This area covers four ideas that underlie speed, scale, recipes and sharing: sharing a quantity in a ratio, scaling a model, converting units inside a rate, and deciding whether two quantities are really in proportion.
How do the parts connect?
- Sharing a quantity in a ratio: turn a ratio into equal parts.
- Scaling a recipe-like numerical model: multiply everything by the same factor.
- Converting units in a rate: change km/h to m/s without losing a factor.
- Distinguishing proportion from a constant difference: decide if scaling applies at all.
What does one short example look like?
An original problem: a cyclist rides 18 km in 45 minutes. What is the speed in km/h, and how far in 2 hours at the same speed?
First a unit choice: 45 minutes is 45/60 = 0.75 hours. Speed = 18 ÷ 0.75 = 24 km/h. Then distance in 2 hours is 24 × 2 = 48 km.
A ratio check: 45 minutes to 120 minutes is a scale factor of 120/45 = 8/3, and 18 × 8/3 = 48 km. The two routes agree.
The example used a unit conversion, a rate and scaling in a single question. A slip in any of those three gives a different answer.
Who should start where?
| Symptom | Start with |
|---|---|
| Share a total and the parts do not add up | Sharing in a ratio |
| Change a recipe for more people and lose track | Scaling |
| Speed answers come out in the wrong unit | Converting units in a rate |
| Assume everything doubles when one thing doubles | Proportion versus constant difference |
Go back to all foundation skills or use the prerequisite gap finder if unsure.
These skills return in SPM Mathematics and in Physics speed and density work. If you would like a teacher to work through them, online one-to-one Mathematics tuition begins with a one-hour trial class (from RM50).