Skill 10A: Adding and subtracting proper fractions
Add and subtract fractions with different denominators, giving answers in simplest form.
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Each file is an editable Word document (.docx) with 25 questions in five columns. It opens in Word, Google Docs, Pages and LibreOffice, so you can change questions or add working space before printing.
To add or subtract fractions, they must have the same denominator. Find a common denominator, change both fractions, then add or subtract the numerators.
Example 1
Adding, with a mixed number answer
5⁄6 + 3⁄8
Find a common denominator. Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The first number in both lists is 24.
Change both fractions to have 24 as the denominator. Multiply the top and bottom by the same number.
5⁄6 = 20⁄243⁄8 = 9⁄24
Add the numerators and keep the denominator: 20 + 9 = 29.
20⁄24 + 9⁄24 = 29⁄24
29⁄24 is an improper fraction (the top is bigger than the bottom). As a mixed number it is 15⁄24.
So 5⁄6 + 3⁄8 = 15⁄24.
Answer: 15⁄24
Example 2
Subtracting, then simplifying
3⁄4 − 1⁄12
Find a common denominator. Multiples of 4: 4, 8, 12. Multiples of 12: 12. The first number in both lists is 12.
Change both fractions to have 12 as the denominator. Multiply the top and bottom by the same number.
3⁄4 = 9⁄121⁄12 = 1⁄12
Subtract the numerators and keep the denominator: 9 − 1 = 8.
9⁄12 − 1⁄12 = 8⁄12
Simplify: divide the top and bottom by 4. 8⁄12 = 2⁄3.
So 3⁄4 − 1⁄12 = 2⁄3.
Answer: 2⁄3
Top tips
The denominator tells you the size of the pieces: you can only add pieces of the same size.
Use the lowest common multiple so the numbers stay small.
Simplify at the end by dividing top and bottom by the same number.
Watch out for
Adding the denominators as well as the numerators.
Leaving the answer unsimplified.
Try some questions
These are from the worksheet. Work each one out, then open it to check.