Fractions, decimals and percentages Revision Notes for AQA GCSE Maths

Fractions, decimals and percentages

Converting between fractions, decimals and percentages is a fundamental skill in GCSE Mathematics. Understanding these relationships will help you tackle a wide range of mathematical problems with confidence.

Converting decimals to percentages

To change a decimal into a percentage, you need to multiply by 100. This shifts the decimal point two places to the right.

Method:

Take your decimal number
Multiply by 100
Add the percentage symbol (%)

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Worked Example: Converting Decimals to Percentages

$0.6 \times 100 = 60\%$
$0.03 \times 100 = 3\%$
$0.25 \times 100 = 25\%$

This works because 'percent' means 'out of 100', so you're finding how many parts out of 100 your decimal represents.

Converting percentages to fractions

Any percentage can be written as a fraction with 100 as the denominator. After writing it as a fraction, you should always simplify it to its lowest terms.

Method:

Write the percentage as a fraction over 100
Simplify by finding the highest common factor
Divide both numerator and denominator by this factor

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Worked Example: Converting 60% to a Fraction

Step 1: Write as fraction over 100 $60\% = \frac{60}{100}$

Step 2: Find the highest common factor of 60 and 100 (which is 20)

Step 3: Simplify by dividing both parts by 20 $\frac{60 \div 20}{100 \div 20} = \frac{3}{5}$

So $60\% = \frac{3}{5}$ in its simplest form

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Always remember to simplify fractions to their lowest terms unless the question specifically asks you not to.

Essential equivalents to memorise

Learning these common conversions will save you time in exams and help you work more efficiently:

Key equivalents:

$\frac{1}{100} = 0.01 = 1\%$
$\frac{1}{10} = 0.1 = 10\%$
$\frac{1}{5} = 0.2 = 20\%$
$\frac{1}{4} = 0.25 = 25\%$
$\frac{1}{2} = 0.5 = 50\%$
$\frac{3}{4} = 0.75 = 75\%$

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These equivalents appear frequently in GCSE questions, so memorising them will give you a significant advantage in your exams.

Problem-solving strategies

When tackling word problems involving fractions, decimals and percentages, follow this systematic approach:

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Problem-Solving Method:

Step 1: Read the entire question carefully before starting any calculations.

Step 2: Identify what format the answer needs to be in (fraction, decimal, or percentage).

Step 3: Convert all given information to the same format before calculating.

Step 4: Work through your calculations step by step, showing all working.

For example, if you need to find what percentage of a whole something represents, it's often quickest to convert everything to percentages first. Remember that the whole quantity always represents 100%.

Ordering fractions, decimals and percentages

To compare and order different numbers in mixed formats, convert them all to the same type first. Decimals are often the easiest to compare because you can immediately see which is larger.

Method:

Convert all numbers to decimals
Compare the decimal values
Write your answer in the original format requested

This approach eliminates confusion and ensures accuracy when ordering mixed number types.

Exam tips

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Essential Exam Tips:

Show your working clearly - even if your final answer is wrong, you can still gain marks for correct method
Check your conversions - a common mistake is forgetting to multiply or divide by 100 when converting
Simplify fractions fully - always reduce fractions to their lowest terms unless told otherwise
Read questions carefully - make sure you give your answer in the format requested

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Key Points to Remember:

Decimal to percentage: multiply by 100
Percentage to fraction: write over 100, then simplify
Learn the common equivalents - they appear frequently in GCSE questions
Convert to the same format before comparing or calculating with mixed numbers
Always show your working clearly in exam questions

Fractions, decimals and percentages (AQA GCSE Maths): Revision Notes