Everyday maths 1 (Wales)
Everyday maths 1 (Wales)

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Everyday maths 1 (Wales)

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 …

Described image
Figure 33 A cake

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

  1. 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?

  2. 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?

  3. 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

  1. 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)
  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)
  3. 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.

  1. 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?

  2. 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

  1. 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
  2. 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.

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