To scale a recipe, find one scale factor, convert any mixed units, and multiply every ingredient by the same factor. Questions on recipes, paint mixes, maps and model scales all use this skill, and unit conversion is where most marks disappear.
Why does one factor work for everything?
A recipe is a set of quantities in fixed ratios. If you want twice the amount of food, every ingredient doubles. If you want 2.5 times as much, every ingredient is multiplied by 2.5.
Using different factors for different ingredients changes the ratios, so the food tastes different. One factor keeps the recipe balanced.
How to scale, step by step
- Find the factor: new amount ÷ old amount, in the same unit.
- Convert awkward units to a convenient one (g, ml or cm) before multiplying.
- Multiply each quantity by the factor.
- Convert back if the question asks for kg, litres or km.
Worked example
A recipe for 4 people uses 300 g flour, 0.5 litre milk, 80 g sugar and 2 eggs. Scale it for 10 people.
Step 1, factor: 10 ÷ 4 = 2.5.
Step 2, multiply:
| Ingredient | For 4 | For 10 |
|---|---|---|
| Flour | 300 g | 300 × 2.5 = 750 g |
| Milk | 0.5 litre = 500 ml | 500 × 2.5 = 1250 ml = 1.25 litres |
| Sugar | 80 g | 80 × 2.5 = 200 g |
| Eggs | 2 | 2 × 2.5 = 5 |
Check: 10 people is 2.5 times as many, and 2.5 × 4 = 10. The milk is 1250 ml, and 1250 ÷ 500 = 2.5, so the factor is the same throughout.
Now a mixed-unit question.
You have a 2 kg bag of flour. How many people can you serve with the recipe above?
Convert first: 2 kg = 2000 g. The flour for one person is 300 ÷ 4 = 75 g, and 2000 ÷ 75 = 26.67, so you can serve 26 people, not 27, because 27 people need 2025 g.
The mistake to watch for
A common slip is to write a ratio without converting to the same unit.
Mistaken working: ratio of 600 g to 1.5 kg is 600 : 1.5 = 400 : 1.
This says the first amount is 400 times the second, yet 600 g is less than 1.5 kg.
The correction is to convert 1.5 kg = 1500 g, so the ratio is 600 : 1500. Dividing both by 300 gives 2 : 5. A quick sense check helps: the first quantity is smaller, so the first ratio number should be smaller.
Check yourself
1. A recipe for 6 uses 450 g rice, 0.9 litre water and 2 tsp salt. Scale it for 9 people.
Show answer
Factor: 9 ÷ 6 = 1.5.
Rice: 450 × 1.5 = 675 g. Water: 0.9 × 1.5 = 1.35 litres (1350 ml). Salt: 2 × 1.5 = 3 tsp.
675 g, 1.35 litres, 3 tsp.
2. Write 450 ml to 1.2 litres as a ratio in its simplest form.
Show answer
Convert: 1.2 litres = 1200 ml. Ratio 450 : 1200.
Divide both by 150: 450 ÷ 150 = 3 and 1200 ÷ 150 = 8. 3 : 8.
3. A map has a scale of 1 : 50 000. A path is 3.5 cm long on the map. How long is it in real life, in km?
Show answer
Real length: 3.5 × 50 000 = 175 000 cm.
175 000 cm ÷ 100 = 1750 m, and 1750 ÷ 1000 = 1.75 km.
Where this leads next
Next, read distinguishing a ratio from a fraction of the total. For practice with lengths and scales, the map scale practice tool shows the conversions step by step.
If unit conversions keep costing you marks in otherwise correct working, online one-to-one Mathematics tuition gives a teacher the chance to spot the exact step where the units change.