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    Number – Fractions, Decimals & Percentages

    Revision notes · Maths

    Lesson step 1 of 4Fractions

    Fractions

    Fractions are one of the most important building blocks in GCSE Maths, and they come up everywhere — from algebra to probability.

    To simplify a fraction, you need to find the highest common factor (HCF) of the numerator and denominator, then divide both by it. For example, to simplify 1824, the HCF of 18 and 24 is 6, so 1824 becomes 34.

    When adding or subtracting fractions, you must have the same denominator. Find the lowest common multiple (LCM) of both denominators, rewrite each fraction with that denominator, then add or subtract the numerators.

    For multiplying, it's straightforward — multiply the tops together and the bottoms together. For dividing, remember KFC: Keep the first fraction, Flip the second, and Change the ÷ to ×.

    Mixed numbers (like 2¾) should be converted to improper fractions before doing any calculation. Multiply the whole number by the denominator and add the numerator: 2¾ = (2 × 4 + 3)/4 = 114.

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    Key Terms

    HCF
    Highest Common Factor — the largest number that divides exactly into two or more numbers.
    LCM
    Lowest Common Multiple — the smallest number that is a multiple of two or more numbers.
    Recurring decimal
    A decimal that goes on forever with a repeating pattern — like 0.333… or 0.142857142857…
    Multiplier
    The single number you multiply by to apply a percentage change in one step (e.g. multiply by 1.15 to increase by 15%).