4.1 Working with Fractions

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: equivalent fractions, simplifying, comparing, and adding and subtracting fractions. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Find equivalent fractions and write a fraction in its simplest form
• Change between mixed numbers and improper fractions
• Compare and order fractions using a common denominator
• Add and subtract fractions and mixed numbers

Key words

• Numerator: The top number of a fraction: how many parts you have.
• Denominator: The bottom number: how many equal parts the whole is split into.
• Equivalent fractions: Fractions that have the same value, e.g. 2/3 = 4/6.
• Simplest form: A fraction whose numerator and denominator have no common factor except 1.
• Mixed number: A whole number and a fraction, e.g. 2 3/4.
• Improper fraction: A fraction with a numerator bigger than its denominator, e.g. 11/4.

Equivalent fractions and simplifying

Multiply or divide the numerator and the denominator by the same number and the value of the fraction does not change.

Worked example: simplifying

Write 24/36 in its simplest form.
The highest common factor of 24 and 36 is 12. 24 ÷ 12 = 2 and 36 ÷ 12 = 3.
Or divide in steps: 24/36 = 12/18 = 6/9 = 2/3.

Answer: 2/3

Worked example: finding a missing number

5/8 = ?/40. 8 × 5 = 40, so multiply the numerator by 5 too: 5 × 5 = 25.

Answer: 25/40

Mixed numbers and improper fractions

To change a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. To go back, divide: the remainder is the new numerator.

Worked example: both ways

3 2/5 = (3 × 5 + 2)/5 = 17/5
23/6: 23 ÷ 6 = 3 remainder 5, so 23/6 = 3 5/6

Answer: 17/5 and 3 5/6

Comparing and ordering fractions

To compare fractions, write them with a common denominator (the lowest common multiple of the denominators). Then compare the numerators.

Worked example: ordering

Write 3/4, 5/6, 7/12 and 2/3 in order of size, smallest first.
The LCM of 4, 6, 12 and 3 is 12: 3/4 = 9/12, 5/6 = 10/12, 7/12 = 7/12, 2/3 = 8/12.
Order the numerators: 7, 8, 9, 10.

Answer: 7/12, 2/3, 3/4, 5/6

Adding and subtracting fractions

If the denominators are the same, add or subtract the numerators and keep the denominator. If they are different, first change to equivalent fractions with a common denominator.

Worked example: different denominators

1/3 + 1/4 = 4/12 + 3/12 = 7/12
5/6 − 3/8: LCM of 6 and 8 is 24. 20/24 − 9/24 = 11/24

Answer: 7/12 and 11/24

Key fact: Never add the denominators. 1/3 + 1/4 is not 2/7: the parts must be the same size before you add them.

Adding and subtracting mixed numbers

Change the mixed numbers to improper fractions first (or add the whole numbers and the fractions separately). Give the answer as a mixed number in its simplest form.

Worked example: mixed numbers

2 1/2 + 1 2/3 = 5/2 + 5/3 = 15/6 + 10/6 = 25/6 = 4 1/6
4 1/4 − 1 5/6 = 17/4 − 11/6 = 51/12 − 22/12 = 29/12 = 2 5/12

Answer: 4 1/6 and 2 5/12

Common mistakes

• Adding the denominators: 2/5 + 1/3 is not 3/8.
• Changing the denominator but not the numerator when making equivalent fractions.
• Not simplifying the final answer, or not changing an improper answer back to a mixed number.
• Thinking 1/8 is bigger than 1/6 because 8 is bigger than 6.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 18/24 in its simplest form. (Type your answer like 2/5.)

Answer: 3/4

Working: HCF of 18 and 24 is 6: 18/24 = 3/4.

Question 2. Find the missing number: 5/7 = ?/35

Answer: 25

Working: 7 × 5 = 35, so 5 × 5 = 25.

Question 3. Which fraction is the largest? (Choose from: 2/3, 3/5, 7/10, 5/8.)

Answer: 7/10

Working: 2/3 = 0.667, 3/5 = 0.6, 7/10 = 0.7, 5/8 = 0.625. The largest is 7/10.

Related lessons

• Previous lesson: 3.8 Line of Best Fit
• Next lesson: 4.2 Operations with Fractions
• In this chapter: 4.3 Multiplying Fractions
• In this chapter: 4.4 Dividing Fractions
• In this chapter: 4.5 Fractions and Decimals

Continue in the full course

This lesson is section 4.1 (EGCMF0401) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.