GCSE Maths Practice: fractions

Question 6 of 11

This question checks your ability to calculate a multi-step fractional expression. Evaluate brackets first, then solve the numerator and denominator separately before combining them into a single fraction.

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\( \begin{array}{l}\text{Calculate:}\\[8pt]\dfrac{\dfrac{18}{(10 - 4)}}{\dfrac{16}{4}}\end{array} \)

Choose one option:

Follow BIDMAS strictly: brackets → numerator → denominator → division. Write each part separately to stay organised.

This question type involves compound fractions—fractions within fractions. You must follow the correct order of operations (BIDMAS): solve brackets first, simplify the numerator, then the denominator, and finally divide the two results.

Worked Examples

Example 1:
Calculate \( \dfrac{\dfrac{20}{(9 - 4)}}{\dfrac{15}{5}} \)

  1. Brackets: \(9 - 4 = 5\).
  2. Numerator: \(20 \div 5 = 4\).
  3. Denominator: \(15 \div 5 = 3\).
  4. Final step: \( \tfrac{4}{3} \).

Answer: \( \tfrac{4}{3} \)

Example 2:
Calculate \( \dfrac{\dfrac{30}{(8 - 2)}}{\dfrac{25}{5}} \)

  1. Brackets: \(8 - 2 = 6\).
  2. Numerator: \(30 \div 6 = 5\).
  3. Denominator: \(25 \div 5 = 5\).
  4. Final step: \( \tfrac{5}{5} = 1 \).

Answer: 1

Example 3:
Calculate \( \dfrac{\dfrac{14}{(9 - 3)}}{\dfrac{18}{6}} \)

  1. Brackets: \(9 - 3 = 6\).
  2. Numerator: \(14 \div 6 = \tfrac{7}{3}\).
  3. Denominator: \(18 \div 6 = 3\).
  4. Final step: \( \tfrac{7}{3} \div 3 = \tfrac{7}{9} \).

Answer: \( \tfrac{7}{9} \)

Example 4:
Calculate \( \dfrac{\dfrac{28}{(13 - 7)}}{\dfrac{12}{3}} \)

  1. Brackets: \(13 - 7 = 6\).
  2. Numerator: \(28 \div 6 = \tfrac{14}{3}\).
  3. Denominator: \(12 \div 3 = 4\).
  4. Final step: \( \tfrac{\tfrac{14}{3}}{4} = \tfrac{7}{6} \).

Answer: \( \tfrac{7}{6} \)

Common Mistakes

  • Forgetting to simplify the brackets first.
  • Trying to simplify across the main fraction bar before evaluating top and bottom separately.
  • Confusing subtraction and division inside the bracket.
  • Leaving the final fraction unsimplified.

Exam Tip

Always show clear steps: brackets → top → bottom → final fraction → simplify. Even if you make a slip later, correct structure earns method marks.

Try These Yourself

Now test your understanding by solving these (answers appear after you submit):

  • \( \dfrac{\dfrac{33}{(14 - 5)}}{\dfrac{18}{6}} \)
  • \( \dfrac{\dfrac{24}{(11 - 9)}}{\dfrac{20}{5}} \)
  • \( \dfrac{\dfrac{45}{(21 - 12)}}{\dfrac{15}{3}} \)

These follow exactly the same logic as the examples above.