Fraction Calculator — Add, Subtract, Multiply, Divide

How fraction arithmetic works

Every operation here is done in whole numbers and only converted to a decimal at the very end. That matters: a computer adding 1/3 + 1/3 + 1/3 as decimals gets 0.9999999999999999, while adding them as fractions gets exactly 1.

Operation	Rule	Example
Add	Put both over a common denominator, then add the numerators	1/2 + 1/3 = 3/6 + 2/6 = 5/6
Subtract	Same, then subtract	3/4 − 1/4 = 1/2
Multiply	Multiply across the top and across the bottom	2/3 × 3/5 = 6/15 = 2/5
Divide	Flip the second fraction, then multiply	1/2 ÷ 1/4 = 1/2 × 4/1 = 2

How to add fractions by hand

Find a common denominator. Multiplying the two denominators always works; the lowest common multiple keeps the numbers smaller.
Rewrite both fractions over that denominator, scaling each numerator by the same factor you used on its denominator.
Add or subtract the numerators and leave the denominator alone.
Simplify by dividing the top and bottom by their greatest common divisor.

Formulaa/b + c/d = (a·d + c·b) / (b·d)

Multiplication and division skip step one entirely, which is why they are the easier pair despite feeling harder at school.

Mixed numbers

A mixed number like 2 ½ is shorthand for 2 + ½. Before any arithmetic it becomes an improper fraction: multiply the whole number by the denominator and add the numerator, so 2 ½ becomes 5/2.

The sign lives with the whole number. −2 ½ means −(2 + ½) = −5/2, not −2 + ½. This calculator follows that convention, which is the standard one.

2 ½ ÷ ¾

2 ½ becomes 5/2. Flip ¾ to 4/3 and multiply: 5/2 × 4/3 = 20/6, which simplifies to 10/3 — or 3 ⅓ as a mixed number, 3.333… as a decimal.

Simplifying, and why the answer sometimes looks different

Every result is reduced to its lowest terms using the greatest common divisor. 6/15 and 2/5 are the same number, but 2/5 is the conventional way to write it, so that is what you get.

When the result is an improper fraction — the top bigger than the bottom — both forms are shown. Improper fractions are what you want for further calculation; mixed numbers are what you want for a recipe or a tape measure.

A zero denominator is refused rather than silently ignored: a fraction with nothing on the bottom is undefined, not zero. Dividing by a fraction that equals zero is refused for the same reason.

Where fractions still matter

Cooking: halving or tripling a recipe that calls for ¾ cup.
Construction and woodworking: imperial measurements are fractions of an inch, and 3/16 + 5/8 is a daily calculation.
School maths: homework where the answer must be an exact fraction, not a decimal.
Music: note lengths, time signatures and tuplets.
Probability: odds are naturally fractions, and rounding them early loses accuracy.

Frequently asked questions

How do I add fractions with different denominators?

Rewrite both over a shared denominator first. For 1/2 + 1/3, sixths work for both: 3/6 + 2/6 = 5/6. Multiplying the two denominators (2 × 3 = 6 here) always gives a workable common denominator, even if it is not the smallest one.

What is an improper fraction?

One where the numerator is larger than the denominator, like 10/3. It is a perfectly valid number — 3⅓ — and improper form is usually easier to carry into the next calculation. This calculator shows both.

How do I turn a decimal into a fraction?

Write the decimal over a power of ten and simplify: 0.75 is 75/100, which reduces to 3/4. Terminating decimals always convert exactly; repeating ones like 0.333… need a different method and give 1/3.

Can I use negative fractions?

Yes. Put the minus sign on the whole number if there is one (−2 ½), or on the numerator if there is not (−1/2). A negative denominator also works and is normalised to the numerator in the answer.

Why does the calculator refuse a denominator of zero?

Because it has no value. A fraction is a division, and dividing by zero is undefined — not zero, and not infinity in ordinary arithmetic. Returning any number there would be a wrong answer dressed up as a right one.

Does it handle decimals in the input boxes?

No, and deliberately so. Numerators and denominators must be whole numbers, because that is what makes a fraction a fraction. If you have a decimal, convert it first — 1.5/2 is really 3/4.