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Fractions, decimals and percentages are three ways of expressing parts of a whole. Being fluent at converting between them and calculating with them is a core KS3 skill.
| Type | Description | Example |
|---|---|---|
| Proper fraction | Numerator < denominator | 3/5 |
| Improper fraction | Numerator ≥ denominator | 7/4 |
| Mixed number | Whole number + proper fraction | 1 3/4 |
Converting: 7/4 = 1 3/4 (divide 7 by 4: 1 remainder 3) 1 3/4 → 7/4 (multiply whole number by denominator and add numerator: 1×4+3 = 7)
Two fractions are equivalent if they represent the same value: 2/3 = 4/6 = 8/12.
To simplify, divide numerator and denominator by their HCF. 36/48: HCF = 12 → 36/48 = 3/4
Find a common denominator (LCM of the denominators), then add/subtract the numerators.
Example: 2/3 + 3/4 → LCM of 3 and 4 = 12 = 8/12 + 9/12 = 17/12 = 1 5/12
Multiply numerators together and denominators together. Simplify if possible.
Example: 3/5 × 10/9 = 30/45 = 2/3
(Cancel first: 3 and 9 share factor 3; 10 and 5 share factor 5 → 1/1 × 2/3 = 2/3)
Keep, Change, Flip (KCF): keep the first fraction, change ÷ to ×, flip the second fraction.
Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333… | 33.3…% |
| 2/3 | 0.666… | 66.6…% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Fraction → Decimal: divide numerator by denominator. 3/8 = 3 ÷ 8 = 0.375 Decimal → Percentage: multiply by 100. 0.375 × 100 = 37.5% Percentage → Fraction: write over 100 and simplify. 35% = 35/100 = 7/20
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