# Unit 7 Section 2 : Direct Proportion

Direct proportion involves situations where two values vary, but the ratio between the values stays the same.
You can use direct proportion to answer questions like the one below:

## Example Question

If 10 calculators cost £120, how much will 8 calculators cost?

Starting fact: 10 calculators cost £120

To solve this, we need to change "10 calculators" into "8 calculators".
We start by finding out what 1 calculator costs, by dividing both parts of our fact by 10:

New fact: 1 calculator costs £12

Now we need to change "1 calculator" into "8 calculators".
We can do this by multiplying both parts of our fact by 8:

Method
Every time we want to answer a question like this, we start by altering the fact so that it just shows what one of
something costs. In the above example, we worked out what one calculator costed. We could then use this to
work out what eight calculators costs. This is sometimes called the unitary method.

Practice Questions
Work out the answer to each of these questions then click on the button marked to see whether you are correct.

(a) If 5 bags of sweets contain 90 sweets in total, calculate how many sweets seven bags will contain? (b) If 25 floppy disks cost £5.50, calculate the cost of 11 floppy disks. ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
If 5 tickets for a play cost £40, calculate the cost of:
 (a) 6 tickets    £  (b) 9 tickets    £  (c) 20 tickets    £  Question 2
To make 3 glasses of orange squash you need 600ml of water.
Work out how much water you need to make:
 (a) 5 glasses of squash     ml  (b) 7 glasses of squash     ml  (c) 1 glass of squash     ml  Question 3
If 10 litres of petrol cost £8.20, calculate the cost of:
 (a) 4 litres    £  (b) 12 litres    £  (c) 30 litres    £  Question 4
A baker uses 1800 grams of flour to make 3 loaves of bread.
How much flour will he need use if he wants to make:
 (a) 2 loaves    grams  (b) 7 loaves    grams  (c) 24 loaves    grams  Question 5
Ben buys 21 football stickers for 84p.
Calculate the cost of:
 (a) 7 stickers    pence  (b) 12 stickers    pence  (c) 50 stickers    £  Question 6
A 20 metre length of rope costs £14.40.
 (a) Calculate the cost of 12m of rope: £  (b) Work out the cost of the rope per metre: pence per metre  Question 7
16 teams, each with the same number of people, enter a quiz.
At the semi-final stage there are 12 people left in the competition.

How many people entered the competition?
people  Question 8
Three identical coaches can carry a total of 162 passengers.

How many passengers can be carried on seven of these coaches?
people  Question 9
The total mass of 200 concrete blocks is 1460kg.

Calculate the mass of 900 concrete blocks.
kg  You have now completed Unit 7 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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