Everyday maths for Health and Social Care and Education Support 1

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# 7 Ratios

Along with proportion (which you’ll look at in the next section), you use ratio both in everyday activities and at work, such as cooking, cleaning, preparing a milk formula for a baby or planning a staff rota.

Figure 26 Talking ratios

Ratio is where one number is a multiple of the other. To find out more about ratios, read the following example.

## Example: How to use ratios

Suppose a hospital worker needs to make up one litre (1,000 ml) of bleach solution. The label says that to create a solution you need to add one part bleach to four parts water.

This is a ratio of 1 to 4, or 1:4. This means that the total solution will be made up of:

One part + four parts = five parts

If we need 1,000 ml of solution, this means that one part is:

1,000 ml ÷ 5 = 200 ml

The solution needs to be made up as follows:

Bleach: one part × 200 ml = 200 ml

Water: four parts × 200 ml = 800 ml

So to make one litre (1,000 ml) of solution, you will need to add 200 ml of bleach to 800 ml of water.

You can check your answer by adding the two amounts together. They should equal the total amount needed:

200 ml + 800 ml = 1,000 ml

Hint: m3 = cubic metres (m × m × m). You will look at volume later in the course.

## Activity 18: Using ratios

1. The ratio of patients to staff on an emergency assessment ward is 3:1.

There are 60 people in total.

How many of these are patients and how many are staff?

2. Alex is making bunting for a fayre at a residential care home. She uses 1 blue flag for every 4 cream flags

Alex used 120 flags in total.

How many blue flags and how many cream flags did she need?

3. Alex also prepares dilute juice for visitors at the fayre.

The instructions on the bottle say: Dilute: add 1 part concentrate to 7 parts water.

How much concentrate and water is needed to make 16 litres of juice?

1. A ratio of 3:1 means three parts plus one part, making four parts in total.

If four parts are 60 people, this means that one part is:

• 60 ÷ 4 = 15

So one part is 15 people:

• 3 parts × 15 people = 45 people.

1 part × 15 people = 15 people.

So there are 45 patients and 15 staff.

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

• 45 patients + 15 staff = 60 people
2. The ratio of 1:4 means one part blue flags to four parts cream flags, making five parts in total.

Alex used 120 flags in total. If five parts are worth 120 flags, this means that one part is worth:

• 120 flags ÷ 5 = 24 flags

So 120 flags requires:

• Blue flags: 1 part × 24 = 24 flags

Cream flags: 4 parts × 24 = 96 flags

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

• 24 + 96 = 120 flags
3. A ratio of 1:7 means one part of concentrate to seven parts of water, making eight parts in total.

We need 16 litres of juice. If eight parts are worth 16 litres, this means that one part is worth:

• 16 litres ÷ 8 = 2 litres

So 16 litres of juice requires:

• Concentrate: 1 part × 2 litres = 2 litres

Water: 7 parts × 2 litres = 14 litres

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

• 2 litres + 14 litres = 16 litres

## Summary

You have now learned how to use ratio to solve problems in everyday life and work. This could be when you are mixing a cleaning solution, preparing drinks or ensuring that there are enough staff on duty to safely care for all of the patients in a hospital ward. Can you think of any more examples where you might need to use ratio?

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