Fraction Calculator

What this calculator does

So, this is the all-in-one. Rather than a separate page for adding, another for subtracting, and so on, this one holds all of it behind a single dropdown: add, subtract, multiply, divide, and compare two fractions. You set the two fractions, choose what to do with them, and it answers.

Each fraction has three boxes, a whole number, a numerator, and a denominator, so mixed numbers go straight in. It is the tool to reach for when you are working through a problem and do not yet know which operation you will need next, or when you want the one option the single-purpose tools skip entirely: telling you which of two fractions is larger.

How to use it

1. Enter Fraction 1: whole number if any, then numerator over denominator.
2. Pick an operation from the dropdown: Add, Subtract, Multiply, Divide, or Compare.
3. Enter Fraction 2 the same way.
4. Press Calculate.

As with every fraction tool, a denominator cannot be zero. For the four arithmetic options you get a fraction and its decimal value; for Compare you get a plain-language verdict instead of a number.

The five operations, and how each is worked out

Under the hood, each option uses the standard method for that operation:

• Add and Subtract put both fractions over a common denominator, the product of the two bottoms, then add or subtract the tops. This is the cross-multiplication you would do by hand: for a/b and c/d, the new top is a×d combined with c×b, over b×d.
• Multiply goes straight across, tops together and bottoms together, no common denominator needed.
• Divide flips the second fraction and multiplies, since dividing by a fraction is the same as multiplying by its reciprocal.
• Compare turns each fraction into its decimal value and checks which is larger.

Whichever you choose, a mixed number is folded into a single top-heavy fraction first, as whole × denominator + numerator, before the operation runs.

The one the single tools do not have: Compare

Add, subtract, multiply and divide each have their own dedicated page. Compare does not, which is a good reason to keep this calculator handy. It answers a question that comes up constantly: of two fractions, which is bigger? That is genuinely hard to eyeball. Is 5/8 more than 3/5? The denominators are different, so you cannot just glance at the tops.

Compare settles it by converting each fraction to a decimal and seeing which value is higher, then telling you in words whether the first is greater, the first is less, or the two are equal. It is also the quickest way to catch equivalent fractions hiding behind different numbers: ask it to compare 2/4 and 3/6 and it reports that they are equal, because both are one half.

How it reduces every answer

Every arithmetic answer comes back in lowest terms with any whole number split off, so you get a clean mixed number rather than a top-heavy fraction. This calculator does that reducing with its own routine rather than an outside library. It finds the greatest common divisor of the top and bottom using the Euclidean algorithm, the old repeat-the-remainder method where the divisor of one step becomes the number divided in the next, until nothing is left over. Then it divides both parts by that divisor. It is why 8/12 comes back as 2/3 and 10/4 comes back as 2 1/2. The decimal alongside is rounded to two places for a clean read.

A couple of worked examples

Add 1/2 and 1/3. Over a common bottom of 6 that is 3/6 plus 2/6, which is 5/6. There is no whole number and nothing to reduce, so the answer is 5/6, or 0.83 as a decimal.

Compare 5/8 and 3/5. As decimals those are 0.625 and 0.6, so the verdict is that the first fraction, 5/8, is the greater of the two. Numbers that close are exactly the kind you would struggle to rank by sight.

When to use this and when to use a focused tool

Reach for this calculator when you want everything in one place, when the operation might change from one problem to the next, or when you specifically need Compare. If you only ever need one operation and want a page built around just that, the dedicated adding, subtracting, multiplying and dividing calculators cover the same arithmetic with the single operation fixed in place. The answers agree; the difference is only in how much the page is trying to do at once.

Questions people ask

What operations can it do?

Five: add, subtract, multiply, divide, and compare two fractions. The first four give a fraction and a decimal; compare tells you which fraction is larger.

How does Compare decide which fraction is bigger?

It converts each fraction to its decimal value and checks which is higher, then reports the result in words. Equal values, like 2/4 and 3/6, are flagged as equal.

Does it simplify the answers?

Yes. It reduces every arithmetic result to lowest terms using the greatest common divisor, and splits off any whole number into a mixed number.

Can it handle mixed numbers?

Yes. Use the whole-number box on either fraction, and it folds the mixed number into a single fraction before the operation.

Why are there separate adding and multiplying calculators too?

Those focus on a single operation, with the page written entirely around it. This one trades that focus for breadth and adds Compare. Use whichever fits how you are working.

References

On the reducing step and the notation. This calculator reduces its answers with the Euclidean algorithm for the greatest common divisor, one of the oldest procedures in mathematics, written down by Euclid around 300 BC and still the standard way to put a fraction in lowest terms. The horizontal bar between numerator and denominator is credited to the Moroccan mathematician al-Hassar in the twelfth century and reached Europe through Fibonacci's Liber Abaci in 1202.

1. Euclid, Elements, Book VII, Propositions 1 and 2 (c. 300 BC), the Euclidean algorithm for the greatest common divisor, used here to reduce every result to lowest terms.
2. al-Hassar (12th century) and Leonardo of Pisa, Fibonacci, Liber Abaci (1202), for the horizontal fraction bar in the form used today.