Number
Grade 3-5Adding & Subtracting Fractions
Adding and subtracting fractions is straightforward once the denominators match, and almost every mistake in this topic happens before that point, in finding the right common denominator. This lesson covers fractions with matching denominators, fractions that need a common denominator first, and mixed numbers.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Fractions with the same denominator
When two fractions already share a denominator, simply add or subtract the numerators and keep the denominator the same. Simplify the result fully at the end.
3/8 + 2/8 = 5/8, since the denominators already match and only the numerators are added.
Fractions with different denominators
Find the lowest common multiple of the two denominators, then convert each fraction to an equivalent fraction with that denominator before adding or subtracting the numerators. Whatever you multiply the denominator by, multiply the numerator by the same amount.
1/3 + 1/4: the LCM of 3 and 4 is 12, so 1/3 becomes 4/12 and 1/4 becomes 3/12. Adding gives 4/12 + 3/12 = 7/12.
Adding and subtracting mixed numbers
Deal with the whole numbers and fraction parts together, converting the fractions to a common denominator first. When subtracting, if the second fraction part is bigger than the first, borrow 1 from the whole number and add it to the first fraction before subtracting.
4 1/3 - 2 3/4: convert to twelfths, 4 4/12 - 2 9/12. Since 4/12 is smaller than 9/12, borrow 1 from the 4 to make 3 16/12, then subtract: 3 16/12 - 2 9/12 = 1 7/12.
Fractions in worded problems
Word problems often describe fractions of a total being used up, and ask what fraction remains. Add the fractions already accounted for, then subtract that total from 1 (representing the whole amount) to find what is left.
If 1/4 of a salary goes on rent and 2/5 goes on food, the amount spent so far is 1/4 + 2/5 = 5/20 + 8/20 = 13/20.
Worked Examples
Three exam-style questions, fully solved.
Work out 3/8 + 2/8. Give your answer in its simplest form.
Easy- 1.The denominators already match, so add the numerators: 3 + 2 = 5
- 2.Keep the denominator the same
Answer: 5/8
Work out 1/3 + 1/4. Give your answer as a fraction in its simplest form.
Medium- 1.Find the LCM of the denominators 3 and 4, which is 12
- 2.Convert each fraction to twelfths: 1/3 = 4/12, and 1/4 = 3/12
- 3.Add the numerators: 4/12 + 3/12
Answer: 7/12
Work out 4 1/3 - 2 3/4. Give your answer as a mixed number in its simplest form.
Hard- 1.Convert both fractions to twelfths: 4 1/3 = 4 4/12, and 2 3/4 = 2 9/12
- 2.4/12 is smaller than 9/12, so borrow 1 from the 4, making it 3 16/12
- 3.Subtract: 3 16/12 - 2 9/12 = 1 7/12
Answer: 1 7/12
Avoid These
The most common mistakes students make.
Adding or subtracting the denominators as well as the numerators, for example writing 1/3 + 1/4 as 2/7 instead of finding a common denominator.
Converting a fraction to a common denominator but forgetting to scale the numerator by the same factor.
Leaving the final answer unsimplified, instead of dividing the numerator and denominator by their highest common factor.
When subtracting mixed numbers, not borrowing from the whole number when the second fraction part is bigger than the first.
In "what fraction is left" word problems, forgetting to subtract the total used from 1 to find the remaining fraction.
FAQ
Questions parents and students ask.
Before this topic, make sure you know
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