 Everyday maths 1 (Wales)

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7 Ratios

Along with proportion (which you’ll look at in the next section), you use ratio in everyday activities such as gardening, cooking, cleaning and DIY. Figure 32 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 you need 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

Activity 37: Using ratios

1. There are 17 students in a class: ten are male and seven are female. Write the ratio of male to female students.
2. The ratio of sand to cement required to make concrete is 3:1.

If you have 40kg of cement, how much sand should you have?

3. Read the label from a bottle of wallpaper stripper:

• Dilute: add 1 part wallpaper stripper to 7 parts water.

How much wallpaper stripper and water is needed to make 16 litres of solution?

4. To make a solution of hair colourant you need to add one part of hair colourant to four parts of water. How much hair colourant and water is needed to make 400 ml of solution?

1. 10:7
2. A ratio of 3:1 means three parts of sand to one part of cement, making four parts in total. If the cement (one part) is 40kg, then the sand (three parts) will be:
• 3 × 40 kg = 120 kg
3. A ratio of 1:7 means one part of wallpaper stripper to seven parts of water, making eight parts in total.

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

• 16 litres ÷ 8 = 2 litres

So 16 litres of solution requires:

• Wallpaper stripper: one part × 2 litres = 2 litres

Water: seven 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
4. The ratio of 1:4 means one part hair colourant to four parts water, making five parts in total.

We need 400 ml of solution. If five parts are worth 400 ml, this means that one part is worth:

• 400 ml ÷ 5 = 80 ml

So 400 ml of solution requires:

• Hair colourant: one part × 80 ml = 80 ml

Water: four parts × 80 ml = 320 ml

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

• 80 ml + 320 ml = 400 ml

Summary

You have now learned how to use ratio to solve problems in everyday life. This could be when you are mixing concrete, hair colourant or screen wash. Can you think of any more examples where you might need to use ratio?

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