Everyday maths for Health and Social Care and Education Support 1

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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 …

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)

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?

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?

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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