Different names, same idea
A part of a whole can be shown as a ratio, a fraction, a decimal or a percentage. They are just different ways of writing the same relationship. If 1 out of 4 pupils walks to school, the fraction is 1/4, the decimal is 0.25, the percentage is 25%, and the ratio of walkers to the rest is 1 : 3.
Key idea / Key idea
Fraction → decimal: divide. Decimal → percentage: × 100. Percentage → fraction: write over 100 and simplify. Ratio a : b → fraction of the whole: a/(a+b).
Converting and comparing
| Fraction | Decimal | Percentage |
| 1/2 | 0.5 | 50% |
| 3/4 | 0.75 | 75% |
| 2/5 | 0.4 | 40% |
Worked example / Worked example
In a class the ratio of pass to fail is 3 : 1. What percentage passed?
Total parts = 3 + 1 = 4. Passers = 3/4 of the class.
3/4 = 3 ÷ 4 = 0.75 = 0.75 × 100 = 75%.
So 75% of the class passed.
Percentages make comparing easy because they all share a base of 100. To take a percentage of an amount, change it to a fraction or decimal first: 20% of RM50 = 0.2 × RM50 = RM10.
Remember / Remember
- Ratio, fraction, decimal and percentage can describe the same part.
- Percentage means "out of 100".
- × 100 to get a percentage; ÷ 100 to remove it.
- For a : b, the first part is a/(a+b) of the whole.