MathematicsExam code: 0580
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
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
Exam tip
Write the common-denominator line down
Before you add or subtract fractions, write both of them over a common denominator on a line of their own. The mark schemes give a method mark for that line alone, so it still scores if the arithmetic after it slips. The denominator need not be the lowest: 25/6 − 7/4 written as 100/24 − 42/24 earns the mark just as 50/12 − 21/12 does.