GCSE Maths Number FDP Percentages

One Number as a Percentage of Another

# One Number as a Percentage of Another

Here we will learn how to write one number as a percentage of another.
There are also percentages worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

## What is one number as a percentage of another?

One number as a percentage of another is where we have two numbers with one number expressed as a percentage of the other.

To do this we write a fraction and work out an equivalent fraction with a denominator of 100.  This is because percentages are “per one hundred”.

E.g.

Express 20 out of 50 as a percentage

$\frac{20}{50}=\frac{40}{100}=40\%$

Alternatively we can write the fraction and multiply by 100.

E.g.

$\frac{20}{50}\times100=40\%$

So 20 out of 50 is 40%.

### What is one number as a percentage of another? ## How to express one number as a percentage of another

Method 1: In order to express one number as a percentage of another

1. Write the numbers as a fraction
2. Find the equivalent fraction with a denominator of 100 (this may take multiple steps)
3. Write down the percentage

### Explain how to express one number as a percentage of another in 3 steps ## One number as a percentage of another examples

### Example 1: finding an equivalent fraction with a denominator of 100

Express 23 out of 50 as a percentage.

1. Write the numbers as a fraction

23 out of 50

23 is the numerator and 50 is the denominator.

$\frac{23}{50}$

2Find the equivalent fraction with a denominator of 100

50 is a factor of 100.

$50\times2=100$

$\frac{23}{50}\times\frac{2}{2}=\frac{46}{100}$

3Write down the percentage

$\frac{46}{100}=46\%$

So 23 out of 50 is 46%.

### Example 2: finding an equivalent fraction with a denominator of 100

Express 13 out of 20 as a percentage.

13 out of 20

13 is the numerator and 20 is the denominator.

$\frac{13}{20}$

20 is a factor of 100.

$20\times5=100$

$\frac{13}{20}\times\frac{5}{5}=\frac{65}{100}$

$\frac{65}{100}=65\%$

So 13 out of 20 is 65%.

## How to express one number as a percentage of another

Method 2: In order to express one number as a percentage of another:

1. Write the numbers as a fraction
2. Multiply the fraction by 100
3. Write down the percentage

### Example 3: write the fraction and multiply by 100

Without a calculator – Express 12 out of 30 as a percentage.

12 out of 30

12 is the numerator and 30 is the denominator.

$\frac{12}{30}$

$\frac{12}{30}\times100=\frac{12}{30}\times\frac{100}{1}=40$

When you are not using a calculator, try to cancel common factors in the numerator and denominator.

Here we can cancel with a common factor of 10.

### Example 4: write the fraction and multiply by 100

Without a calculator express 66 out of 150 as a percentage.

66 out of 150

66 is the numerator and 150 is the denominator.

$\frac{66}{150}$

$\frac{66}{150}\times100=\frac{66}{150}\times\frac{100}{1}=44$

When you are not using a calculator, try to cancel common factors in the numerator and denominator.

Here we can cancel with a common factor of 10 and then 3.

### Example 5: write the fraction and multiply by 100

With a calculator express 33 out of 60 as a percentage.

33 out of 60

33 is the numerator and 60 is the denominator.

$\frac{33}{60}$

$\frac{33}{60}\times100=55$

### Example 6: write the fraction and multiply by 100

With a calculator express 39 out of 75 as a percentage.

39 out of 75

39 is the numerator and 75 is the denominator.

$\frac{39}{75}$

$\frac{39}{75}\times100=52$

### Common misconceptions

• Use the same units of measurement for both numbers

Express 300m as a percentage of 2km.

2km = 2000m

$\frac{300}{2000}=\frac{30}{200}=\frac{15}{100}=15\%$

• The first number is usually the numerator, but not always

Of 40, what percent is 24?

The “of” number is always the denominator.

$\frac{24}{40}=\frac{6}{10}=\frac{60}{100}=60\%$

• A percentage does not have to be a whole number, it can also be a decimal number

Express 62 out of 80 as a percentage.

$\frac{62}{80}\times100=77.5$

• Make sure that you have the correct denominator

In a house there are 2 dogs and 3 cats.  What percentage of the pets are cats?

The denominator needs to be the total number of pets. There are 5 pets altogether.

$\frac{3}{5}=\frac{60}{100}=60\%$

• The fraction can be an improper fraction, with the denominator being a smaller number than the numerator

Work out the percentage increase from 40 to 90.

40 is the original amount. This is the denominator.

The increase is 90 – 40 = 50.  This is the numerator.

$\frac{50}{40}\times100=125$

The percentage increase is 125%.

One number as a percentage of another is part of our series of lessons to support revision on percentages. You may find it helpful to start with the main percentages lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

### Practice one number as a percentage of another questions

1. Without a calculator express 4 out of 10 as a percentage.

4\% 40\% 6\% 60\% Express the quantities as a fraction and multiply by 100 ,

\frac{4}{10} \times 100 = 40\%

2. Without a calculator express 7 out of   20 as a percentage.

7\% 35\% 28\% 27\% Express the quantities as a fraction and multiply by 100 ,

\frac{7}{20} \times 100 = 35\%

3. Without a calculator express 12 out of   50 as a percentage.

62\% 38\% 12\% 24\% Express the quantities as a fraction and multiply by 100 ,

\frac{12}{50} \times 100 = 24\%

4. Express 42 out of 60 as a percentage.

42\% 60\% 18\% 70\% Express the quantities as a fraction and multiply by 100 ,

\frac{42}{60} \times 100 = 70\%

5. Express 36 out of 80 as a percentage.

42\% 45\% 36\% 44\% Express the quantities as a fraction and multiply by 100 ,

\frac{36}{80} \times 100 = 45\%

6. Express 216 out of 300 as a percentage.

84\% 36\% 72\% 18\% Express the quantities as a fraction and multiply by 100 ,

\frac{216}{300} \times 100 = 72\%

### One number as a percentage of another GCSE questions

1.  Gary found 60 trees altogether in a wood.

18 of them were beech trees.

What percentage of the trees were beech trees?

(2 marks)

\frac{18}{60}

(1)

\frac{18}{60}=\frac{3}{10}=\frac{30}{100}=30\%

(1)

2.  With a calculator.

Jack buys a pack of 12 cans of drinks.

The pack costs \pounds 7.32

Jack sells all 12 cans for 70p .

Work out Jack’s percentage profit.

(3 Marks)

12\times70=840

(1)

840-732=108

\frac{108}{732}

(1)

\frac{108}{732}\times100=14.75…=14.8\%

(1)

3. Without a calculator.

Work out the percentage increase from 40 to 240 .

(3 Marks)

240-40=200

(1)

\frac{200}{40}

(1)

\frac{200}{40}\times\frac{100}{1}=500

The percentage increase is 500\%

(1)

### Percentage calculator tips

To calculate with percentages using a calculator you can either use the fraction button or use the divide button.

E.g.
What is 39 out of 75 as a percentage?

Using the fraction button:

$\frac{39}{75}\times100=52$

Using the divide button:

$39\div75\times100=52$

## Learning checklist:

You have now learned how to:

• Express one number as a percentage of another
• Use equivalent fractions to work out one whole number as a percentage of another whole number
• Use a calculator to what percentage one number is of another number accurately

## Still stuck?

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