Fractions Quizzes

Fractions Practice for GCSE Maths Foundation – Simplify, Add, Subtract, Multiply & Divide

Difficulty: Foundation

Curriculum: GCSE

Start Quiz

Fractions Questions for GCSE Higher Tier Maths – Simplify, Add, Subtract, Multiply, Divide

Difficulty: Higher

Curriculum: GCSE

Start Quiz
Fractions featured image

Visual overview of Fractions.

Fractions – GCSE Maths Explained with Examples

Understanding fractions is one of the most important foundations in GCSE Maths. Fractions appear in exam questions, real-life problems, and topics such as percentages, ratios, and algebra. Learning how to add, subtract, multiply, and divide fractions accurately will help you gain confidence and improve your overall grade.

Illustration showing pizza divided into fractions

Fractions represent equal parts of a whole — like slices of a pizza.

What is a Fraction?

A fraction represents part of a whole. It is written as a/b, where:

  • a is the numerator – the number of parts you have
  • b is the denominator – the total number of equal parts

Example: \( \frac{3}{4} \) means three parts out of four equal parts.

Diagram showing proper, improper and mixed fractions

Types of Fractions

  • Proper fractions: Numerator is less than denominator (e.g. \( \frac{2}{5} \))
  • Improper fractions: Numerator ≥ denominator (e.g. \( \frac{7}{4} \))
  • Mixed numbers: Whole number and proper fraction (e.g. \( 1 \frac{3}{4} \))
  • Equivalent fractions: Different fractions with the same value (e.g. \( \frac{1}{2} = \frac{2}{4} \))

How to Work with Fractions

1️⃣ Adding and Subtracting Fractions

  1. Find a common denominator.
  2. Add or subtract the numerators only.
  3. Keep the denominator the same.
  4. Simplify if possible.

Example: \( \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \)

2️⃣ Multiplying Fractions

  1. Multiply numerators together.
  2. Multiply denominators together.
  3. Simplify the result.

Example: \( \frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5} \)

3️⃣ Dividing Fractions

  1. Flip the second fraction (take its reciprocal).
  2. Multiply the first by the reciprocal.
  3. Simplify your final answer.

Example: \( \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \)

Visual diagram showing how to add and multiply fractions

Worked Examples

Example 1 – Foundation

Add \( \frac{1}{2} + \frac{1}{3} \):

  1. LCM of 2 and 3 → 6
  2. \( \frac{1}{2} = \frac{3}{6} \), \( \frac{1}{3} = \frac{2}{6} \)
  3. Add numerators → \( 3 + 2 = 5 \)
  4. Answer: \( \frac{5}{6} \)

Example 2 – Higher

Subtract \( \frac{7}{4} - \frac{5}{6} \):

  1. LCM of 4 and 6 → 12
  2. \( \frac{7}{4} = \frac{21}{12} \), \( \frac{5}{6} = \frac{10}{12} \)
  3. \( 21 - 10 = 11 \)
  4. Answer: \( \frac{11}{12} \)

Example 3 – Multiplication

\( \frac{3}{5} \times \frac{2}{7} = \frac{6}{35} \)

Example 4 – Division

\( \frac{5}{8} \div \frac{2}{3} = \frac{5}{8} \times \frac{3}{2} = \frac{15}{16} \)

Common Mistakes

  • Forgetting to find a common denominator before adding/subtracting.
  • Not simplifying the final result.
  • Mixing numerator and denominator positions.
  • Forgetting to flip the second fraction during division.

Real-Life Applications

  • Cooking: measuring \( \frac{1}{2} \) cup or \( \frac{3}{4} \) teaspoon
  • Shopping: calculating \( \frac{1}{4} \) discounts or deals
  • DIY projects: measuring \( \frac{3}{5} \) of a length
  • Algebra: simplifying fractional coefficients
Fractions in real life examples such as cooking and discounts

Tips for Exams

  • Memorise common fractions and their decimal equivalents.
  • Write working clearly — fractions often carry 2–3 marks each in GCSE exams.
  • Always reduce to simplest form to get full marks.
  • Double-check by converting to decimals to see if the answer makes sense.

Summary

Fractions are the foundation for higher maths topics like algebra, percentages, and ratios. The key to mastering them is practice and repetition. Try the interactive Fraction Quizzes

Worked Solutions

Solution — Example 1 (Foundation): \( \frac{1}{2} + \frac{1}{3} \)

Step 1: Find the lowest common denominator (LCD) of 2 and 3 → 6.

Step 2: Convert: \( \frac{1}{2}=\frac{3}{6} \), \( \frac{1}{3}=\frac{2}{6} \).

Step 3: Add numerators: \( 3+2=5 \). Keep denominator 6.

Answer: \( \frac{5}{6} \) (already in simplest form).

Quick check: as decimals, \(0.5+0.333\ldots \approx 0.833\ldots = \frac{5}{6}\).

Solution — Example 2 (Higher): \( \frac{7}{4} - \frac{5}{6} \)

Step 1: LCD of 4 and 6 → 12.

Step 2: Convert: \( \frac{7}{4}=\frac{21}{12} \), \( \frac{5}{6}=\frac{10}{12} \).

Step 3: Subtract numerators: \( 21-10=11 \). Keep denominator 12.

Answer: \( \frac{11}{12} \) (cannot be simplified further).

Spot-check size: \( \frac{7}{4}=1.75 \) and \( \frac{5}{6}\approx 0.833\ldots \Rightarrow 1.75-0.833\ldots \approx 0.916\ldots = \frac{11}{12}\).

Solution — Example 3 (Multiplication): \( \frac{3}{5} \times \frac{2}{7} \)

Step 1: Multiply numerators: \( 3 \times 2 = 6 \).

Step 2: Multiply denominators: \( 5 \times 7 = 35 \).

Step 3: Simplify if possible: \( \frac{6}{35} \) has no common factors → already simplest.

Answer: \( \frac{6}{35} \).

Pro move: look for cross-cancellation before multiplying to keep numbers small.

Solution — Example 4 (Division): \( \frac{5}{8} \div \frac{2}{3} \)

Step 1: Keep–Change–Flip: \( \frac{5}{8} \times \frac{3}{2} \).

Step 2: Multiply: numerators \( 5 \times 3 = 15 \), denominators \( 8 \times 2 = 16 \).

Step 3: Simplify: \( \frac{15}{16} \) is already simplest.

Answer: \( \frac{15}{16} \).

Check reasonableness: dividing by \( \frac{2}{3} \) (less than 1) should make the result larger than \( \frac{5}{8} \); \( \frac{15}{16} \approx 0.9375 > 0.625 \).