 # Convert Ratios to Fractions

In this worksheet, students practise converting a fraction into a ratio. 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, Calculations with Ratio

Difficulty level:   ### QUESTION 1 of 10

Ratio and proportion are two very closely linked topics.

Proportion is used to show parts of a whole and ratios are used to compare two (or more) amounts.

Converting fractions into ratios is slightly easier if you look at it the other way round first.

Example 1: I have red and green beads in the ratio of 7: 3. What fraction of the beads are red?

Firstly, we need to know how many parts there are in total. If I have a ratio of 7:3, this means there are 10 parts in total, (Just add them together)

If 7 of these parts are red, the fraction of red balls is 7/10

So how do we do this the other way round.

Example 2: Write 3/4 as a ratio.

3/4 means 'three out of four'. If we wrote this as a ratio, we are looking for 4 parts in total and one of the numbers in the ratio must be 3.

The only way we can do this is if the ratio is 3:1

Is it always this easy?

Unfortunatly no, there is one exception. This exception is if we use a fraction doesn't represent part of a whole.

Example 3: James has 3/5 as many marbles as John. Write the total number of marbles as a simplified ratio.

We know that James has 3/5 of a marble for each one that John has. We could write this as ...

 3 5
: 1

But we know that we can't have a fraction in a ratio so I multiply both sides by 5. This gives me 3:5

Give me some algebra!

Situation 1: A fraction of a whole.

 a b
= a: b - a

Situation 2: Fraction used as a rlationship between two variables

 a b
: a: b

Complete the following sentence.

Can you finish the sentence?

Write 3/4 as a ratio.

3:1

3:4

Write 4/5 as a ratio.

4:5

4:1

Match the ratio to the fraction.

## Column B

3:2
3/5
5:6
1/3
1:2
3/10
3:7
5/11

Match the fraction to the ratio

## Column B

2/7
3:6
1/3
4:6
3/11
3:8
2/5
2:5

What is 2/7 as a ratio?

What is 3/10 as a ratio?

Andy gets 2/5 of the sweets from a pack and Louise gets the rest.

What is the ratio of sweets that Andy and Louise get?

Rick is 4/5 of the age of Rob. Write the age of Rick to Rob in it's simplest form.

• Question 1

Complete the following sentence.

EDDIE SAYS
Proportion is all about representing part of a whole. Don't forget these can be written as fractions, decimals and percentages.
• Question 2

Can you finish the sentence?

EDDIE SAYS
Ratios are all about showing the relationship between two or more items so that we can compare them.
• Question 3

Write 3/4 as a ratio.

3:1
EDDIE SAYS
This fraction isn't defining any quantities so we just use the denominator (4) to show how many parts are in the ratio altogether. The 3 must be one of the numbers in the ratio,
• Question 4

Write 4/5 as a ratio.

4:1
EDDIE SAYS
This fraction isn't defining any quantities so we just use the denominator (4) to show how many parts are in the ratio altogether. The 4 must be one of the numbers in the ratio,
• Question 5

Match the ratio to the fraction.

## Column B

3:2
3/5
5:6
5/11
1:2
1/3
3:7
3/10
EDDIE SAYS
Remember, the denominator is given by adding together the numbers in the ratio. The numerator is given by one of the numbers in the ratio.
• Question 6

Match the fraction to the ratio

## Column B

2/7
2:5
1/3
3:6
3/11
3:8
2/5
4:6
EDDIE SAYS
This is actually easier if you work backwards. Example 4:6 must have a denominator of 10 (4+6 = 10) and a numerator of 4. But 4/10 isn't in the list! Did you remember to cancel?
• Question 7

What is 2/7 as a ratio?

2:5
5:2
EDDIE SAYS
When we are converting a fraction into a ratio. The two numbers must add up to the denominator (7) and one of the numbers must be the numerator (2). This only leaves us with two options.
• Question 8

What is 3/10 as a ratio?

3:7
7:3
EDDIE SAYS
When we are converting a fraction into a ratio. The two numbers must add up to the denominator (10) and one of the numbers must be the numerator (3). This only leaves us with two options.
• Question 9

Andy gets 2/5 of the sweets from a pack and Louise gets the rest.

What is the ratio of sweets that Andy and Louise get?

EDDIE SAYS
In this question, we are looking at fractions of a whole. Out of 5 parts, Andy gets 2 parts and Louise gets 3 parts. This gives a ratio of 2:3 Note that the order is important, you can't have 3:2 because the question mentions Andy first so he has to be in the ratio first.
• Question 10

Rick is 4/5 of the age of Rob. Write the age of Rick to Rob in it's simplest form.

EDDIE SAYS
Did I catch you out with this one? The fraction here shows the relationship between two amount, not the relationship to the whole. This means the ages can be written as 4/5 : 1 which simplifies to ...
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