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Fractions Explained: Add, Multiply, Divide and Simplify

Learn how fractions work, with step-by-step examples for adding, multiplying, dividing and simplifying them. Ideal for KS3 and middle school.

  • ⏱ 3 min read
  • ✏️ 3 worked examples
  • 🎯 5 practice questions
  • 📶 Beginner
KS3Middle School
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Curriculum fit: GCSE Maths Number (Foundation and Higher); KS3 fractions. US: Grade 3-6 fractions, reviewed in Algebra I.

On this page

What Is It?

A fraction shows part of a whole. The numerator (top number) says how many parts you have, and the denominator (bottom number) says how many equal parts the whole is split into. In 3/4 you have 3 of 4 equal parts.

Fractions can be equivalent: 1/2, 2/4 and 5/10 all show the same amount. Most fraction work involves finding equivalent fractions, simplifying, and adding, subtracting, multiplying or dividing.

3/4 (three quarters)6/8 (six eighths)× 2 on the top and bottomSame shaded amount, so 3/4 = 6/8.
3/4 and 6/8 cover the same amount of the bar, so they are equivalent fractions. Multiply the top and the bottom by the same number to make one.

Key Formulas and Ideas

  • Equivalent fractions: multiply or divide the top and bottom by the same number.
  • Add or subtract: write both fractions with a common denominator, then add or subtract the numerators.
  • Multiply: multiply the numerators and multiply the denominators.
  • Divide: multiply by the reciprocal of the second fraction (turn it upside down).

Worked Examples

Example 1

Adding

Question

Work out 3/4 + 1/6.

  1. The lowest common denominator of 4 and 6 is 12.
  2. 3/4 = 9/12 and 1/6 = 2/12.
  3. Add the numerators: 9/12 + 2/12 = 11/12.

✓ Answer 11/12

Example 2

Multiplying

Question

Work out 2/3 × 3/4.

  1. Multiply the numerators: 2 × 3 = 6.
  2. Multiply the denominators: 3 × 4 = 12.
  3. Simplify 6/12 by dividing by 6.

✓ Answer 1/2

Example 3

Dividing

Question

Work out 3/5 ÷ 1/10.

  1. Turn the second fraction upside down: 10/1.
  2. Multiply: 3/5 × 10 = 30/5.
  3. Simplify: 30 ÷ 5 = 6.

✓ Answer 6

Common Mistakes to Avoid

  • Adding the denominators as well as the numerators, so 1/2 + 1/3 becomes 2/5.
  • Adding fractions without first finding a common denominator.
  • Forgetting to flip the second fraction when dividing.
  • Not simplifying the final answer.

Practice Questions

0 of 5 answered
Q1What is 1/2 + 1/3?
Q2Simplify 6/8.
Q3What is 2/3 × 3/4?
Q4What is 1/2 ÷ 1/4?
Q5Which fraction is equivalent to 2/5?

Frequently Asked Questions

Why do I need a common denominator to add fractions?

Because you can only add parts that are the same size. Rewriting makes the pieces equal in size so they can be counted together.

Is 4/4 a fraction?

Yes. It equals 1 whole, because all four parts are present.

How do I find a common denominator?

Find a number that both denominators divide into, such as their lowest common multiple. For 4 and 6 it is 12.

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Sources and Review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.