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Solved math examples

Worked examples for every practice topic, from easy to hard. Each one shows every step, and every answer is computed and checked by Sumzo’s math engine.

  • Addition and subtraction

    Add and subtract whole numbers using place value.

    9 solved examples

  • Multiplication and division

    Times tables, long multiplication and exact division.

    9 solved examples

  • Negative numbers

    Add, subtract, multiply and divide with negative numbers.

    9 solved examples

  • Decimals

    Add, subtract, multiply and divide decimals, and write fractions as decimals.

    9 solved examples

  • Order of operations

    Brackets, powers, × and ÷, then + and − (BIDMAS / PEMDAS).

    9 solved examples

  • Fractions

    Simplify, add, subtract, multiply and divide fractions.

    9 solved examples

  • Area and perimeter

    Rectangles, triangles, parallelograms and trapeziums.

    9 solved examples

  • Percentages

    Percentages of amounts, one number as a percentage of another, and percentage change.

    9 solved examples

  • Ratio and proportion

    Simplify ratios, share amounts and solve proportions.

    9 solved examples

  • Powers and roots

    Squares, cubes and other powers, square and cube roots, and the index laws.

    9 solved examples

  • HCF and LCM

    Highest common factors and lowest common multiples, with word problems.

    9 solved examples

  • Probability

    The chance of an event as a fraction: counters, dice and repeated picks.

    9 solved examples

  • Linear equations

    Solve one-step, two-step and both-sides equations.

    9 solved examples

  • Averages and range

    Mean, median, mode and range of a data set.

    9 solved examples

  • Pythagoras’ theorem

    Find missing sides of right triangles.

    9 solved examples

  • Expanding brackets

    Multiply out single and double brackets.

    9 solved examples

  • Quadratic equations

    Solve quadratics by square roots, factorising or the formula.

    9 solved examples

  • Straight-line graphs

    Gradients and intercepts of straight lines, from equations and from two points.

    9 solved examples

  • Simultaneous equations

    Solve two linear equations in x and y together.

    9 solved examples

  • Trigonometry: exact values

    sin, cos and tan of special angles.

    9 solved examples

  • Differentiation

    Differentiate polynomials with the power rule.

    9 solved examples