# Use Unitary Proportion

In this worksheet, students will practise using the information provided in the question to find the value of one item, then applying this knowledge to solve a related problem.

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 may sound like a challenging concept, but it is actually quite simple when we break it down.

The word UNI means one (think of a unicycle with one wheel) and proportion refers to the relationship between objects.

So unitary proportion is all about finding the value of 1 item and then using this information to solve related problems.

Let's work through an example to see this in action.

e.g. 5 pens cost 55 p. What is the cost of 8 pens?

5 pens = 55 pence

1 pen = 11 pence (55 ÷ 5)

8 pens = 88 pence (11 × 8)

It's really as simple as that!

In this activity, we will practise using the information provided in the question to find the value of one item, then applying this knowledge to solve a related problem.

Type the same number into both spaces to complete the sentence below.

5 pens cost 60 p.

What is the cost of 1 pen?

Match each pair of items and cost on the left with its equivalent on the right which has the same cost per single unit.

## 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
5 rulers cost 75 p
6 rulers cost 54 p
20 rulers cost £1.80

If 3 greeting cards cost 36 p, how much do 8 cards cost?

39 p

12 p

96 p

12 biscuits can be made with 60 g of butter.

How much butter would 9 biscuits need?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

39 p

12 p

96 p

75 maths textbooks cost £900.

How much will 10 textbooks cost?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

39 p

12 p

96 p

If 75 maths textbooks costs £900, how many textbooks can a school buy with £200?

39 p

12 p

96 p

300 kg of oranges cost £186.

How much will 200 kg cost?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

39 p

12 p

96 p

A car uses 25 litres of petrol to travel 400 miles.

How far would it travel on 40 litres

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

39 p

12 p

96 p

A car uses 25 litres of petrol to travel 400 miles.

How much petrol would I need to travel 320 miles?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

39 p

12 p

96 p

• Question 1

Type the same number into both spaces to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
Just remember the prefix 'uni-' means one, and this is the essential thing to achieve in all questions referring to unitary proportion - find the value of one item. Remember this crucial fact to support you in the rest of this activity.
• Question 2

5 pens cost 60 p.

What is the cost of 1 pen?

CORRECT ANSWER
EDDIE SAYS
Let's apply what we know from the question to find the value of one unit. 5 pens = 60 pence 1 pen = 12 pence (60 ÷ 5)
• Question 3

Match each pair of items and cost on the left with its equivalent on the right which has the same cost per single unit.

CORRECT ANSWER

## 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 all the scenarios on the left, and then find the matching single unit cost on the right. For example, if 5 rulers cost 65 p then 1 ruler costs 13 p (65 ÷ 5). 8 rulers cost 104 p, 1 ruler costs 13 p (104 ÷ 8). These two options must go together as both have a single unit cost of 13 p. Can you use this example to help you find the other three matches independently?
• Question 4

If 3 greeting cards cost 36 p, how much do 8 cards cost?

CORRECT ANSWER
96 p
EDDIE SAYS
3 cards = 36 pence 1 card = 12 pence (36 ÷ 3) 8 cards = 96 pence (12 × 8) It's vital to also apply common sense at the end to check that our answer is viable - could 8 greeting cards possibly cost less than 3?
• Question 5

12 biscuits can be made with 60 g of butter.

How much butter would 9 biscuits need?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

CORRECT ANSWER
EDDIE SAYS
If 12 biscuits need 60 g of butter, then 5 g is required to make one biscuit (60 ÷ 12). To make 9 biscuits, we need to multiply the amount required for one by 9: 5 × 9 = 45 g
• Question 6

75 maths textbooks cost £900.

How much will 10 textbooks cost?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

CORRECT ANSWER
EDDIE SAYS
If 75 textbooks cost £900, then the cost for one textbook is £12 (900 ÷ 75). To find the cost of 10 textbooks, we need to multiply the cost for one by 10: 12 × 10 = £120
• Question 7

If 75 maths textbooks costs £900, how many textbooks can a school buy with £200?

CORRECT ANSWER
EDDIE SAYS
We know from the previous question that the cost per textbook is £12. Then we need to know how many the school can buy with a £200 budget. If we divide 200 by 12, the school can buy 16.67 textbooks (rounded to 2 decimal places). The school can't buy part of a textbook, so we need to round this amount down to the nearest whole value, which is 16 textbooks.
• Question 8

300 kg of oranges cost £186.

How much will 200 kg cost?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

CORRECT ANSWER
EDDIE SAYS
It is easier to find the cost of 100 kg as the calculations are simpler to work with, but this method will still work if you choose to use 1 kg instead. If 300 kg of oranges cost £186, then the cost for 100 kg is £62 (186 ÷ 3). To find the cost of 200 kg, we need to multiply the cost for 100 kg by 2: 62 × 2 = £124
• Question 9

A car uses 25 litres of petrol to travel 400 miles.

How far would it travel on 40 litres

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

CORRECT ANSWER
EDDIE SAYS
We can find the value of 5 litres this time as the calculations are easier to work with, but this method will still work if you choose to use 1 litre instead. If a car can travel 400 miles on 25 litres of petrol, then the distance for 5 litres is 80 miles (400 ÷ 5). To find the distance which can be travelled on 40 litres of petrol, we need to multiply the distance for 5 litres by 8: 80 × 8 = 640 miles
• Question 10

A car uses 25 litres of petrol to travel 400 miles.

How much petrol would I need to travel 320 miles?

Take care to only write numbers in the space, as the unit of measurement has already been provided for you.

CORRECT ANSWER
EDDIE SAYS
We know from the previous question that, using 5 litres of petrol, a car can travel 80 miles. 320 ÷ 80 = 4 So if we multiply the number of litres by 4, we will find the number of litres required to travel 320 miles: 5 × 4 = 20 litres You can now use the information provided in the question to find the value of one item, then apply this knowledge to solve a related problem.
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