How to Add and Subtract Fractions
7 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Fractions are easy once you know one rule: you can only add or subtract pieces of the same size. That is why denominators matter. This guide covers like and unlike denominators, mixed numbers, and the multiplication and division rules.
Same denominator: just add the tops
3/8 + 2/8 = 5/8. The denominator names the size of the piece, so it stays the same. Subtraction works the same way: 7/10 − 3/10 = 4/10 = 2/5.
Different denominators: find a common one
- Find a common denominator (the LCM of the denominators is the smallest choice).
- Rewrite each fraction with that denominator.
- Add or subtract the numerators.
- Simplify.
Example: 2/3 + 3/4. The LCM of 3 and 4 is 12. 2/3 = 8/12 and 3/4 = 9/12, so the sum is 17/12 = 1 5/12.
Subtraction example: 7/8 − 1/6. LCM(8, 6) = 24. 7/8 = 21/24 and 1/6 = 4/24, so the answer is 17/24.
A shortcut that always works is to multiply the denominators (3 × 4 = 12) and cross-multiply the tops, which is what the fraction calculator does before simplifying.
Multiplying and dividing
Multiply straight across: 5/6 × 9/10 = 45/60 = 3/4. Divide by flipping the second fraction and multiplying: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. No common denominator is needed for either.
Mixed numbers
Convert to improper fractions first. 2 1/3 + 1 3/4 = 7/3 + 7/4 = 28/12 + 21/12 = 49/12 = 4 1/12. You can also add wholes and fractions separately: 2 + 1 = 3 and 1/3 + 3/4 = 13/12 = 1 1/12, so 3 + 1 1/12 = 4 1/12.
Simplifying
Divide the top and bottom by their greatest common factor. See how to simplify fractions. Always check the final answer is in lowest terms.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Add 2/3 + 3/4.
Show answer
Simplified fraction: 17/12
- Find the GCF and LCM of 18 and 24.
Show answer
GCF (greatest common factor): 6 · LCM (least common multiple): 72
- Write 0.85 as a fraction.
Show answer
Fraction (lowest terms): 17/20
Frequently asked questions
Why can’t I add the denominators?
The denominator tells you the size of the pieces, not how many you have. 1/2 + 1/3 is not 2/5 because halves and thirds are different sizes.
What is the least common denominator?
The smallest number that both denominators divide into evenly, the LCM.
How do I subtract mixed numbers when the fraction is too small?
Borrow one whole from the whole-number part and add it to the fraction, or convert to improper fractions.
Do I always need a common denominator?
Only to add or subtract. Not to multiply or divide.
Try it yourself
Fraction CalculatorAdd, subtract, multiply and divide fractions with simplified and mixed-number answers.
GCF and LCM CalculatorFind the greatest common factor and least common multiple of up to 8 numbers.Decimal to Fraction CalculatorTurn any decimal into a simplified fraction or mixed number.Keep learning
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