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QR questions frequently involve decimals (prices like £4.75, measurements like 2.5 kg) and fractions (1/4 of a total, 2/3 of a distance). Being able to convert fluently between decimals, fractions, and percentages — and to calculate with all three forms — eliminates hesitation and saves valuable seconds.
Every rational number can be expressed as a fraction, a decimal, or a percentage. Fluent conversion between these three forms is essential.
| Fraction | Division | Decimal |
|---|---|---|
| 1/2 | 1 ÷ 2 | 0.5 |
| 1/4 | 1 ÷ 4 | 0.25 |
| 3/4 | 3 ÷ 4 | 0.75 |
| 1/5 | 1 ÷ 5 | 0.2 |
| 1/8 | 1 ÷ 8 | 0.125 |
| 1/3 | 1 ÷ 3 | 0.333... |
| 2/3 | 2 ÷ 3 | 0.667... |
| Decimal | ×100 | Percentage |
|---|---|---|
| 0.35 | 35 | 35% |
| 0.08 | 8 | 8% |
| 1.25 | 125 | 125% |
| 0.667 | 66.7 | 66.7% |
| Percentage | Fraction | Simplified |
|---|---|---|
| 25% | 25/100 | 1/4 |
| 40% | 40/100 | 2/5 |
| 75% | 75/100 | 3/4 |
| 12.5% | 12.5/100 | 1/8 |
These conversions appear so frequently that you should know them instantly:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333 | 33.3% |
| 2/3 | 0.667 | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.167 | 16.7% |
| 5/6 | 0.833 | 83.3% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
Why memorise these? In QR, you often need to express a proportion as a percentage. If you calculate 240/960 and immediately recognise this as 1/4 = 25%, you save the time of a full division on the calculator.
Different forms are easier for different operations:
| Operation | Best Form | Why |
|---|---|---|
| "What fraction of X is Y?" | Fraction | Natural expression of part/whole |
| "What percentage of X is Y?" | Fraction → percentage | Calculate fraction, then ×100 |
| "Find 35% of 480" | Decimal (0.35 × 480) or building blocks | 10% + 25% = 48 + 120 = 168 |
| "Increase by 15%" | Decimal multiplier (×1.15) | One-step multiplication |
| "Decrease by 20%" | Decimal multiplier (×0.80) | One-step multiplication |
| Adding fractions | Fractions with common denominator | Standard method |
| Comparing proportions | Percentages or decimals | Easy to rank numerically |
Treat them like whole numbers, keeping track of the decimal point.
Example: 4.75 + 3.80
Example: 12.30 − 8.65
Or use the complement method: count up from 8.65 to 12.30.
Strategy: Ignore the decimal points, multiply the whole numbers, then put the decimal point back.
Example: 2.5 × 4.8
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