 # Use Basic Unitary Proportion

In this worksheet, students practise using unitary proportion to find the cost of items. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Direct and Inverse Proportion

Difficulty level:   ### QUESTION 1 of 10

Unitary proportion sounds scary, but its quite simple. The word UNI means one (think of unicycle - one wheel) and proportion is about the relationship between objects.

So Unitary proportion is all about finding the value of 1 item and then using this.

Example: 5 pens cost 55 p, what is the cost of 8 pens?

5 pens = 55 pence

1 pen = 11 pence (Just divide by 5)

8 pens = 88 pence (Multiply by 8)

Complete the following sentence...

5 pens cost 60 p.

What is the cost (in pence) of 1 pen?

Match the amounts.

## Column B

5 rulers cost 65p
8 rulers costs £1.04
2 rulers cost 30 p
3 rulers cost 30p
12 rulers cost £1.20
20 rulers cost £1.80
6 rulers cost 54 p
5 rulers cost 75 p

If 3 pencils cost 36 p, do 8 rulers cost...

96 p

12 p

12 biscuits need 60 g of butter. How much butter would 9 biscuits need?

75 Maths textbooks costs £900. How much will 10 textbooks cost?

75 Maths textbooks costs £900.How many textbooks can I buy for £200?

300 kg of coal cost £186. How much will 200 kg cost?

A car uses 25 Litres of petrol to travel 400 miles. How far would it travel on 40 Litres.

(Don't worry about the units here)

A car uses 25 Litres of petrol to travel 400 miles. How much fuel would I need to travel 320 miles

(Don't worry about the units here)

• Question 1

Complete the following sentence...

EDDIE SAYS
Just remember, UNI means the number 1. It's all about finding one,
• Question 2

5 pens cost 60 p.

What is the cost (in pence) of 1 pen?

12
EDDIE SAYS
All we need to do here is to divide by 5. This will give the cost of 1 pen.
• Question 3

Match the amounts.

## Column B

5 rulers cost 65p
8 rulers costs £1.04
2 rulers cost 30 p
5 rulers cost 75 p
12 rulers cost £1.20
3 rulers cost 30p
6 rulers cost 54 p
20 rulers cost £1.80
EDDIE SAYS
To match these, we need to find the cost of 1 ruler in both the question and the answers. For example... If 5 rulers cost 65 p, 1 ruler costs 13 p 8 rulers cost 104 p, 1 ruler costs 13 p These two options must go together.
• Question 4

If 3 pencils cost 36 p, do 8 rulers cost...

96 p
EDDIE SAYS
It's vital here to think if your answer is correct, could 8 pencils cost less than 3? This is a really common mistake, people often forget to do the multiply at the end.
• Question 5

12 biscuits need 60 g of butter. How much butter would 9 biscuits need?

45
EDDIE SAYS
if 12 biscuits need 60 g This means 1 will need 5 g All we need to do is try and find how many 9 biscuits will need,
• Question 6

75 Maths textbooks costs £900. How much will 10 textbooks cost?

120
£120
£ 120
EDDIE SAYS
If 75 books cost £900, we can work out that one book costs £12. It's then just a case of finding the cost of 10.
• Question 7

75 Maths textbooks costs £900.How many textbooks can I buy for £200?

16
EDDIE SAYS
If 75 books cost £900, we can work out that one book costs £12. Then we need to know how many we can buy for £200 If we divide 200 by 12 we can buy 16.67 textbooks. We can't buy part of a textbook so we can only get .....
• Question 8

300 kg of coal cost £186. How much will 200 kg cost?

124
£124
£ 124
EDDIE SAYS
We know that we need to find the cost of 1 kg. 186 ÷ 300 = £ 0.62 How can we use this to find the cost of 200 kg?
• Question 9

A car uses 25 Litres of petrol to travel 400 miles. How far would it travel on 40 Litres.

(Don't worry about the units here)

EDDIE SAYS
The thing that is changing here is the amount of petrol, so we need to find the distance for 1 litre. 25 L = 400 miles 1 L = 16 miles
• Question 10

A car uses 25 Litres of petrol to travel 400 miles. How much fuel would I need to travel 320 miles

(Don't worry about the units here)

20
EDDIE SAYS
The thing that is changing here is the distance, so we need to know is how much fuel per miles 400 miles = 25 L 1 mile = 0.0625 L
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