 # Find One Number as a Percentage of Another

In this worksheet, students will find percentages of one number out of a total with and without a calculator, which may or may not require conversion so it can be equated to 100. 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:   ### QUESTION 1 of 10 When you were younger, you were probably sent out into the school car park at some point, to count the different colours of cars.

You likely used this information to draw a bar chart or something similar.

Now we have progressed from bar charts, we can use this type of information in lots of ways, such as to find percentages

Percent means out of 100.

Writing a percentage, means writing something as a number out of 100.

e.g. Imagine that the school car park has 100 cars and 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, this would be 43%; 19 blue cars would be 19%; etc.

But what happens if there are not 100 cars in the car park?

Let's see...

e.g. 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, but it would be far easier to calculate the % if there were 100 cars.

Let's make it 100 cars then...

We need to multiply 50 by 2 to get 100, and whatever we do to one part of the question, we have to do exactly the same to the other part.

So let's multiply 8 by 2 to get 16.

This is easier now...

16 out of 100 cars are green, so that is 16%.

If we cancel down 16 out of 100, we get back to 8 out of 50, so we know this is correct. Take note: You many also need to cancel the 'out of ' down to reach 100.

e.g. What is 52 out of 400 as a %?

We would divide both numbers by 4 (as 400 ÷ 4 = 100) to get 13 out of 100  = 13%.

Now for the tricky part...

The 'out of' may not be that simple to convert.

e.g. What would we do if we wanted to write 8 out of 32 as a percentage?

32 obviously does not multiply up to 100.

Could we multiply it up to 200?

The best way to find out is divide 200 by 32 to see if it goes into it equally.

What did you get?

A decimal number, not helpful really.

Let's try another option... how about 300

Another decimal, not great.

Keep going until it works... try 400, 500, etc.

In this case, our best bet is 800 - phew! I thought we were 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, we need to divide by 8 and then do the same to the 200.

Did you get 25%?

Magic! In this activity, we will find percentages of one number out of a total which we may or may not need to convert so we can equate it to 100.

Look out for a magical tip halfway through to give you an alternative method and a speedy shortcut!

You may want to have a calculator handy so that you can concentrate on practising these methods and not stretching your mental maths brain.

Match each statement below with its correct percentage.

## Column B

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

A football team scored 50 goals in one season.

18 of these goals were penalties. What percentage of the goals scored were penalties?

## Column B

42 out of 100
39%
39 out of 100
30%
4 out of 50
42%
12 out of 25
8%
3 out of 10
48%
21 out of 20
105% At the swimming club, there are 25 members.

12 of these members are female.

What percentage of the membership is female?

## Column B

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

Match each statement below with its correct percentage.

## Column B

36 out of 60
20%
24 out of 40
60%
30 out of 150
60%
56 out of 80
30%
42 out of 35
70%
54 out of 180
70% 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 to work out this one, using the shorter method we introduced in the last question.

## Column B

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

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

Write or round each answer to the nearest whole percent

## Column B

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

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 measurements as a percentage.

40%

60%

30%

20% Jay, Karen and Emily are looking at their test results.

There scores are recorded in this table:

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

Who has the highest score as a percentage?

Jay

Karen

Emily

Which of the amounts of money below represents the highest % of its overall total?

£11 out of £24

£12 out of £32

£15 out of £34

• Question 1

Match each statement below with its correct percentage.

## 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
If our number is already 'out of 100' then we are onto a winner! We just need to take these numbers as they are, and pop a % sign on the end: 42 out of 100 = 42% 39 out of 100 = 39% For the other options, we need to multiply our 'out of' value until it is 100. 4 out of 50 = × both numbers by 2 to get 8 out of 100 = 8% 12 out of 25 = × both numbers by 4 to get 48 out of 100 = 48% 3 out of 10 = × both by 10 to get 30 out of 100 = 30% 21 out of 20 = × both by 5 to get 105 out of 100 = 105% Don't worry if your % goes over 100, this does not mean it is incorrect. How did you get on with those?
• Question 2

A football team scored 50 goals in one season.

18 of these goals were penalties. What percentage of the goals scored were penalties?

