Ratio and proportion
A ratio compares quantities multiplicatively. In direct proportion y/x is constant; in inverse proportion xy is constant. Decide which relationship the situation states rather than assuming that every increase must be proportional.
What this guide covers
Ratios, distance and area scales, direct proportion and inverse proportion. Convert quantities to the same unit before comparing them.
Syllabus reference: 2026 Mathematics 4052, N2, page 5. These are Mentora search groupings, not new official syllabus categories.
Worked example
y is inversely proportional to x. When x = 4, y = 15. Find y when x = 10.
Write y = k/x, so k = xy = 4 × 15 = 60. When x = 10, y = 60/10 = 6. The product remains 60, which checks the relationship.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Simplify the ratio 0.6 kg : 150 g.
Show worked answer
Convert 0.6 kg to 600 g. Then 600 : 150 = 4 : 1.
Check 2
Share $84 in the ratio 2 : 5.
Show worked answer
There are 7 parts, so one part is $12. The shares are $24 and $60; they total $84.
Check 3
A map scale is 1 : 20 000. What actual distance does 3.5 cm represent?
Show worked answer
Actual distance = 3.5 × 20 000 = 70 000 cm = 700 m. A length scale applies here; an area conversion would require squaring the scale factor.
Common mistakes to watch for
- Keep the order of the quantities consistent when writing a ratio.
- A ratio of parts does not directly give a tion of the whole: 2 : 5 means the first share is 2/7 of the total.
- Do not apply a length scale once to an area; area scale factors are squared.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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More G3 Math topicsPublished by Mentora · Sources checked 11 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.