Add and subtract fractions

Objective. Calculate with mixed numbers and unlike denominators.

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2. Worked example
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Learn: the key idea

Adding and subtracting fractions requires a common denominator so that the pieces being combined are the same size. First convert any mixed numbers to improper fractions, then find the lowest common multiple of the denominators and rewrite each fraction with that denominator before adding or subtracting the numerators. For example, 1½ + ⅔ becomes 3/2 + 2/3, which rewrites as 9/6 + 4/6 = 13/6, converting back to 2⅙. Always simplify the final answer and convert an improper result back to a mixed number if the question began with mixed numbers.

Worked example

Calculate 2⅓ − 1½, giving your answer as a mixed number in lowest terms.

1 $Convert to improper fractions: 2⅓ = 7/3 and 1½ = 3/2$
2 $Find a common denominator of 6: 14/6 - 9/6$
3 $Subtract the numerators: 14 - 9 = 5, giving 5/6$
4 $Check: 5/6 is already in lowest terms and less than 1, so it stays as 5/6$

Answer: 5/6

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Common mistake. Pupils often add fractions by adding numerators and denominators separately, turning ½ + ⅓ into 2/5 instead of finding the common denominator of 6 to get 3/6 + 2/6 = 5/6.

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