GCSE Fraction arithmetic Practice Questions

Free GCSE Fraction arithmetic practice questions with full step-by-step worked solutions. Covers adding fractions, same denominator, subtracting fractions, simplifying. Practise exam-style problems and check your method.

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.
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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
1 markeasy
Work out 12\frac{1}{2} of 35\frac{3}{5}.
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Worked solution

  1. "Of" means multiply

    12 of 35=12×35\frac{1}{2} \text{ of } \frac{3}{5} = \frac{1}{2} \times \frac{3}{5}

    Finding a fraction OF another fraction means multiplying the two fractions together.

  2. Multiply the tops and the bottoms

    12×35=310\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}

    The top is 11 times 3=33 = 3, and the bottom is 22 times 5=105 = 10.

  3. State the answer

    310\frac{3}{10}

    The answer is 310\frac{3}{10}.

Answer
310\frac{3}{10}
Question 3
2 marksintermediate
Work out 23+34\frac{2}{3} + \frac{3}{4}. Give your answer as a mixed number.
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Worked solution

  1. Find the common denominator

    LCD of 3 and 4=12\text{LCD of } 3 \text{ and } 4 = 12

    The lowest number both 33 and 44 divide into is 1212, so change both fractions into twelfths.

  2. Rewrite the first fraction

    23=812\frac{2}{3} = \frac{8}{12}

    Multiply the top and bottom of the first fraction by 44.

  3. Rewrite the second fraction

    34=912\frac{3}{4} = \frac{9}{12}

    Multiply the top and bottom of the second fraction by 33.

  4. Add the numerators

    812+912=1712\frac{8}{12} + \frac{9}{12} = \frac{17}{12}

    The bottoms match now, so add the tops to get 1717 over 1212.

  5. Write it as a mixed number

    1712=1512\frac{17}{12} = 1\frac{5}{12}

    The improper fraction 1712\frac{17}{12} becomes the mixed number 15121\frac{5}{12}.

  6. State the answer

    15121\frac{5}{12}

    The answer is 15121\frac{5}{12}.

Answer
15121\frac{5}{12}
Question 4
4 markshard
Work out 23×(34+12)\frac{2}{3} \times \left(\frac{3}{4} + \frac{1}{2}\right). Give your answer in its simplest form.
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Worked solution

  1. Do the brackets first

    23×(34+12)\frac{2}{3} \times \left(\frac{3}{4} + \frac{1}{2}\right)

    Work out the bracket before multiplying.

  2. Find the common denominator

    LCD of 4 and 2=4\text{LCD of } 4 \text{ and } 2 = 4

    Both 44 and 22 divide into 44.

  3. Add inside the bracket

    34+24=54\frac{3}{4} + \frac{2}{4} = \frac{5}{4}

    One half is two quarters, so the bracket is five quarters.

  4. Rewrite the calculation

    23×54\frac{2}{3} \times \frac{5}{4}

    Now multiply two thirds by five quarters.

  5. Multiply straight across

    2×53×4=1012\frac{2 \times 5}{3 \times 4} = \frac{10}{12}

    The top is 1010 and the bottom is 1212.

  6. Simplify

    1012=56\frac{10}{12} = \frac{5}{6}

    Ten twelfths simplifies to five sixths.

  7. Sense check with a decimal

    23×(34+12)≈0.833\frac{2}{3} \times \left(\frac{3}{4} + \frac{1}{2}\right) \approx 0.833

    As a decimal this is about 0.8330.833, which is the right size — a quick reassurance that the answer is reasonable.

  8. Check by cancelling first

    23×54=56\frac{2}{3} \times \frac{5}{4} = \frac{5}{6}

    Cancelling the 22 and the 44 before multiplying gives the same answer.

  9. Confirm it is in simplest form

    gcd⁡(5,6)=1\gcd(5, 6) = 1

    The top and bottom share no common factor, so 56\frac{5}{6} cannot be simplified any further.

  10. State the answer

    56\frac{5}{6}

    The answer is 56\frac{5}{6}.

Answer
56\frac{5}{6}
Question 5
6 markschallenging
Work out 313−112×1193\frac{1}{3} - 1\frac{1}{2} \times 1\frac{1}{9}. Give your answer as a mixed number.
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Worked solution

  1. Apply the order of operations

    313−112×1193\frac{1}{3} - 1\frac{1}{2} \times 1\frac{1}{9}

    Multiplication comes before subtraction, so multiply first.

  2. Convert the first factor

    112=321\frac{1}{2} = \frac{3}{2}

    11 times 22 plus 11 is 33, so it is three halves.

  3. Convert the second factor

    119=1091\frac{1}{9} = \frac{10}{9}

    11 times 99 plus 11 is 1010, so it is ten ninths.

  4. Multiply

    32×109=3018\frac{3}{2} \times \frac{10}{9} = \frac{30}{18}

    Multiply the tops (3×10=30)(3\times 10=30) and the bottoms (2×9=18)(2\times 9=18).

  5. Simplify the product

    3018=53\frac{30}{18} = \frac{5}{3}

    Divide top and bottom by 66.

  6. Convert the first number

    313=1033\frac{1}{3} = \frac{10}{3}

    33 times 33 plus 11 is 1010, so it is ten thirds.

  7. Set up the subtraction

    103−53\frac{10}{3} - \frac{5}{3}

    Both fractions are already in thirds.

  8. Subtract the thirds

    103−53=53\frac{10}{3} - \frac{5}{3} = \frac{5}{3}

    Subtract the tops: 10−5=510 - 5 = 5.

  9. Convert to a mixed number

    53=123\frac{5}{3} = 1\frac{2}{3}

    Three thirds make one whole, leaving two thirds.

  10. Sense check with a decimal

    313−112×119≈1.6673\frac{1}{3} - 1\frac{1}{2} \times 1\frac{1}{9} \approx 1.667

    As a decimal this is about 1.6671.667, which is the right size — a quick reassurance that the answer is reasonable.

  11. Watch for the common error

    (313−112)×119≠123\left(3\frac{1}{3} - 1\frac{1}{2}\right) \times 1\frac{1}{9} \ne 1\frac{2}{3}

    Subtracting before multiplying breaks the order of operations.

  12. Notice the answer is exact

    53\frac{5}{3}

    Every step used exact fractions, so the answer is exact with no rounding.

  13. Sense check the size

    313−123≈1.673\frac{1}{3} - 1\frac{2}{3} \approx 1.67

    Taking about 1.671.67 from 3.333.33 leaves about 1.671.67, which matches one and two thirds.

  14. Reflect on the method

    multiply, then subtract

    Doing the multiplication first was essential to reach the correct answer.

  15. State the answer

    1231\frac{2}{3}

    The answer is 1231\frac{2}{3}.

Answer
1231\frac{2}{3}

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