To scale a recipe-like quantity, find one scale factor, then multiply every quantity by it. Nothing is added; everything is multiplied.
What is the small gap?
Students change one number (say, servings) and then adjust the rest by eye or by adding the same difference. Every quantity must change by the same factor, so the factor needs to be found first and written down.
How do you scale step by step?
- Find the scale factor: new size ÷ old size.
- Multiply every quantity by that factor.
- Check one quantity the other way round: divide by the factor to get back to the start.
A scaffolded example
An original problem: a kuih recipe for 6 servings uses 240 g of rice flour, 180 ml of coconut milk and 90 g of sugar. Scale it to serve 15.
The scale factor is 15 ÷ 6 = 2.5.
| Ingredient | For 6 | × 2.5 | For 15 |
|---|---|---|---|
| Rice flour | 240 g | 240 × 2.5 | 600 g |
| Coconut milk | 180 ml | 180 × 2.5 | 450 ml |
| Sugar | 90 g | 90 × 2.5 | 225 g |
Reverse check on sugar: 225 ÷ 2.5 = 90. Correct.
What does the common mistake look like?
A student sees that 15 is 9 more than 6 and adds 9 g to each: 249 g, 189 ml, 99 g. Adding a fixed amount to every quantity throws the proportions off, because the recipe for 15 would be mostly flour and hardly sweet.
A quick sense check: 15 servings is more than double 6, so flour must more than double. 249 g does not.
Self-check
A paint mix for 4 litres uses 3 parts blue to 1 part white. A painter needs 10 litres in the same shade. How much blue and white?
Answer
The factor is 10 ÷ 4 = 2.5. For 4 litres, blue is 3 litres and white is 1 litre (3 + 1 = 4 parts of 1 litre).
Scaled: blue 3 × 2.5 = 7.5 litres, white 1 × 2.5 = 2.5 litres. The total is 10 litres, and the ratio 7.5 : 2.5 is still 3 : 1.
Where does this show up in SPM?
In SPM Mathematics, scaling sits in similar shapes, maps and variation. In Science, preparing a solution of a given concentration at a different volume uses exactly this factor.
Scaling only works for proportional situations, so read proportion versus a constant difference. To split a whole between parts, see sharing a quantity in a ratio. The hub shows the order.
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