GCSE Maths Fractions, Decimals & Percentages Notes
Fractions, decimals and percentages are three ways to write the same value. Converting fluently between them is a core GCSE skill worth easy marks.
Key concepts
- Fraction
- A part of a whole, written as numerator/denominator, e.g. 3/4.
- Converting to a percentage
- Multiply a decimal by 100, or make the fraction out of 100.
- Equivalent fractions
- Multiply or divide top and bottom by the same number to keep the value the same.
Key formulas
Fraction → decimal
divide numerator by denominator
Decimal → percentage
× 100
Percentage → fraction
put over 100, then simplify
Worked example
Write 3/8 as a decimal and a percentage.
- 1Divide to get the decimal: 3 ÷ 8 = 0.375.
- 2Multiply by 100 for the percentage: 0.375 × 100 = 37.5%.
Answer: 0.375 and 37.5%
Common mistakes
✗ Adding fractions by adding tops and bottoms, e.g. 1/2 + 1/3 = 2/5.
✓ Use a common denominator first: 3/6 + 2/6 = 5/6.
✗ Confusing 0.5% with 0.5.
✓ 0.5% = 0.005; 0.5 = 50%. Divide a percentage by 100 to get the decimal.
✗ Not simplifying the final fraction.
✓ Divide top and bottom by their HCF to give lowest terms.
Quick check
Try these, then reveal the answers.
Write 0.6 as a fraction in its simplest form.Reveal answer
3/5
Convert 45% to a decimal.Reveal answer
0.45
Work out 1/4 + 1/2.Reveal answer
3/4
Exam tips
- To order a mixed list, convert everything to decimals first — it is easiest to compare.
- For 'fraction of an amount', divide by the denominator then multiply by the numerator.
- Simplify fractions fully or you may lose the final accuracy mark.
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Frequently asked questions
How do I add fractions with different denominators?+
Find a common denominator, rewrite each fraction, then add the numerators and keep the denominator.
How do I turn a recurring decimal into a fraction?+
Use algebra: set the decimal equal to x, multiply to shift the digits, then subtract to remove the recurring part.
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