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.
Ratio is where one number is a multiple of the other. To find out more about ratios, read the following example.
Case study _unit2.7.1 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:
Extract _unit2.7.1
One part + four parts = five parts
If we need 1,000 ml of solution, this means that one part is:
Extract _unit2.7.2
1,000 ml ÷ 5 = 200 ml
The solution needs to be made up as follows:
Extract _unit2.7.3
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:
Extract _unit2.7.4
200 ml + 800 ml = 1,000 ml
Use the example above to help you with the following activity. Remember to check your answers once you have completed the questions.
Box _unit2.7.1
Hint: m^{3} = cubic metres (m × m × m). You will look at volume later in the course.
Activity _unit2.7.1 Activity 18: Using ratios
The ratio of sand to cement required to make concrete is 3:1.
How much of each is needed in order to make 60 m^{3} of concrete?
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?
 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?
Answer
A ratio of 3:1 means three parts of sand to one part of cement, making four parts in total.
We need 60 m^{3} of concrete. If four parts are worth 60 m^{3}, this means that one part is worth:
 60 m^{3} ÷ 4 = 15 m^{3}
So 60 m^{3} of concrete requires:

Sand: three parts × 15 m^{3} = 45 m^{3}
Cement: one part × 15 m^{3} = 15 m^{3}
You can confirm that these figures are correct by adding them and checking that they match the amount needed:
 45 m^{3} + 15 m^{3} = 60 m^{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
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?