Scaling and Recipes

In a Nutshell

To scale a recipe up or down, find the scale factor and multiply every ingredient by it.

A recipe is a set of quantities in proportion. To change the number of servings, find the scale factor:

Scale factor=New servingsOriginal servings\text{Scale factor} = \frac{\text{New servings}}{\text{Original servings}}

Then multiply every ingredient by this factor. For example, if a recipe serves 4 and you need it for 6:

Scale factor=64=1.5\text{Scale factor} = \frac{6}{4} = 1.5

So every ingredient is multiplied by 1.5.

Proportion table A table showing Original (g) values 100,200,50,150,250 and Scaled (g) values that are each 1.5 times Original (g). The multiplier is 1.5. Original (g) Scaled (g) 100 150 ×1.5 200 300 ×1.5 50 75 ×1.5 150 225 ×1.5 250 375 ×1.5 Scaled (g) = 1.5 × Original (g)

The table shows each original ingredient multiplied by the scale factor. Try changing the multiplier to scale for different numbers of servings.

Watch it work

Question: A cake recipe for 8 people uses 240 g of flour, 160 g of sugar and 4 eggs. How much of each ingredient is needed for 12 people?

Have a go

Q1. A recipe for 4 uses 200 g of pasta. How much pasta is needed for 10 people?

Q2. A smoothie for 2 people uses 300 ml of milk and 4 bananas. How much milk and how many bananas for 5 people?

Q3. A recipe for 6 uses 450 g of chicken. How much chicken is needed for 2 people?

Q4. A recipe for 5 needs 125 ml of oil. How much oil for 8 people?