O-Level E-Math and SEC G3 Mathematics K310
N2: Ratio and proportion
Translate ratios, scales, direct comparisons, and proportional change into a consistent working method.
Core notes
Ratio compares quantities multiplicatively. Proportion turns that comparison into a relationship that can be scaled, modelled on a map, or expressed as a direct or inverse formula.
Ratios with rational numbers
A ratio may contain fractions or decimals. Clear denominators or decimal places across every part, then divide by the greatest common factor. Keep the order tied to the labels in the question.
Map scales
A linear scale compares distances. If the linear scale factor is , the area scale factor is . Convert map and actual measurements to the same unit before applying either relationship.
Direct and inverse proportion
For direct proportion, the ratio is constant, so . For inverse proportion, the product is constant, so . Find from one complete pair before using the model.
Formulae and methods
| Relationship | Use |
|---|---|
| Direct proportion. | |
| Inverse proportion. | |
| Convert a linear scale factor into an area scale factor. |
Worked examples
Example 1: Simplify .
- Write .
- Multiply every part by to clear denominators.
- Obtain , then divide by .
Answer: The simplified ratio is .
Example 2: The time is inversely proportional to the number of workers . If workers take hours, find the time for workers.
- Write .
- Find .
- Use .
Answer: The time is hours.
Chapter checkpoint
- Convert quantities to common units before forming or simplifying a ratio.
- Identify whether the scale applies to lengths, areas, or another quantity.
- Test whether the relationship is direct or inverse before writing its constant of proportionality.
Exam traps and retrieval check
Avoid these traps
- Comparing quantities before converting their units.
- Squaring the numerical map length instead of the linear scale factor when finding an area scale.
- Assuming every increasing relationship is directly proportional.
Check from memory
What stays constant in direct proportion?
The ratio .
What stays constant in inverse proportion?
The product .
If lengths scale by , how do areas scale?
Areas scale by .
Official K310 coverage
This chapter maps to 4 official outcomes: N2.1, N2.2, N2.3, N2.4. Check the official 2027 K310 syllabus for exact assessable wording and paper details.