Fraction calculator
The four operations on fractions, simplified at the end and with the intermediate step visible, which is where you see why the answer is what it is.
Your figures
Result
- As a mixed number
- —
- As a decimal
- 0.583333
- As a percentage
- 58.3333%
- Numerator
- 7
- Denominator
- 12
Step by step
| Step | Fraction |
|---|---|
| First fraction | 1/3 |
| Second fraction | 1/4 |
| Result before simplifying | 7/12 |
| Simplified result | 7/12 |
What we assume
- The result is always fully simplified.
- The sign goes on the numerator:
-1/2, never1/-2. - Numerators and denominators must be whole numbers.
- The common denominator uses the product, not the lowest common multiple: the simplified result is the same.
How it is calculated
Each operation has its own rule, and only two of the four need a common denominator.
Adding and subtracting
a/b ± c/d = (a×d ± c×b) / (b×d)
A third plus a quarter: (1×4 + 1×3) / 12 = 7/12. You cannot add them directly because the pieces are not the same size; the common denominator makes them match.
Multiplying
a/b × c/d = (a×c) / (b×d)
The easiest of the four: multiply straight across and you are done. No common denominator needed, and that is exactly the most common confusion.
Dividing
a/b ÷ c/d = (a×d) / (b×c)
It is multiplying by the reciprocal: flip the second fraction over. Dividing by
1/2 is multiplying by 2, which is why dividing by a fraction below one makes the
answer bigger.
Simplifying
At the end, numerator and denominator are divided by their greatest common divisor.
6/8 becomes 3/4 by dividing by 2. It is what makes two fractions
worth the same amount get written the same way, and it is why we show the unsimplified step:
so you can see where it came from.
Why the product and not the lowest common multiple
To add 1/6 and 1/4, the lowest common multiple is 12 and the product is 24. Both routes reach the same place, because the final simplification cleans up the difference: 10/24 reduces to 5/12. We use the product because the intermediate step can then be followed by eye without first working out another lowest common multiple.
An example
1/3 + 1/4: the common denominator is 12, so it becomes 4/12 + 3/12 = 7/12. As a decimal that is 0.583333, and as a percentage, 58.3333%.
Frequently asked questions
Why does dividing give a bigger number?
Because dividing by a fraction below one is multiplying by its reciprocal, which is above one. "How many halves fit in 3?" is six, so 3 ÷ 1/2 = 6. The intuition that dividing always shrinks things only holds for divisors above one.
Can I use negative fractions?
Yes, with the minus sign on the numerator or the denominator, it makes no difference: the result always comes out with the sign on the numerator, which is the canonical form.
What is a mixed number?
A way of writing an improper fraction with the whole part split off: 7/4 is 1 3/4. It is common in cooking and in measurements, and rarer in maths, because it gets in the way when calculating.
Why does the decimal sometimes never end?
Because only fractions whose simplified denominator breaks down into twos and fives give exact decimals. 1/4 gives exactly 0.25; 1/3 gives 0.333... forever. Six decimal places are shown here.
Keep calculating
All tools →- Greatest common factor and lowest common multiple Both at once, for as many numbers as you like, with each one broken into primes alongside. Which is where you see why the answers are what they are.
- Percentage calculator Enter a percentage and a number. Instead of making you pick an operation first, we give you all four answers at once.
- Rule of three calculator Solve a direct or inverse proportion. We show the working, not only the result.
Updated on 2026-09-11. Calculations run in your browser; nothing you type is sent to a server.