Ratio questions test whether you can split an amount, scale a quantity up or down, or compare two rates. They are quick once you use the "one part" method.
Sharing in a ratio
- Add the parts of the ratio (3 : 2 has 5 parts).
- Divide the total by the number of parts to find one part.
- Multiply by each share.
Example: $400 shared 3 : 2. One part = 400 ÷ 5 = $80, so the shares are $240 and $160.
Scaling
If a recipe for 4 needs 300 g of rice, a recipe for 10 needs 300 × 10 ÷ 4 = 750 g. Write it as "amount ÷ old size × new size" every time.
Comparing rates
To find the better value, convert both to the same unit: price per 100 g, kilometres per litre, doses per day. Comparing different units is the most common trap.
💡 Check whether the question gives a part-to-part ratio (boys : girls) or a part-to-whole ratio (boys : all students).