Fractions can only be added or subtracted when they describe pieces of the same size, which means they need a common denominator. This calculator handles up to six fractions or mixed numbers in a single expression, chooses the least common denominator, shows each fraction rewritten over it, combines the numerators and simplifies the result.
How to use the calculator
- Choose how many fractions you want to combine, from 2 to 6.
- Enter each fraction. Use the left box for the whole part of a mixed number (2 1/3) or leave it empty for a simple fraction. Put a minus sign on the whole number or numerator for a negative value.
- Between fractions, choose + add or − subtract. The expression reads left to right, like a sentence.
- The tape shows the answer as a mixed number and as a simplified fraction, the decimal value and the least common denominator. The full expression and answer are shown under the steps.
The method
- Convert mixed numbers to improper fractions: 2 1/3 = (2 × 3 + 1)/3 = 7/3.
- Find the least common denominator (LCD), the least common multiple of all the denominators.
- Rewrite each fraction over the LCD by multiplying its numerator and denominator by LCD ÷ its denominator.
- Add or subtract the numerators and keep the LCD as the denominator.
- Simplify by dividing by the greatest common factor, and convert to a mixed number if the result is improper.
Worked example: 1/2 + 2/3 − 3/4
- The denominators are 2, 3 and 4. Their least common multiple is 12 (4 = 2², 3 = 3, so LCD = 2² × 3).
- Rewrite: 1/2 = 6/12, 2/3 = 8/12, 3/4 = 9/12.
- Combine the numerators: 6 + 8 − 9 = 5.
- The answer is 5/12, already in lowest terms (≈ 0.4167).
Finding the LCD quickly
| Denominators | Shortcut | LCD |
|---|---|---|
| 4 and 8 | One divides the other — use the larger | 8 |
| 3 and 5 | No common factor — multiply them | 15 |
| 6 and 8 | List multiples of 8 until one is divisible by 6 | 24 |
| 4, 6 and 9 | Prime factors 2², 2·3, 3² → 2² × 3² | 36 |
For long lists or large denominators, the LCD calculator shows the prime-factor method in detail.
Mixed numbers and negatives
Mixed numbers are converted to improper fractions first, so 2 1/3 − 1 1/6 becomes 7/3 − 7/6 = 14/6 − 7/6 = 7/6 = 1 1/6. A negative mixed number such as −2 1/3 means −(2 + 1/3) = −7/3; the minus sign applies to the whole number, not just its whole part. If you would rather add the whole parts and fraction parts separately, the mixed number calculator shows that method too.
Checking your answer
Estimate before you calculate: 1/2 + 2/3 − 3/4 is about 0.5 + 0.67 − 0.75 ≈ 0.42, and 5/12 ≈ 0.4167, so the answer is sensible. The estimating fractions calculator teaches this benchmark habit. For multiplying and dividing fractions as well as adding them, use the fraction calculator.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator — the least common multiple of the denominators is the smallest choice — and rewrite each fraction over it by multiplying its top and bottom by the same number. Then add the numerators, keep the denominator and simplify.
Why can't you just add the denominators?
The denominator names the size of the pieces, and you can only count pieces of the same size. 1/2 + 1/3 is not 2/5; written in sixths it is 3/6 + 2/6 = 5/6. Adding the denominators would change the piece size.
How do I subtract a larger fraction from a smaller one?
Work the same way; the numerator simply becomes negative. For 1/4 − 2/3, rewrite as 3/12 − 8/12 = −5/12. The calculator handles negative results and negative inputs automatically.
Do I have to use the least common denominator?
No — any common denominator works, such as the product of the denominators. The least one keeps the numbers small, so there is less simplifying at the end.