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Find One Number as a Percentage of Another

In this worksheet, students will be able to find one number as a percentage of another. Students will also be able to convert units when necessary in order to be accurate in their work.

'Find One Number as a Percentage of Another' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel

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

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

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

car

When you were younger, I know you were sent out into the school car park, to count the different colours of cars.

 I was, times don't change that much. To be honest I never knew why other than we had to draw a bar chart.

Now we have progressed from bar charts , we can use this type of information in lots of ways.  

This a great way to learn about percentages

 

Let's think about things.

 

'Per cent' means 'out of 100'

Writing a percentage means writing it as a number out of 100.

 

The school car park has 100 cars.  26 of these cars are blue.  

To write this as a percentage  we say 26 out of 100 are blue, therefore 26%.

If there were 43 blue cars in the same car park it would be 43%,  19 blue cars, 19%  etc.

Uh Oh.. but what happens if there are not 100 cars (or 100 of anything for that matter)..Let's see

Suppose there were 50 cars and 8 of them were green.  What percentage are green?

We know that 8 out of 50 cars are green.  It would be far easier if there were 100 cars.

Let's make it 100 cars then.

Multiply 50 by 2 to get 100.

 

 Whatever we do to one part of the question, we have to do exactly the same to the other part.

Multiply 8 by 2 to get 16.  

 This is easier now... 16 out of 100 cars are green...so that is 16% (if you cancel down 16 out of 100 you get back to 8 out of 50 so you know this is correct)

More examples   6 out of 25 as a percentage would be     25 x 4 = 100  and 6 x 4 = 24   therefore 24%  

                                          

Take note

                                      You many have to cancel the 'out of '  down to 100    

So 52 out of 400  You would divide both numbers by 4 to get  13 out of 100  = 13%

Now for the tricky part

The 'out of' may not be that simple to convert.  What would you do if you had to write  8 out of 32 as a percentage?  Besides cry..

32 obviously does not multiply up to 100.  Could it multiply up to 200?  

The best way to find out is divide 200 by 32 to see if it goes in equally.   What did you get?

A decimal number, not helpful really.  Let us try 300 .  Another decimal..?

Keep going until it works.. try 400, 500 etc  in this case it is 800 !!!! I thought I was never going to get there..

800 divided by 32 = 25.  Now multiply 8 by 25 which gives us 200.  We now have 200 out of 800.

To turn 800 into 100 divide by 8 and then do the same to the 200.

Did you get 25%?

Magic..

eye Look out for an added extra through out the activities

 

 

 

 

Match the questions with the answers

Column A

Column B

42 out of 100
105%
39 out of 100
39%
4 out of 50
48%
12 out of 25
8%
3 out of 10
30%
21 out of 20
42%

A football team scored 50 goals in one season.  18 of these goals were penalties.

 

What percentage of goals scored were penalties?

Write your answer as  ....%

 

At the swimming club there are 25 members.

12 of these members are female.

 

Another match up to try.

Column A

Column B

36 out of 60
20%
24 out of 40
70%
30 out of 150
70%
56 out of 80
60%
42 out of 35
30%
54 out of 180
60%

 

After that last question I thought you deserved a treat.  Chocolate, every ones favourite.

 

There are  55 chocolates in a tin.  33 of the chocolates are milk chocolate.  The rest are dark chocolate.  What percentage are dark chocolate?   Use your calculator for this one.

Write your answer as ....%

Use your calculator to write each of the following amounts as a percentage

Write your answers as  ....%

Curtis receives £5.60 pocket money from his parents each week. He also receives £2.40 from his grandparents each week.

What percentage of his total pocket money comes from  his grandparents?

 

40%

60%

30%

20%

Express each of the following as a percentage

Write your answers to 1 decimal place if necessary.

Write your answers as  ....%

40%

60%

30%

20%

 

 

Jay, Karen and Emily are looking at their test results.  Who has the greatest percentage score?

  Test Score  Full Marks
Jay 12 14
Karen 14 20
Emily 20 23

 

What would you choose?

 

 £11 out of £24 £12 out of £32 £15 out of £34
choose
  • Question 1

Match the questions with the answers

CORRECT ANSWER

Column A

Column B

42 out of 100
42%
39 out of 100
39%
4 out of 50
8%
12 out of 25
48%
3 out of 10
30%
21 out of 20
105%
EDDIE SAYS
Out of 100 is easy..winner Remember to multiply the' out of' up to 100 when necessary. 4 out of 50 x both numbers by 2 to get 8 out of 100 = 8% 12 out of 25 x both numbers by 4 to get 48 out of 100 = 48% 3 out of 10 multiply both by 10 21 out of 20 multiply both by 5
  • Question 2

A football team scored 50 goals in one season.  18 of these goals were penalties.

 

What percentage of goals scored were penalties?

