Adding Fractions Calculator
Add or subtract up to four fractions in one go. Enter plain fractions or mixed numbers, choose each operation, and get the exact LCD, a fully reduced answer, a mixed number, and a decimal, with every step shown.
Formula
Worked example
1/2 + 1/3: LCD(2,3) = 6. Rewrite as 3/6 + 2/6 = 5/6. GCD(5,6) = 1, already in lowest terms. Decimal = 0.833333.
How to add and subtract fractions step by step
Fractions can only be added or subtracted once they share a common denominator, because the denominator defines the size of each part you are counting. The most efficient common denominator is the least common denominator (LCD), which is the least common multiple of all the denominators involved. Start by finding the LCD, then rewrite each fraction as an equivalent fraction over that LCD by multiplying numerator and denominator by the appropriate scaling factor. Once every fraction has the same denominator you simply add or subtract the numerators and keep the denominator. The formula for two fractions is (a/b) plus or minus (c/d) equals (a times L/b plus or minus c times L/d) all over L, where L is lcm(b,d). For three or four fractions you extend the same idea: find lcm of all denominators, rewrite, combine.
Simplifying the result and converting to mixed number or decimal
After combining the numerators over the LCD, the result may not yet be in lowest terms. Divide both the numerator and denominator by their greatest common divisor (GCD) to reach the simplest form. If the simplified numerator is larger in absolute value than the denominator, you have an improper fraction; rewrite it as a mixed number by extracting the whole-number part with integer division and leaving the remainder as the fraction part. The decimal equivalent is simply the numerator divided by the denominator and is useful for quick comparisons, although repeating decimals such as 1/3 = 0.333... cannot be represented exactly in finite decimal form.
Adding mixed numbers
To add or subtract mixed numbers, first convert each one to an improper fraction: multiply the whole-number part by the denominator, add the numerator, and keep the same denominator. For example, 1 and 2/3 becomes (1 times 3 plus 2) / 3 = 5/3. Once in improper-fraction form, the same LCD procedure applies. Switch to "Mixed numbers" mode in the input style selector to use this automatically.
Why LCD is better than multiplying denominators
Multiplying the denominators together always produces a valid common denominator, but it is rarely the smallest one. Using a larger-than-necessary common denominator means the numerators grow bigger and the simplification step at the end requires more work. The LCD keeps the numbers as small as possible throughout, which reduces arithmetic errors, especially when working with three or four fractions. For example, 1/4 and 1/6: multiplying gives a common denominator of 24, but the LCD is 12. Using 12 gives 3/12 + 2/12 = 5/12 immediately, whereas using 24 gives 6/24 + 4/24 = 10/24, which still needs to be reduced to 5/12.
Common fraction addition examples
| Expression | LCD | Simplified result | Decimal |
|---|---|---|---|
| 1/2 + 1/4 | 4 | 3/4 | 0.75 |
| 1/3 + 1/6 | 6 | 1/2 | 0.5 |
| 2/3 + 1/4 | 12 | 11/12 | 0.9167 |
| 3/4 - 1/3 | 12 | 5/12 | 0.4167 |
| 1/2 + 1/3 + 1/6 | 6 | 1 | 1.0 |
| 1/4 + 1/6 + 1/12 | 12 | 1/2 | 0.5 |
| 5/6 - 1/4 | 12 | 7/12 | 0.5833 |
| 1/2 - 1/3 | 6 | 1/6 | 0.1667 |
Quick-reference results for frequently added fraction pairs, fully simplified.
Frequently asked questions
Do I have to use the least common denominator?
No, any common multiple of the denominators works, including the product of all the denominators. However, using the LCD keeps the numbers smaller throughout the calculation, which makes the final simplification step easier. The final reduced answer is identical either way.
How do I subtract a larger fraction from a smaller one?
The procedure is exactly the same. Find the LCD, rewrite each fraction, subtract the numerators. If the result is negative, the answer is a negative fraction. For example, 1/4 minus 1/2: LCD is 4, giving 1/4 minus 2/4 = -1/4.
What happens if a denominator is zero?
A denominator of zero is mathematically undefined because you cannot divide a quantity into zero parts. The calculator returns no result until every denominator is a non-zero integer.
How do I add mixed numbers?
Select "Mixed numbers (w n/d)" from the input style selector. Enter the whole-number part in the first field and the numerator and denominator in the following fields. The calculator converts each mixed number to an improper fraction internally, finds the LCD, adds the fractions, and converts the answer back to a mixed number.
Can I add more than two fractions?
Yes. Toggle on "Add more fractions" to reveal slots for a third and fourth fraction, each with its own plus or minus operator. The calculator finds the LCD of all denominators at once and sums all numerators in one pass.
Why does the decimal sometimes repeat?
A fraction produces a terminating decimal only when the denominator (after full simplification) has no prime factors other than 2 and 5. Any denominator with a factor of 3, 7, 11, or other primes produces a repeating decimal. The calculator shows 6 decimal places, which is enough for most purposes.