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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

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