EDDIE SAYS
Did you think that these types of questions were always presented as something out of 100? Sadly not, but now we have the skills to multiply up when necessary. 50 × 2 = 100 and 18 × 2 = 36 36 out of 100 = 36% Did you type those numbers in correctly? Back of the net!
• Question 3 At the swimming club, there are 25 members.

12 of these members are female.

What percentage of the membership is female?

EDDIE SAYS
Here we have 25 as our starting total - how can we convert this into 100? We can multiply by 4: 25 × 4 = 100 12 × 4 = 48 48 out of 100 = 48% This is going swimmingly well!
• Question 4

Match each statement below with its correct percentage.

## 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
Did you remember to multiply the 'out of' up to a hundred and, if this is not possible, then to a multiple of 100? 36 out of 60: 300 ÷ 60 = 5, so if we multiply both numbers by 5, we will reach a multiple of 100. 60 × 5 = 300 36 × 5 = 180 180 out of 300 --> ÷ 3 = 60 out of 100 = 60% Can you follow this example to match the other pairs independently? NOW... As you know what we are doing now, here is an even quicker way. With a calculator, we can type: 36 ÷ 60 × 100 = 60% It may seem frustrating that there was a quicker way all along, but it is important that you are confident with both methods.
• Question 5 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 to work out this one, using the shorter method we introduced in the last question.

EDDIE SAYS
Did you read the question carefully here? Firstly, we need to find out the percentage of milk chocolate: 33 ÷ 55 × 100 = 60% But we don't want milk chocolate, do we? To find dark chocolate, we need to calculate: 100% - 60% = 40% Sorry, that was a bit of a sneaky question! Well done if you spotted the potential trap there.
• Question 6

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

Write or round each answer to the nearest whole percent

EDDIE SAYS
It's easier now we can use our calculator, isn't it? 15 ÷ 24 × 100 = 62.5% Should we round this up to 63 or down to 62? 221 ÷ 260 × 100 = 85% 116 ÷ 212 × 100 = 54.7% Should we round this up or down to the nearest whole %? 323 ÷ 850 × 100 = 38% In case you were wondering why we multiply by 100, remember what percent means.
• 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? 30%
EDDIE SAYS
This is one of those questions you need to read carefully. Did you spot the word 'total'? This helps us to find the 'out of' element: 5.60 + 2.40 = 8.00 so this is the total amount of pocket money he receives Of this £8, Curtis receives £2.40 from his grandparents: 2.40 ÷ 8 × 100 = 30% So 30% of his total pocket money comes from his grandparents.
• Question 8

Express each of the following measurements as a percentage.

EDDIE SAYS
You are used to finding percentages of an amount now, so it is time for this sneaky question. You have to be careful of the units of measurement here. They both have to be in the same format before we can complete an accurate calculation. £5 of £20: Our units are the same so 5 ÷ 20 × 100 = 25% 25 minutes of 1 hour: We need to convert the hour to minutes first. 25 divide; 60 × 100 = 41.6% 3 hours of 1 day: We need to convert the day into hours first. 3 ÷ 24 × 100 =12.5% 25 cm of 3 m: Let's convert our m into cm to start. 25 ÷ 300 × 100 = 8.3%
• Question 9 Jay, Karen and Emily are looking at their test results.

There scores are recorded in this table:

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

Who has the highest score as a percentage?

Emily
EDDIE SAYS
Let's work out each of the student's scores as a % and then compare them to 1 decimal place. Jay: 12 ÷ 14 × 100 = 85.7% Karen: 14 ÷ 20 × 100 = 70% Emily: 20 ÷ 23 × 100 = 86.9% So who scored the highest?
• Question 10

Which of the amounts of money below represents the highest % of its overall total?

£11 out of £24
EDDIE SAYS
£11 out of £24: 11 ÷ 24 × 100 = 45.8% £12 out of £32: 12 ÷ 32 × 100 = 37.5% £15 out of £34: 15 ÷ 34 × 100 = 44.1% Which of these percentages is the highest? Great job on this activity - you are becoming a percentages pro!
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