Proportion is used to scale quantities up or down by the same ratio. This is shown in the following example: a machine produces 400 bolts in a day. Calculate the number of bolts produced by four machines in five days?
Use the example above to help you with the following activity. Remember to check your answers after you have completed the questions.
Activity 19: Scaling up
Three engine parts cost £360. Calculate the cost of eight parts.
The total mass of 40 house bricks weighs 100 kg. Calculate the total mass of 500 bricks.
10 litres of emulsion costs £25.00 What would you pay for 25 litres?
360 ÷ 3 = 120
120 x 8 = £960
Eight parts cost £960
100 ÷ 40 = 2.5
2.5 x 500 = 1250 kg
500 house bricks weigh 1250 kg
25 ÷ 10 = 2.5
2.5 x 25 = 62.5
10 litres would cost £62.50
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.
A label on a bottle of curtain whitener says that you should add one part concentrated curtain whitener to nine parts water.
How much curtain whitener and water is needed to make up a 2,000 ml solution?
If it takes two men five days to build a wall, how long will it take ten men?
A ratio of 1:9 means one part curtain whitener to nine parts water, making ten parts in total.
You need 2,000 ml of solution. If ten parts are worth 2,000 ml, this means that one part is worth:
- 2,000 ml ÷ 10 = 200 ml
So 2,000 ml of solution requires:
Curtain whitener: one part × 200 ml = 200 ml
Water: nine parts × 200 ml = 1,800 ml
You can confirm that these figures are correct by adding them and checking that they match the amount needed:
- 200 ml + 1,800 ml = 2,000 ml
2 x 5 = 10
10 ÷ 10 = 1
It will take ten men one day.
In this section you have learned how to use proportion to solve simple problems in everyday life.