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Adding and Subtracting Fractions
To add or subtract unlike fractions, rewrite them with a common denominator, combine the numerators, then simplify.
How it works
A common denominator makes the pieces the same size. The least common denominator often keeps calculations smaller, but any common multiple works if the final answer is simplified.
Worked example
Calculate 2/3 + 1/4.
- A common denominator is 12.
- 2/3 = 8/12 and 1/4 = 3/12.
- 8/12 + 3/12 = 11/12.
2/3 + 1/4 = 11/12.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Adding denominators as well as numerators.
- Changing a denominator without scaling its numerator.
- Forgetting to reduce the final fraction.
Challenge
Find two different fractions whose sum is 5/6 and whose denominators are different.
Questions learners ask
Can I add fractions without a common denominator?
No; the pieces must first be expressed in the same-sized units.
Must I use the least common denominator?
No, but it usually makes the arithmetic and simplification easier.