# Use Fractions as Operators

In this worksheet, students will find fractions of amounts by applying the rule: 'Divide by the denominator, multiply by the numerator'.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Fractions, Decimals and Percentages

Curriculum subtopic:   Structure and Calculation, Ordering Fractions, Decimals and Percentages

Difficulty level:

### QUESTION 1 of 10

Using fractions as operators is quite a mouthful, so we usually simplify it to 'finding a fraction of an amount'.

Imagine that you have a budget which you need to share between members of a team.

You may want to give a quarter of the budget to one person and three-quarters to another.

How would you do this?

You need to remember one key fact when finding fractions of an amount:

Divide by the denominator, multiply by the numerator.

e.g. Work out

 2 7
of 35

To work this out, we need to know that the word of in maths just means multiply.

So what we're actually working out is:

 2 7
x 35

If we look back to our rule: Divide by the denominator, multiply by the numerator.

We need to divide 35 by 7 which gives us 5.

We then must multiply 5 by 2 to get 10.

So two-sevenths of 35 is 10.

Job done!

In this activity, you will find fractions of amounts by applying the rule:

Divide by the denominator, multiply by the numerator.

What is three quarters of 20?

Find the answer for the sum:

 1 5
of 40

For each of the following sums, state if it is correct or incorrect.

Complete the sentence below.

Which of the options in the list is the answer to the sum:

 7 15
of 210
98

14

7

Work out the value of:

 3 7
of 21

Find the answer to the sum:

 2 9
of 45

Find the answer for the sum:

 1 3
of 60kg

Think very carefully before you answer this question.

Find the answer for the sum:

 7 10
of £2

Remember what you learnt in the last question about units.

Find the answer for the sum:

 5 12
of 1 hour
• Question 1

What is three quarters of 20?

15
fifteen
EDDIE SAYS
Here is one to get us started! 'Three quarters' in words means 3/4. So to find 3/4 of 20, we need to divide by 4 and then times by 3. (20 ÷ 4) x 3 = 15
• Question 2

Find the answer for the sum:

 1 5
of 40
8
EDDIE SAYS
Here we have to divide by 5 then times this answer by 1. (40 ÷ 5) x 1 = 8 Are you getting the hang of this?
• Question 3

For each of the following sums, state if it is correct or incorrect.

EDDIE SAYS
Remember that we always need to apply the same rule: Divide by the denominator, multiply by the numerator. (35 ÷ 5) x 3 = 21 so this sum is correct. (30 ÷ 3) x 2 = 20 not 10, so this sum is not correct. (90 ÷ 9) x 1 = 10 so this sum is correct too. (99 ÷ 9) x 7 = 77 not 66, so this sum is incorrect too. How did you get on with those?
• Question 4

Complete the sentence below.

EDDIE SAYS
What's our golden rule? Divide by the denominator then multiply by the numerator. Hopefully these questions are getting easier. If not, return to the information page at the beginning and refresh the method in your mind before attempting the next challenge.
• Question 5

Which of the options in the list is the answer to the sum:

 7 15
of 210
98
EDDIE SAYS
If we divide the 210 by 15, we get 14. Since we then have to multiply by the numerator, the answer must be greater than 14 so 98 is the only viable option in the list. 210 ÷ 15 = 14 14 x 7 = 98
• Question 6

Work out the value of:

 3 7
of 21
9
EDDIE SAYS
Start by working out how many 7s go into 21 (3). Then, we need to multiply this answer by 3 (9). So three-sevenths of 21 is 9. We can check out answer is sensible by estimating. Three-sevenths is a little less than a half. Half of 21 is 10.5, so 9 seems like an accurate guess.
• Question 7

Find the answer to the sum:

 2 9
of 45
10
EDDIE SAYS
Finding 2/9 of 45 means we have to divide 45 by 9 then times this answer by 2. (45 ÷ 9) x 2 = 10
• Question 8

Find the answer for the sum:

 1 3
of 60kg

Think very carefully before you answer this question.

20kg
20 kg
EDDIE SAYS
Did you notice that there were units in this question? If there are units in a question, there must be the same units in the answer. 1/3 of 60 = (60 ÷ 3) x 1 = 20 But this answer is not good enough! We need to add the units back onto the end so '20 kg' is what examiners will be looking for.
• Question 9

Find the answer for the sum:

 7 10
of £2

Remember what you learnt in the last question about units.

£1.40
£ 1.40
140p
140 p
EDDIE SAYS
This was another slightly tricky one! How do you divide £2 by 10? In a question like this with a large unit, convert it into something more manageable. In this case, it is simplest to convert £2 into pence, so it becomes 200 pence. So we need to calculate the sum: (200 ÷ 10) x 7 = 140 Don't forget to put your units back in though! You could write this as 140p or £1.40. Which one are you more likely to say?
• Question 10

Find the answer for the sum:

 5 12
of 1 hour
25 minutes
25 mins
25 m
EDDIE SAYS
One thing you must remember for this question is that there are 60 minutes in 1 hour. Therefore, we're trying to find 5/12 of 60. Don't forget to put those units back in! Well done if you got this right! That's another activity completed.
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