Fraction arithmetic Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Fraction arithmetic questions. See exactly how to solve problems on adding fractions, same denominator, subtracting fractions, simplifying.

adding fractionssame denominatorsubtracting fractionssimplifyingmultiplying fractionsdividing fractions
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Work out 17+37\frac{1}{7} + \frac{3}{7}. Give your answer as a fraction.

Worked solution

  1. Check the denominators

    17+37\frac{1}{7} + \frac{3}{7}

    Both fractions are already in sevenths, so they are ready to combine.

  2. Add the numerators

    1+37=47\frac{1 + 3}{7} = \frac{4}{7}

    With the denominators the same, add the tops and keep the bottom as 77.

  3. State the answer

    47\frac{4}{7}

    The answer is 47\frac{4}{7}, already in its simplest form.

Answer
47\frac{4}{7}
Question 2
2 markseasy
Work out 59−29\frac{5}{9} - \frac{2}{9}. Give your answer in its simplest form.

Worked solution

  1. Check the denominators

    59−29\frac{5}{9} - \frac{2}{9}

    Both fractions are already in ninths, so they are ready to combine.

  2. Subtract the numerators

    5−29=39\frac{5 - 2}{9} = \frac{3}{9}

    With the denominators the same, subtract the tops and keep the bottom as 99.

  3. Simplify and state the answer

    39=13\frac{3}{9} = \frac{1}{3}

    Divide the top and bottom by 33 to write it in its simplest form.

Answer
13\frac{1}{3}
Question 3
1 markeasy
Work out 13×14\frac{1}{3} \times \frac{1}{4}.

Worked solution

  1. Multiply the tops and the bottoms

    13×14=1×13×4\frac{1}{3} \times \frac{1}{4} = \frac{1 \times 1}{3 \times 4}

    To multiply fractions, multiply the numerators together and the denominators together.

  2. Work out the numerator and denominator

    1×13×4=112\frac{1 \times 1}{3 \times 4} = \frac{1}{12}

    The top is 11 times 1=11 = 1, and the bottom is 33 times 4=124 = 12.

  3. State the answer

    112\frac{1}{12}

    The product is 112\frac{1}{12}, already in its simplest form.

Answer
112\frac{1}{12}
Question 4
2 markseasy
Work out 38+18\frac{3}{8} + \frac{1}{8}. Give your answer in its simplest form.

Worked solution

  1. Check the denominators

    38+18\frac{3}{8} + \frac{1}{8}

    Both fractions are already in eighths, so they are ready to combine.

  2. Add the numerators

    3+18=48\frac{3 + 1}{8} = \frac{4}{8}

    With the denominators the same, add the tops and keep the bottom as 88.

  3. Simplify and state the answer

    48=12\frac{4}{8} = \frac{1}{2}

    Divide the top and bottom by 44 to write it in its simplest form.

Answer
12\frac{1}{2}
Question 5
1 markeasy
Work out 25×13\frac{2}{5} \times \frac{1}{3}.

Worked solution

  1. Multiply the tops and the bottoms

    25×13=2×15×3\frac{2}{5} \times \frac{1}{3} = \frac{2 \times 1}{5 \times 3}

    To multiply fractions, multiply the numerators together and the denominators together.

  2. Work out the numerator and denominator

    2×15×3=215\frac{2 \times 1}{5 \times 3} = \frac{2}{15}

    The top is 22 times 1=21 = 2, and the bottom is 55 times 3=153 = 15.

  3. State the answer

    215\frac{2}{15}

    The product is 215\frac{2}{15}, already in its simplest form.

Answer
215\frac{2}{15}

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