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Fractions Toolkit

Number

Working with a common denominator

  • Fractions can only be added or subtracted once they share a denominator
  • Find the lowest common denominator, which is the lowest common multiple of the two denominators
  • Scale each fraction up so that both sit over that shared denominator
  • Combine the numerators and keep the denominator unchanged
    • Denominators are never added together
  • Simplify the result, returning it to mixed-number form where the question demands that

When a mixed number appears

  • Convert every mixed number to an improper fraction before starting
  • Carry out the addition or subtraction as usual, then convert back at the end
Exam tip

Write the two fractions over a common denominator on their own line before adding. That line is the method mark, and it is still earned even if the arithmetic after it goes wrong.

Worked example

Subtracting mixed numbers

Work out 4 1/6 − 1 3/4, giving the answer as a mixed number.

Solution:

  • Convert both to improper fractions: 4 1/6 = 25/6 and 1 3/4 = 7/4
  • The lowest common multiple of 6 and 4 is 12
  • Rewrite over 12: 25/6 = 50/12 and 7/4 = 21/12
  • Subtract the numerators: 50 − 21 = 29, giving 29/12
  • Convert back: 29 ÷ 12 = 2 remainder 5, so the answer is 2 5/12