Write your answer as  ....%

CORRECT ANSWER
36%
EDDIE SAYS
Did you think that these types of questions were always presented as something out of 100. Sadly not. You now have the skill though to multiply up when necessary. 50 x 2 = 100 and 18 x 2 = 36 36 out of 100 = 36% Back of the net!
  • Question 3

 

At the swimming club there are 25 members.

12 of these members are female.

 

CORRECT ANSWER
EDDIE SAYS
You should easily recognise that the word percentage leads you to finding something out of 100. Just multiply up like you have been doing. 25 x 4 = 100 12 x 4 = 48 so 48 out of 100 = 48% By reading the text carefully and picking out words to help us can only make us smile, because the question is leading us straight to the answer. This is going swimmingly well.
  • Question 4

Another match up to try.

CORRECT ANSWER

Column A

Column B

36 out of 60
60%
24 out of 40
60%
30 out of 150
20%
56 out of 80
70%
42 out of 35
70%
54 out of 180
30%
EDDIE SAYS
This is a long explanation. Don't skip it. You may kick yourself if you do. Did you remember to multiply the out off, up to hundreds? 36 out of 60 ( 300 ÷60 = 5) multiply both numbers by 5 to get 180 out of 300 then divide by 3 to get 60 out of 100 which is 60% 24 out of 40 200÷ 40 = 5) multiply both numbers by 5 then divide by 2 30 out of 150. 300 ÷ 150 = 2. So multiply by 2 then divide by 3 56 out of 80. 400 ÷ 80 = 5. So multiply up by 5 then divide by 4. Persevere with this explanation as you will love it in the end. Trust me. 42 out of 35. 700 ÷ 35 = 20. Multiply up by 20 and divide by 7. 54 out of 180. 900 ÷ 180 = 5. Multiply up by 5 and divided by 9. NOW... As you know what you are doing I am going to show you a quicker way. With a calculator you can do 36 ÷ 60 x 100 = 60% 30 ÷ 150 x 100 = 20% I know all that work and you could have done this quicker. It is important that you can do both methods. Got there in the end. I might need a lie down now.
  • Question 5

 

After that last question I thought you deserved a treat.  Chocolate, every ones favourite.

 

There are  55 chocolates in a tin.  33 of the chocolates are milk chocolate.  The rest are dark chocolate.  What percentage are dark chocolate?   Use your calculator for this one.

Write your answer as ....%

CORRECT ANSWER
40%
EDDIE SAYS
Did you read the question carefully? First find out the percentage of milk chocolate which is 33 divided by 55 x 100 = 60%. We don't want milk chocolate do we. NO. To find dark chocolate 100% - 60% = 40%. Sorry a little bit naughty after the last question. Have you forgiven me yet? If you knew the calculator way from the beginning you wouldn't have worked answers out without it would you?
  • Question 6

Use your calculator to write each of the following amounts as a percentage

Write your answers as  ....%

CORRECT ANSWER
EDDIE SAYS
Easy now isn't it 15 divided by 24 x 100 = 62.5% 221 divided by 260 x 100 = 85% 116 divided by 212 x 100 = 54.7 323 divided by 850 x 100 = 38% In case you were wondering why we multiply by 100. Remember what percent means. You have forgiven me now I can tell.
  • Question 7

Curtis receives £5.60 pocket money from his parents each week. He also receives £2.40 from his grandparents each week.

What percentage of his total pocket money comes from  his grandparents?

 

CORRECT ANSWER
30%
EDDIE SAYS
It is one of those questions you need to read carefully. Did you spot the word 'total' which should have led you to finding the 'out of ' part. £5.60 + £2.40 = £8.00 2.40 divided by 8 = 0.3 0.3 x 100 = 30%
  • Question 8

Express each of the following as a percentage

Write your answers to 1 decimal place if necessary.

Write your answers as  ....%

CORRECT ANSWER
EDDIE SAYS
You are used to finding percentages of an amount now, so it is time for the sneaky question. You have to be careful of the units of measurement here. They both have to be the same before you can do an accurate calculation. £5 of £20 units are the same so 5 divided by 20 x 100 =25% 25 minutes of 1 hour. Convert the hour to minutes. 25 divided by 60 x 100 =41.6% 3 hours of 1 day. Convert the day into hours 3 divided by 24 x 100 =12.5% 25cm of 3m. Convert m to cm. 25 divided by 300 x 100 = 8.3%
  • Question 9

 

 

Jay, Karen and Emily are looking at their test results.  Who has the greatest percentage score?

  Test Score  Full Marks
Jay 12 14
Karen 14 20
Emily 20 23

 

CORRECT ANSWER
Emily
EDDIE SAYS
Jay 12 divided by 14 x 100 = 85.7% Karen 14 divided by 20 x 100 = 70% Emily 20 divided by 23 x 100 = 86.9
  • Question 10

What would you choose?

 

CORRECT ANSWER
 £11 out of £24 £12 out of £32 £15 out of £34
choose
EDDIE SAYS
£11 out of £24 = 45.8% £12 out of £32 = 37.5% £15 out of £34 = 44.1% I know which one I would choose. I think you have earned this.
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