 # Understand One Amount as a Fraction of Another

In this worksheet, students practise finding one amount as a fraction of another. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Fractions, Decimals and Percentages

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Fractions

Difficulty level:   ### QUESTION 1 of 10

There are a number of times when you need to be able to write one number as a fraction of another (finding percentages in an exam, making juice etc)

Luckily it's really easy to do.

Example 1: Write 25 as a fraction of 35.

The first step here is to write the number as a fraction.

 25 35

Job done? Not quite, we have to cancel fractions when we can. For this, we need to look for the Highest Common Factor (HCF)

To remind you, the HCF is the biggest number you can divide both the values by. In this case, it's 5.

 25 35
=
 25 ÷ 5 35 ÷ 5
=
 5 7

Example 2: Write 10 m as a fraction of 30 m

In this one, we have units. In this example, that's not a problem as the units are the same (they will cancel in the fraction)

 10 30
=
 10 ÷ 10 30 ÷ 10
=
 1 3

Example 3: Write 25 p as a fraction of £3

This one gets a bit more complicated. As the units aren't the same, all we have to do is make them the same.

Write 25 p as a fraction of 300p

Now the units are the same, we can just proceed as we did before,

 25 300
=
 25 ÷ 25 300 ÷ 25
=
 1 12

Write the following fraction as a fraction in it's simplest form. Give your answer in the form a/b.

 30 75

Which of the following fractions represents 12 out of 18?

12/18

2/3

4/6

6/9

1/4

When we write one number as a fraction of another, we have to make sure they have the _______ units.

12/18

2/3

4/6

6/9

1/4

Match the worded question to the fraction.

## Column B

15 as a fraction of 25
15/25
20 as a fraction of 30
40/80
40p as a fraction of 80p
20/30
4m as a fraction of 10m
4/10

Match the worded question to the fraction.

## Column B

15 as a fraction of 25
2/3
20 as a fraction of 30
1/2
40p as a fraction of 80p
2/5
4m as a fraction of 10m
3/5

What is 10 out of 20 as a fraction in it's simplest form. Give your answer in the form a/b

What is 32 kg as a fraction of 80 kg.Give you answer as a simplified fraction in the form a/b

What is 30 p as a fraction of £2.

Simplify as far as possible and give your answer in the form a/b

For each question, state if the fraction is both correct and completely simplified.

Is the following correct?

5 minutes as a fraction of 1 hr is 1/20

Correct

Incorrect

• Question 1

Write the following fraction as a fraction in it's simplest form. Give your answer in the form a/b.

 30 75

2/5
EDDIE SAYS
To solve this, we have to divide by the Highest Common Factor. The largest number we can divide both of these by is 15. This will give the answer...
 2 5
• Question 2

Which of the following fractions represents 12 out of 18?

12/18
2/3
4/6
6/9
EDDIE SAYS
If we start by writing this as an unsimplified fraction. We get 12/18. All of the other except 1/4 are cancelled versions of this.
• Question 3

When we write one number as a fraction of another, we have to make sure they have the _______ units.

EDDIE SAYS
Not remembering this is where a lot of student lose a mark on this question. To write a number as a fraction of another, they must have the same units.
• Question 4

Match the worded question to the fraction.

## Column B

15 as a fraction of 25
15/25
20 as a fraction of 30
20/30
40p as a fraction of 80p
40/80
4m as a fraction of 10m
4/10
EDDIE SAYS
A nice easy one here, im just testing if you understand how to put these numbers as a fraction. A as a fraction of B always gives A/B
• Question 5

Match the worded question to the fraction.

## Column B

15 as a fraction of 25
3/5
20 as a fraction of 30
2/3
40p as a fraction of 80p
1/2
4m as a fraction of 10m
2/5
EDDIE SAYS
A nice easy one here, im just testing if you understand how to put these numbers as a fraction.. A as a fraction of B always gives A/B Remember that you always have to cancel down if you can.
• Question 6

What is 10 out of 20 as a fraction in it's simplest form. Give your answer in the form a/b

1/2
EDDIE SAYS
If we start by putting this as a fraction, we get 10/20. The HCF here is 10 so the cancelled fraction 1/2
• Question 7

What is 32 kg as a fraction of 80 kg.Give you answer as a simplified fraction in the form a/b

2/5
EDDIE SAYS
The units here are the same so we don't need to do anything there. As a fraction, we first get 32/80. The HCF for this is 16 which gives us 2/5
• Question 8

What is 30 p as a fraction of £2.

Simplify as far as possible and give your answer in the form a/b

3/20
EDDIE SAYS
As the units are different, we have to rewrite this as 30 p as a fraction of 200 p This gives a fraction of 30/200. All we then have to do is cancel.
• Question 9

For each question, state if the fraction is both correct and completely simplified.

EDDIE SAYS
There are two mistakes you could make here. 1) Not cancelling - Did you always try to simplify? 2) Cancelling incorrectly - Remember that you have to be able to divide both the numerator and the denominator by the same amount.
• Question 10

Is the following correct?

5 minutes as a fraction of 1 hr is 1/20

Incorrect
EDDIE SAYS
This is a really common mistake. 5 minutes out of an hour is the same as 5 minutes out of 60 This gives a fraction od 5/60 which does not cancel to 1/20
---- OR ----

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