Appears in: Functional Skills Level 1 · Functional Skills Level 2 · GCSE foundation
Fractions, decimals and percentages
Fractions, decimals and percentages are three ways of writing the same thing. Exams test whether you can move between them, order a mixed list, and calculate with them. Learn a handful of equivalents by heart and the rest is one of two conversions.
The conversions
- Fraction → decimal: top ÷ bottom. 3/8 = 3 ÷ 8 = 0.375.
- Decimal → percentage: × 100. 0.375 = 37.5%. Percentage → decimal: ÷ 100.
- Decimal → fraction: write it over 10, 100 or 1,000 and simplify. 0.6 = 6/10 = 3/5. Percentage → fraction: over 100 and simplify. 45% = 45/100 = 9/20.
- To compare or order a mixed list, convert everything to decimals (or all to percentages) first.
- Fraction of an amount: divide by the bottom, multiply by the top. 3/8 of 96 → 96 ÷ 8 = 12, × 3 = 36.
- Adding or subtracting fractions: make the bottoms the same first, then add the tops. Never add tops and bottoms separately.
- Know these cold: ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ¾ = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%, 1/3 ≈ 0.333 ≈ 33.3%.
Worked examples
Example 1
Write 3/8 as a decimal and as a percentage.
- 3 ÷ 8 = 0.375.
- 0.375 × 100 = 37.5%.
Example 2
Put 0.7, 2/3 and 65% in order, smallest first.
- Convert to decimals: 0.7; 2/3 = 0.667…; 65% = 0.65.
- Order: 65%, 2/3, 0.7.
Example 3
Work out 3/8 of 96.
- 96 ÷ 8 = 12.
- 12 × 3 = 36.
Example 4
Work out 2/5 + 1/4.
- The bottoms need to be the same. 20 works for both: 2/5 = 8/20 and 1/4 = 5/20.
- 8/20 + 5/20 = 13/20.
Where the marks go missing
- Adding the tops and the bottoms: 2/5 + 1/4 is not 3/9. Find a common denominator first.
- Turning 5% into 0.5. Divide by 100: 0.05.
- Comparing 2/3 and 0.6 by eye. Convert both to decimals: 0.667 is bigger.
Frequently asked questions
How do you convert a fraction to a percentage?
Divide the top by the bottom to get a decimal, then multiply by 100. 5/8 = 0.625 = 62.5%.
How do you work out a fraction of an amount?
Divide the amount by the bottom of the fraction, then multiply by the top. 2/3 of 45 is 45 ÷ 3 = 15, × 2 = 30.