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:

Answer: 8 calculators cost 96

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 Click on this button below to see the correct answer 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.



Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct 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 Click on this button to see the correct answer 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
(b) 7 glasses of squash
(c) 1 glass of squash
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
(b) 7 loaves
(c) 24 loaves
Question 5
Ben buys 21 football stickers for 84p.
Calculate the cost of:
(a) 7 stickers
(b) 12 stickers
(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?

Question 8
Three identical coaches can carry a total of 162 passengers.

How many passengers can be carried on seven of these coaches?

Question 9
The total mass of 200 concrete blocks is 1460kg.

Calculate the mass of 900 concrete blocks.

You have now completed Unit 7 Section 2
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Produced by A.J. Reynolds October 2003