Add and subtract fractions
Objective. Calculate with fractions whose denominators differ.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Adding or subtracting fractions requires a common denominator so the pieces being combined are the same size. First find the lowest common multiple of the denominators, convert each fraction, then add or subtract the numerators while keeping the denominator unchanged. For example, 1/4+1/6 becomes 3/12+2/12=5/12 once both are written over twelfths. With mixed numbers, convert to improper fractions first, or add the whole-number parts and fraction parts separately, carrying over if the fraction part exceeds 1. Always simplify the final answer fully.
Worked example
Work out 5/6 − 3/8, giving your answer as a fraction in its simplest form.
- 1Find the LCM of 6 and 8, which is 24.
- 2Convert: 5/6=20/24 and 3/8=9/24.
- 3Subtract the numerators: 20−9=11, giving 11/24.
- 4Check 11 and 24 share no common factor, so it is fully simplified.
Answer: 11/24
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often add numerators and denominators straight across, turning 1/3+1/4 into the wrong answer 2/7. Insist on a common denominator before any addition takes place.
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