Adding and Subtracting Fractions with Unlike Denominators
Adding and Subtracting Fractions with Unlike Denominators covers adding or subtracting fractions whose denominators are different, which requires converting them to equivalent fractions sharing a common denominator before combining the numerators. It is a core non-calculator 11+ skill, tested both as a stand-alone calculation and hidden inside worded problems that ask what fraction of something remains or has been used.
Before you start
Make sure you're comfortable with these topics first:
Method
- Check whether the denominators are already the same; if so, simply add or subtract the numerators and keep the denominator.
- If the denominators differ, find a common denominator, ideally the lowest common multiple of the two denominators, to keep the numbers as small as possible.
- Convert each fraction to an equivalent fraction with the common denominator, multiplying the numerator by the same factor as the denominator.
- Add or subtract the numerators of the converted fractions, keeping the common denominator unchanged.
- Simplify the resulting fraction fully, dividing the numerator and denominator by their highest common factor.
- For mixed numbers, either convert to improper fractions first, or add or subtract the whole-number parts and fraction parts separately, carrying or borrowing a whole number where needed.
- Check your answer is sensible: an answer greater than 1 from adding two fractions each less than 1 should be written as a mixed number if the question expects one.
Worked example
Work out 3/4 - 2/5, giving your answer as a fraction in its simplest form.
- Find the lowest common multiple of 4 and 5: since they share no common factor, the lowest common multiple is 4 x 5 = 20.
- Convert 3/4 to twentieths: multiply the numerator and denominator by 5, giving 15/20.
- Convert 2/5 to twentieths: multiply the numerator and denominator by 4, giving 8/20.
- Subtract the numerators: 15/20 - 8/20 = 7/20.
- Check the fraction is fully simplified: 7 and 20 share no common factor other than 1, so 7/20 is the final answer.
Practice questions
Try each question, then tap to reveal the answer.
Q1Work out 1/3 + 1/6.Show answer
Answer: Common denominator 6: 2/6 + 1/6 = 3/6 = 1/2.
Q2Work out 5/6 - 1/2.Show answer
Answer: Common denominator 6: 5/6 - 3/6 = 2/6 = 1/3.
Q3Work out 2/5 + 1/4.Show answer
Answer: Common denominator 20: 8/20 + 5/20 = 13/20.
Q4Work out 7/8 - 1/3.Show answer
Answer: Common denominator 24: 21/24 - 8/24 = 13/24.
Q5Work out 1 1/2 + 2/3.Show answer
Answer: Convert to sixths: 9/6 + 4/6 = 13/6 = 2 1/6.
Q6Work out 3/4 + 1/6.Show answer
Answer: Common denominator 12: 9/12 + 2/12 = 11/12.
Q7Work out 5/9 - 1/3.Show answer
Answer: Common denominator 9: 5/9 - 3/9 = 2/9.
Q8Work out 2 1/4 - 1 1/2.Show answer
Answer: Convert to quarters: 9/4 - 6/4 = 3/4.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A tank is 2/3 full of water. A further 1/5 of the tank's capacity is added. What fraction of the tank is now full? Give your answer as a fraction in its simplest form, and state whether it is possible for the tank to now be more than full.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Ali eats 3/8 of a pizza. Bea eats 1/6 of the same pizza. (a) What fraction of the pizza have they eaten altogether? (b) What fraction of the pizza is left?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the adding and subtracting fractions with unlike denominators worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 40 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on adding and subtracting fractions with unlike denominators, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.