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 19: 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 20: 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 mushrooms (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.