Fractions
Equivalent fractions, mixed numbers, improper fractions, adding, subtracting, multiplying and dividing fractions.
What is Fractions?
Fractions represent parts of a whole. In the 11+ exam, you need to understand how to simplify fractions, find equivalent fractions, convert between mixed numbers and improper fractions, and carry out all four operations with fractions.
Fraction questions appear regularly and are often combined with other topics such as percentages, decimals and word problems. Being confident with fractions is one of the most important skills for the 11+ maths paper.
Step-by-Step Method
Find common denominators for adding and subtracting
You can only add or subtract fractions when they have the same denominator. Find the lowest common multiple of both denominators.
Convert mixed numbers to improper fractions
Multiply the whole number by the denominator, add the numerator. For example, 2 3/4 = (2×4+3)/4 = 11/4.
Multiply numerators and denominators separately
To multiply fractions, multiply the tops together and the bottoms together. For example, 2/3 x 4/5 = 8/15.
To divide, flip the second fraction and multiply
Dividing by a fraction is the same as multiplying by its reciprocal. For example, 3/4 / 2/5 = 3/4 x 5/2 = 15/8.
Always simplify your answer
Divide the numerator and denominator by their highest common factor. Convert improper fractions to mixed numbers if needed.
Worked Examples
2/5 + 1/3 = ?
Working
- Find the common denominator: LCM of 5 and 3 is 15.
- 2/5 = 6/15 and 1/3 = 5/15.
- 6/15 + 5/15 = 11/15.
3/4 x 2/5 = ?
Working
- Multiply numerators: 3 x 2 = 6.
- Multiply denominators: 4 x 5 = 20.
- 6/20 simplifies to 3/10 (divide both by 2).
Convert 3 2/7 to an improper fraction.
Working
- Multiply the whole number by the denominator: 3 x 7 = 21.
- Add the numerator: 21 + 2 = 23.
- Keep the same denominator: 23/7.
Common Mistakes
Adding the denominators as well as the numerators (e.g. 1/3 + 1/4 = 2/7).
Find a common denominator first: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
Forgetting to simplify the final answer.
Always check if the numerator and denominator share a common factor.
Incorrectly converting mixed numbers (e.g. writing 2 1/3 as 2/3).
Multiply the whole number by the denominator, then add the numerator: 2 1/3 = 7/3.
Top Tips
- To find a common denominator quickly, multiply the two denominators together. It may not be the lowest, but it always works.
- Before multiplying fractions, cross-cancel to make the numbers smaller and easier to work with.
- Remember: “of” means multiply. So 3/4 of 20 means 3/4 x 20 = 15.
- If a fraction has the same numerator and denominator (e.g. 5/5), it equals 1.
- Practise converting between fractions, decimals and percentages – these appear together in many questions.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions