Arithmetic & Numbers

Fraction Calculator

Enter two fractions, mixed numbers or decimals, choose an operation, and get the answer in lowest terms with every step shown — common denominator, simplification, mixed number and decimal.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Try an example:

Answer5/6

Decimal: 0.833333

Step-by-step working 6 steps

1
Write the problem
```
1/2 + 1/3
```
Both numbers are already fractions.
2
Find a common denominator
```
LCM(2, 3) = 6
```
The least common multiple of 2 and 3 is 6, so use 6 as the denominator.
3
Rewrite both fractions
```
1×3/2×3 + 1×2/3×2 = 3/6 + 2/6
```
Multiply top and bottom of each fraction so the denominators match.
4
Add the numerators
```
3 + 2 = 5  →  5/6
```
Keep the denominator unchanged.
5
Simplify
5 and 6 share no common factor other than 1, so the fraction is already in lowest terms.
6
Decimal and percent
```
5/6 ≈ 0.833333  =  83.3333%
```

How to use the fraction calculator

Type each number as a fraction (3/4), mixed number (2 1/2) or decimal (0.75).
Pick add, subtract, multiply or divide.
Read the answer, then open the steps to follow the method.
Use the examples above to see each operation worked.

The four rules

a/b + c/d = (ad + bc) / bd   (or use the LCD)
a/b − c/d = (ad − bc) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = a/b × d/c

Always reduce the final fraction by dividing top and bottom by their greatest common factor.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

1/2 + 1/3

Answer5/6

Decimal: 0.833333

Step-by-step working 6 steps

1
Write the problem
```
1/2 + 1/3
```
Both numbers are already fractions.
2
Find a common denominator
```
LCM(2, 3) = 6
```
The least common multiple of 2 and 3 is 6, so use 6 as the denominator.
3
Rewrite both fractions
```
1×3/2×3 + 1×2/3×2 = 3/6 + 2/6
```
Multiply top and bottom of each fraction so the denominators match.
4
Add the numerators
```
3 + 2 = 5  →  5/6
```
Keep the denominator unchanged.
5
Simplify
5 and 6 share no common factor other than 1, so the fraction is already in lowest terms.
6
Decimal and percent
```
5/6 ≈ 0.833333  =  83.3333%
```

3/4 − 5/6

Answer−1/12

Decimal: −0.083333

Step-by-step working 6 steps

1
Write the problem
```
3/4 − 5/6
```
Both numbers are already fractions.
2
Find a common denominator
```
LCM(4, 6) = 12
```
The least common multiple of 4 and 6 is 12, so use 12 as the denominator.
3
Rewrite both fractions
```
3×3/4×3 − 5×2/6×2 = 9/12 − 10/12
```
Multiply top and bottom of each fraction so the denominators match.
4
Subtract the numerators
```
9 − 10 = −1  →  −1/12
```
Keep the denominator unchanged.
5
Simplify
1 and 12 share no common factor other than 1, so the fraction is already in lowest terms.
6
Decimal and percent
```
−1/12 ≈ −0.083333  =  −8.3333%
```

2 1/2 × 1 1/5

Answer3

Decimal: 3

Step-by-step working 4 steps

1
Write the problem
```
5/2 × 6/5
```
Convert mixed numbers and decimals to fractions first: 2 1/2 = 5/2; 1 1/5 = 6/5.
2
Multiply across
```
(5 × 6) / (2 × 5) = 30/10
```
Multiply the numerators together and the denominators together.
3
Simplify
```
30/10 ÷ 10/10 = 3
```
The greatest common factor of 30 and 10 is 10; divide both by it.
4
Decimal and percent
```
3 ≈ 3  =  300%
```

3/8 ÷ 9/16

Answer2/3

Decimal: 0.666667

Step-by-step working 5 steps

1
Write the problem
```
3/8 ÷ 9/16
```
Both numbers are already fractions.
2
Flip the second fraction
```
9/16 → 16/9
```
Dividing by a fraction is the same as multiplying by its reciprocal.
3
Multiply across
```
(3 × 16) / (8 × 9) = 48/72
```
Multiply numerators together and denominators together.
4
Simplify
```
48/72 ÷ 24/24 = 2/3
```
The greatest common factor of 48 and 72 is 24; divide both by it.
5
Decimal and percent
```
2/3 ≈ 0.666667  =  66.6667%
```

Common mistakes to avoid

Adding denominators

1/2 + 1/3 is not 2/5. Denominators describe the size of the pieces; you must make them match before adding numerators.

Flipping the wrong fraction when dividing

Only the second fraction (the divisor) is inverted. The first stays exactly as written.

Forgetting to convert mixed numbers

Turn 2 1/2 into 5/2 before multiplying or dividing — multiplying whole parts and fraction parts separately gives the wrong answer.

Stopping before simplifying

A fraction like 10/12 is correct but unfinished; most teachers expect 5/6.

Frequently asked questions

Can I enter negative fractions?

Yes. Put the minus sign at the front: -3/4 or -1 1/2.

What happens if I divide by zero?

The calculator tells you the operation is undefined instead of returning a number.

Does it simplify automatically?

Yes. The final answer is always reduced to lowest terms, and a mixed-number form is shown for improper fractions.