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Key points

Fractions expressed as can be easier to understand.
Expressing a fraction as a percentage means the same as converting a fraction to a percentage.
Percent means per hundred or out of 100. The percentage symbol % is a shorthand representation of this.
Knowing how to find , recognising and , and understanding division are useful when converting fractions to percentages without a calculator.
To change a fraction to a percentage, you can divide the by the then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.

Converting fractions to percentages using a denominator of 100

Write an with 100 as the denominator.
The numerator of the equivalent fraction is the percentage. Write this number followed by the percentage symbol %

This method is ideal when the denominator of the fraction is a factor or a multiple of 100.

Examples

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Convert 13⁄20 to a percentage.
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The denominator (20) is a factor of 100. 20 x 5 = 100. Write an equivalent fraction with 100 as the denominator.
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Fractions are equivalent when both the numerator and denominator are multiplied by the same number. The denominator (20) has been multiplied by 5. The numerator (13) is also multiplied by 5. 13⁄20 is equivalent to 65⁄100. This is 65%
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Convert 78⁄300 to a percentage.
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The denominator (300) is a multiple of 100. 300 ÷ 3 = 100. Write an equivalent fraction with 100 as the denominator.
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Fractions are equivalent when both the numerator and denominator are divided by the same number. The denominator (300) has been divided by 3. The numerator (78) is also divided by 3. 78⁄300 is equivalent to 26⁄100. This is 26%
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Convert 246⁄400 to a percentage.
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The denominator (400) is a multiple of 100. 400 ÷ 4 = 100. Write an equivalent fraction with 100 as the denominator. 246⁄400 is equivalent to 61∙5 over one hundred.
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The fraction has a decimal numerator which cannot be used as an equivalent fraction. But it does give the percentage value of 61∙5%

Question

Convert \( \frac{18}{25} \) to a percentage.

Convert a fraction to a percentage by multiplying by 100

To convert a fraction to a percentage by multiplying by 100, choose your preferred process order:

Either:

Divide the numerator by the denominator
Multiply the result by 100

Or:

Multiply by 100
Divide the result by the denominator

Write the answer followed by the percentage symbol %. You may use short division (the bus stop method) when dividing by the denominator.

Examples

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Image caption,
Fractions can be converted to percentages by multiplying by 100
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A fraction is one way of writing a division. 2⁄5 means the numerator (2) divided by the denominator (5)
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Convert 2⁄5 to a percentage.
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Divide the numerator (2) by the denominator (5). 2 ÷ 5 = 0∙4
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To convert 2⁄5 to a percentage, divide 2 by 5 and then multiply the result by 100. 0∙4 x 100 = 40. 2⁄5 is 40%. You get the same answer if 2⁄5 is multiplied by 100 first and then divided by 5
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Convert 2⁄5 to a percentage by multiplying the fraction by 100 first. Multiply 2⁄5 by 100 (100⁄1). Multiply the numerators (2 and 100) and multiply the denominators (5 and 1). 2⁄5 × 100 is 200⁄5
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200⁄5 means 200 ÷ 5. This is 40. To convert 2⁄5 to a percentage, multiply 2⁄5 by 100 and then divide by the denominator (5). 2⁄5 is 40%
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Convert 7⁄8 to a percentage.
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Divide the numerator (7) by the denominator (8). 7 ÷ 8 = 0∙875
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To convert 7⁄8 to a percentage, divide 7 by 8 and then multiply by 100. 7⁄8 is 87∙5%

Question

Convert \( \frac{3}{8} \) to a percentage.

Practise converting fractions to percentages

Try this quiz to practise converting fractions to percentages. You may need a pen and paper for some of the questions.

Quiz

Real-world maths

Expressing fractions as percentages is often preferred as they can be easier to understand.

A close up of an L plate on a car with the words 'Learner Driver' under it. In the background are two Black people looking at a clipboard. — Image caption,
Test results such as the driving theory test will often be recorded as a percentage.

Test results are often out of different totals. When taking tests such as the driving theory test, the pass rate may be recorded as a percentage. Eg, the score to pass is \( \frac{43}{50} \) which is 86%.

A close up of an L plate on a car with the words 'Learner Driver' under it. In the background are two Black people looking at a clipboard. — Image caption,
Test results such as the driving theory test will often be recorded as a percentage.

Game - Divided Islands

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