
Being able to move between equivalent ratios fluently is what makes proportion problems quick.
Direct proportion
In direct proportion, quantities rise and fall together at a fixed rate — double the recipe, double every ingredient. If 3 pens cost 90p, one costs 30p, and any number costs 30p each.
Finding the value of one unit first — the 'unitary method' — turns most proportion questions into simple multiplication.
Inverse proportion
Sometimes one quantity rises as another falls: more workers means less time for a job. Here the product stays constant rather than the ratio, so the method differs — multiply to find the constant, then divide.
Spotting whether a problem is direct or inverse is the crucial decision. 'More means more' is direct; 'more means less' is inverse.
Ratios in disguise
Many exam questions are ratio problems without saying so — mixing, scaling, best-value comparisons, map scales, currency conversion. Recognising the hidden ratio is often the hardest part.
If a question relates two quantities that scale together, it is almost certainly ratio or proportion, whatever words it uses.
Frequently asked questions
How do I share an amount in a given ratio?+
Add the parts of the ratio to find the total shares, divide the amount by that to find one share, then multiply each part out. For 40 in 3:5, that is 8 shares, 5 each, giving 15 and 25.
What's the difference between direct and inverse proportion?+
In direct proportion quantities rise and fall together — double one, double the other. In inverse proportion one rises as the other falls, like more workers taking less time, so their product stays constant.
How do I simplify a ratio?+
Divide all parts by their highest common factor, exactly like simplifying a fraction. 20:30 becomes 2:3. Simplified ratios are easier to compare and scale.
What is the unitary method?+
Finding the value of a single unit first, then multiplying. If 3 items cost 90p, one costs 30p, so any number is easy to work out. It solves most proportion problems quickly.
How do I spot a ratio problem?+
If a question relates two quantities that scale together — mixing, map scales, currency, best value — it is almost certainly ratio or proportion, even when those words are not used.
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