How to calculate with fractions
- Enter the numerator and denominator of the first fraction.
- Choose add, subtract, multiply or divide.
- Enter the second fraction.
- Read the simplified answer, plus the mixed number and decimal forms.
- Check the unsimplified line in the breakdown if you want to see the working.
What this calculator gives you
- All four operations on two fractions.
- The result reduced to lowest terms using the greatest common divisor.
- The unsimplified answer as well, so the method is visible.
- A mixed number for any result greater than one.
- The decimal and percentage equivalents.
- Clear errors for a zero denominator or division by a zero numerator.
Why the four operations behave so differently
Multiplication and division are the easy pair. To multiply, multiply the tops and multiply the bottoms: three quarters times two fifths is six twentieths, which simplifies to three tenths. To divide, flip the second fraction and multiply, dividing by two fifths is the same as multiplying by five halves.
Addition and subtraction are harder because you cannot add fractions with different denominators directly. Three quarters plus two fifths is not five ninths. Both have to be rewritten over a common denominator first: fifteen twentieths plus eight twentieths is twenty-three twentieths.
Adding numerators and denominators separately is the single most common fraction error, and it is worth noticing that it always produces an answer that sits between the two originals rather than above both, which is a quick sanity check that something has gone wrong.
Simplifying, and why it matters
Six twentieths and three tenths are the same number. Simplifying divides both parts by their greatest common divisor, which for 6 and 20 is 2. The result is easier to read, easier to compare against another fraction, and is what any marker or specification will expect.
This calculator shows both, because seeing 6/20 before it becomes 3/10 makes the step visible rather than magic.
Mixed numbers and improper fractions
- An improper fraction has a numerator larger than its denominator, such as 23/20.
- A mixed number writes that as a whole part and a remainder: 1 3/20.
Neither is more correct. Mixed numbers read better in everyday contexts. A recipe says one and a half cups, not three halves. Improper fractions are easier to calculate with, which is why algebra keeps them. This calculator gives both so you can use whichever the situation wants.
Where fractions still beat decimals
One third as a decimal is 0.3333 recurring, which cannot be written exactly. As a fraction it is precise and stays precise through further arithmetic. That exactness is why cooking, construction, music notation and probability all keep fractions rather than converting.
It also matters for rounding. Add 0.333 three times and you get 0.999, not 1. Add one third three times and you get exactly one. In any calculation where those small errors accumulate, fractions avoid a class of problem that decimals introduce.
The two errors this tool refuses
A denominator of zero is not a fraction. It describes dividing something into no parts, which has no meaning. And dividing by a fraction whose numerator is zero is dividing by zero once you flip it. Both are reported as errors rather than producing infinity or a silently wrong answer.
For converting a decimal back into a fraction, or for proportional splitting, the ratio calculator handles the related job. The percentage calculator converts between fractions and percentages of a total. Everything runs in your browser.