One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

Percentages Fractions Equivalent fractions Multiplying fractions Dividing fractionsThis topic is relevant for:

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.

**One number as a percentage of anothe**r 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

E.g.

Express

\[\frac{20}{50}=\frac{40}{100}=40\%\]

Alternatively we can write the fraction and multiply by 100.

E.g.

\[\frac{20}{50}\times100=40\%\]

So

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

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

Get your free one number as a percentage of another worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free one number as a percentage of another worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEExpress

**Write the numbers as a fraction**

\[\frac{23}{50}\]

2**Find the equivalent fraction with a denominator of 100**

\[50\times2=100\]

\[\frac{23}{50}\times\frac{2}{2}=\frac{46}{100}\]

3**Write down the percentage**

\[\frac{46}{100}=46\%\]

So

Express

** Write the numbers as a fraction**

\[\frac{13}{20}\]

**Find the equivalent fraction with a denominator of 100**

\[20\times5=100\]

\[\frac{13}{20}\times\frac{5}{5}=\frac{65}{100}
\]

**Write down the percentage**

\[\frac{65}{100}=65\%\]

So

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

- Write the numbers as a fraction
- Multiply the fraction by
100 - Write down the percentage

Without a calculator – Express

**Write the numbers as a fraction**

\[\frac{12}{30}\]

**Multiply the fraction by 100**

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

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

**Write down the percentage**

The final answer is

Without a calculator express

**Write the numbers as a fraction**

\[\frac{66}{150}\]

**Multiply the fraction by 100**

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

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

**Write down the percentage**

The final answer is

With a calculator express

**Write the numbers as a fraction**

33 is the numerator and 60 is the denominator.

\[\frac{33}{60}\]

**Multiply the fraction by 100**

\[\frac{33}{60}\times100=55
\]

**Write down the percentage**

The final answer is

With a calculator express

**Write the numbers as a fraction**

\[\frac{39}{75}\]

**Multiply the fraction by 100**

\[\frac{39}{75}\times100=52\]

**Write down the percentage**

The final answer is

**Use the same units of measurement for both numbe**rs

Express

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

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

Of

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

\[\frac{62}{80}\times100=77.5\]

The final answer is

**Make sure that you have the correct denominator**

In a house there are

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

\[\frac{3}{5}=\frac{60}{100}=60\%\]

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

Work out the percentage increase from

The increase is

\[\frac{50}{40}\times100=125\]

The percentage increase is

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:

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\%

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)**

Show answer

\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.

Give your answer correct to 1 decimal place.

**(3 Marks)**

Show answer

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)**

Show answer

240-40=200

** (1)**

\frac{200}{40}

** (1)**

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

The percentage increase is 500\%

** (1)**

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:

\[39\div75\times100=52\]

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

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.