Fraction Calculator
Work with two fractions and get the answer in lowest terms, as a mixed number and as a decimal, with the common denominator shown.
How it works
Adding and subtracting need a common denominator; multiplying and dividing do not. That asymmetry surprises people — multiplication is the easy case, where you simply multiply across the top and the bottom.
Dividing by a fraction means multiplying by its reciprocal: ÷ 2/3 is the same as × 3/2. Every result is then reduced by dividing both parts by their greatest common divisor, which is what puts it in lowest terms.
The formula
Add or subtract
a/b ± c/d = (a×d ± c×b) ÷ (b×d)
Multiply
a/b × c/d = (a×c) ÷ (b×d)
Divide
a/b ÷ c/d = (a×d) ÷ (b×c)
Simplify
divide both parts by gcd(numerator, denominator)
Worked examples
| Scenario | Working | Result |
|---|---|---|
| 1/2 + 1/3 | (3 + 2) ÷ 6 | 5/6 |
| 3/4 × 2/3 | 6 ÷ 12, simplified | 1/2 |
| 1/2 ÷ 1/4 | 1/2 × 4/1 | 2 |
When you'd use it
- Homework and coursework in arithmetic
- Scaling a recipe up or down
- Combining measurements given in fractions of an inch
- Checking a fraction reduces to the form you expected
Common questions
Why do I need a common denominator to add but not to multiply?
Because addition combines parts of the same size, so the pieces must match first. Multiplication asks for a fraction of a fraction, which works directly — two thirds of a half is simply 2×1 over 3×2.
How do I divide by a fraction?
Flip the second fraction and multiply. Dividing by 1/4 is multiplying by 4, which is why dividing by a fraction smaller than one makes the answer bigger.
What is a mixed number?
A whole number with a fraction beside it, such as 1 1/2 instead of 3/2. They read more naturally in everyday use; improper fractions are easier to calculate with. This tool shows both.