Everyday maths for Health and Social Care and Education Support 1
Everyday maths for Health and Social Care and Education Support 1

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Everyday maths for Health and Social Care and Education Support 1

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 27 A cake

Frank is a support worker in a residential children’s home. He is making a cake with a group of children to celebrate one of their birthdays.

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

They need to adapt the recipe so that there is enough for eight people.

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

  1. This recipe makes ten healthy breakfast bars:
    • 220 g oats
    • 150 g mixed dried fruit
    • 100 g brown sugar
    • 2 apples

    How much of each ingredient is needed to make 20 breakfast bars?

  2. This recipe makes four servings of strawberry fruit smoothie:
    • 800 ml milk
    • 200 g strawberries
    • 4 scoops of natural yoghurt

    How much of each ingredient is needed for two people?

  3. This recipe makes a meal replacement drink 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 breakfast bars you need twice as much of each ingredient:
    • 440 g oats (220 × 2)
    • 300 g mixed dried fruit (150 × 2)
    • 200 g brown sugar (100 × 2)
    • 4 apples (2 × 2)
  2. To make fruit smoothies for two people you need half as much of each ingredient:
    • 400 ml milk (800 ÷ 2)
    • 100 g strawberries (200 ÷ 2)
    • 2 scoops of natural yogurt (4 ÷ 2)
  3. To make a meal replacement drink 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.

  1. A day centre for respite care must have 1 staff member on duty for every 9 service users.

    How many staff members are needed to care for 90 service users?

  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 staff member can look after 9 service users.

    To care for 90 service users:

    • 90 ÷ 9 = 10

    So 10 staff members are required to care for 90 service users.

  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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