Fractions, decimals and percentages
Converting between them and finding fractions and percentages of amounts
Fractions, decimals and percentages are three ways of writing the same thing. ½ = 0.5 = 50%. Being able to switch between them is a super-skill!
Converting
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
| 1/5 | 0.2 | 20% |
| 1/3 | 0.333… | 33.3…% |
- Fraction → decimal: divide the top by the bottom (3 ÷ 8 = 0.375).
- Decimal → percentage: multiply by 100 (0.375 → 37.5%).
- To find a fraction of an amount: divide by the bottom, multiply by the top.
- To find a percentage: find 10% (÷ 10) or 1% (÷ 100) and build up.
Worked examples
Example 1. Find 3/5 of £40.
Example 2. Find 15% of 260.
Example 3. A jacket costs £60. It is reduced by 20%. What is the sale price?
Example 4. Simplify 18/24.
Top tips and common mistakes
- To add fractions, make the bottoms (denominators) the same first: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
- A percentage increase of 10% means multiply by 1.1; a decrease of 10% means multiply by 0.9.
- Percent means “out of 100”.
Shops love percentages. Now I can check if a sale really is a bargain!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Fractions, decimals and percentages worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.