# 8 Proportion

Proportion is used to scale quantities up or down by the same ratio. This is shown in the following example – what happens if you want to adapt a favourite recipe to serve more people?

## Example: Using proportion for more portions …

Here is a recipe for making a sponge cake for four people:

4 oz self-raising flour

4 oz caster sugar

4 oz butter

2 eggs

How much of each ingredient is needed to make a cake for eight people?

### Method

To make a cake for eight people you need twice the amount of each ingredient:

8 oz self-raising flour (4 × 2)

8 oz caster sugar (4 × 2)

8 oz butter (4 × 2)

4 eggs (2 × 2)

Use the example above to help you with the following activity. Remember to check your answers once you have completed the questions.

## Activity 38: Scaling up recipes

- This recipe makes ten large cookies:
- 220 g self-raising flour
- 150 g butter
- 100 g caster sugar
- 2 eggs

How much of each ingredient is needed to make 20 cookies?

- This recipe makes four servings of strawberry milkshake:
- 800 ml milk
- 200 g strawberries
- 4 scoops of ice cream

How much of each ingredient is needed for two people?

- This recipe makes dessert for two people:
- 300 ml milk
- 60 g powder

How much of each ingredient is needed to serve six people?

### Answer

- To make 20 cookies you need twice as much of each ingredient:
- 440 g flour (220 × 2)
- 300 g butter (150 × 2)
- 200 g sugar (100 × 2)
- 4 eggs (2 × 2)

- To make milkshakes for two people you need half as much of each ingredient:
- 400 ml milk (800 ÷ 2)
- 100 g strawberries (200 ÷ 2)
- 2 scoops of ice cream (4 ÷ 2)

- To make dessert for six people you need three times the amount of each ingredient:
- 900 ml milk (300 × 3)
- 180 g powder (60 × 3)

Once you have checked your answers and have got them all correct, please have a go at the next activity.

## Activity 39: Looking at ratio and proportion

**Note:** Calculators not allowed.

A label on a bottle of curtain whitener says that you should add one part concentrated curtain whitener to nine parts water.

How much curtain whitener and water is needed to make up a 2 000 ml solution?

Here is a recipe for a low-fat risotto for two people:

- 200 g mushrooms
- 175 g rice
- 180 ml water
- 180 ml evaporated milk
- Salt and pepper

How much of each ingredient is needed if you want to cook enough risotto for six people?

### Answer

A ratio of 1:9 means one part curtain whitener to nine parts water, making ten parts in total.

You need 2 000 ml of solution. If ten parts are worth 2 000 ml, this means that one part is worth:

- 2 000 ml ÷ 10 = 200 ml

So 2 000 ml of solution requires:

Curtain whitener: one part × 200 ml = 200 ml

Water: nine parts × 200 ml = 1 800 ml

You can confirm that these figures are correct by adding them and checking that they match the amount needed:

- 200 ml + 1 800 ml = 2 000 ml

- To make enough risotto for six people you need three times as much of each ingredient:
- 600 g of mushrooms (200 × 3)
- 525 g of rice (175 × 3)
- 540 ml of water (180 × 3)
- 540 ml of evaporated milk (180 × 3)

## Summary

In this section you have learned how to use proportion to solve simple problems in everyday life, for example when adapting recipes.