Mathematics (Core)Exam code: 0580
Operations with Fractions
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
Each step of a mixed-number sum scores
A calculation with two fractions or mixed numbers was set in 12 of the 22 papers, including every Paper 1. When mixed numbers are added or subtracted, the schemes give one mark for the improper fractions, one for both fractions written over a common denominator, and the last for the answer in the form asked. Stopping at 17/10 when the question wants a mixed number in its simplest form (1 7/10) costs that last mark.
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