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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.
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