# Convert Ratios to Fractions

In this worksheet, students will practise expressing fractions as ratios (or vice versa), using the numerator as a number in the ratio and the denominator to represent the total parts present in the ratio.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Difficulty level:

### QUESTION 1 of 10

Ratio and proportion are two very closely linked topics.

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

A common skill to be tested is to convert fractions into ratios using the concepts of proportion.

Let's take a look at this in action in some examples.

e.g. We have a bag of red and green beads which have a ratio of 7:3. What fraction of the beads are red?

Firstly, we need to know how many parts there are in total.

If the ratio is 7:3, this means there are 10 parts in total (7 + 3 = 10).

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

So how do we do this the other way round then?

e.g. Write 3/4 as a ratio.

The numerator (or top number) must appear be somewhere in the ratio, so, in this case, our ratio must be:

3 : _   or  _ : 3

The total number of parts in the ratio must add up to the denominator, which, in this case, is 4.

There are two ratios which satisfies both of these conditions is:

3:1  or  1:3

Is it always this easy?

Unfortunately no, there is one exception.

This exception is if we use a fraction which doesn't represent part of a whole.

Let's review how to tackle this in one, final example.

e.g. James has 3/5 of the number of marbles which John has. Express the total number of marbles which both boys have as a simplified ratio.

We know that James has 3/5 of a marble for every 1 that John has.

We could write this as:

 3 5
: 1

But we know that we can't have a fraction in a ratio of this type, so we need to multiply both sides to reach a ratio without a fraction:

 3 5
× 5 : 1 × 5

= 3:5

Here are some algebraic expressions to summarise these relationships.

Situation 1 - Fraction of a whole:

 a b
= a: b - a

Situation 2 - Fraction as a relationship between two variables:

 a b
: a: b

In this activity, we will express fractions as ratios (or vice versa) applying the method shown above of using the numerator as a number in the ratio and the denominator to represent the total parts present in the ratio.

Type a word in the space to complete the sentence below.

Type a word in the space to complete the sentence below.

What is 3/8 expressed as a ratio?

3:8

3:5

8:3

Write 4/5 as a ratio.

3:8

3:5

8:3

Match each ratio on the right to its matching fraction on the left.

## Column B

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

Match each fraction on the right to its matching ratio on the left.

## Column B

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

What is 2/7 expressed as a ratio?

## Column B

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

What is 3/10 as a ratio?

## Column B

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

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

Write a ratio to express the number of sweets Andy gets compared to Louise, in its simplest form.

## Column B

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

Rick is 4/5 of the age of Rob.

Write a ratio to express the age of Rick in comparison to Rob, in its simplest form.

## Column B

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

Type a word in the space to complete the sentence below.

EDDIE SAYS
Proportion always refers to representing parts of a whole. For example, if you allowed to eat 3/4 of a bag of 32 sweets, you need to work out the proportion of the whole amount which you are allowed to eat. Don't forget that these can be written as fractions, decimals and percentages.
• Question 2

Type a word in the space to complete the sentence below.

EDDIE SAYS
Ratios are used to define the relationship between two or more quantities or amounts, so that we can compare them. For example, to return to our bag of 32 sweets, if we wanted to share these with a friend, we may use a ratio to express how many of the total amount each should receive. Don't forget that ratios must use whole numbers, not fractions or decimals. Recap the info in the Introduction now if you need to, before you move on to tackle the rest of this activity.
• Question 3

What is 3/8 expressed as a ratio?

3:5
EDDIE SAYS
The numerator (or top number) must appear be placed on the left of the ratio, so, in this case, our ratio must start: 3 : _ The total number of parts in the ratio must add up to the denominator, which, in this case, is 8. The only ratio which satisfies both of these conditions, and appears in the options, is: 3:5 It's as simple as that!
• Question 4

Write 4/5 as a ratio.

EDDIE SAYS
Let's apply our process again here. Numerator: 4 Denominator: 5 Answer: 4 : (5 - 4) or (5 - 4) : 4 4:1 or 1:4
• Question 5

Match each ratio on the right to its matching fraction on the left.

## Column B

3:2
3/5
6:5
5/11
1:2
1/3
3:7
3/10
EDDIE SAYS
Remember, the numerator of our fraction is one of the numbers we must see present in the matching ratio, whilst the denominator is the total number of parts in our ratio. e.g. 3/5 --> 3 : (5 - 3) or (5 - 3) : 3--> 3:2 or 2:3 Did you use this information to find those matches successfully?
• Question 6

Match each fraction on the right to its matching ratio on the left.

## 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 we work backwards from our ratios. e.g. 4:6 must have a denominator of 10 (4 + 6 = 10) and a numerator of either 4 or 6. But 4/10 or 6/10 isn't an option! We need to remember that fractions can be cancelled by finding the HCF, which in this case, is 2: 4/10 ÷ 2 = 2/5 6/10 ÷ 2 = 3/5 Which of these options is available to us on the left-hand side? Can you follow this example to find the other matches independently?
• Question 7

What is 2/7 expressed as a ratio?

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 possible options for ratios: 2:5 or 5:2
• Question 8

What is 3/10 as a ratio?

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 possible options for ratios: 3:7 or 7:3
• Question 9

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

Write a ratio to express the number of sweets Andy gets compared to Louise, in its simplest form.

EDDIE SAYS
In this question, we are looking at fractions as part of a whole. Out of 5 parts, Andy gets 2 parts and Louise gets 3 parts. This gives us a ratio of 2:3. Note that the order is important here. We can't write 3:2 because the question specifically mentions that Andy needs o be compared to Louise, so the number related to him needs to be positioned first in our ratio.
• Question 10

Rick is 4/5 of the age of Rob.

Write a ratio to express the age of Rick in comparison to Rob, in its simplest form.

EDDIE SAYS
Did we 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 can be simplified to:
 4 5
× 5 : 1 × 5
= 4:5 Great job! You can now express fractions as ratios (or vice versa), using the numerator as a number in the ratio and the denominator to represent the total parts present in the ratio.
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