Fraction Calculator

A fraction represents part of a whole, written as one number (the numerator) over another (the denominator), separated by a line - for example, 3/4 means 3 parts out of a whole divided into 4 equal parts. The denominator can never be 0, since dividing a whole into zero parts is undefined; the numerator, on the other hand, can be 0, negative, or larger than the denominator without any problem.

Addition and subtraction only make sense when you're counting the same-sized pieces, so 1/4 and 1/6 first have to be rewritten over a shared denominator before their numerators can be combined - this calculator does that automatically by cross-multiplying rather than asking you to find it yourself. Multiplication and division don't have this requirement at all: multiplying is just numerator times numerator over denominator times denominator, and dividing is multiplying by the second fraction flipped upside down, regardless of what either denominator is.

It means dividing the numerator and denominator by their greatest common divisor - the biggest whole number both can be divided by evenly - so the fraction ends up expressed with the smallest possible numbers while keeping its exact value unchanged. For example, 8/12 and 2/3 represent the same amount, but 2/3 is in lowest terms; this calculator reduces every fraction result this way automatically, in every mode, not only in Simplify a Fraction.

Because a fraction with a denominator of 0 is asking "how much is a whole divided into zero equal parts," which has no answer - a whole cannot be split into zero pieces, so the value is undefined rather than some very large or very small number. This calculator rejects any input where a denominator is 0, in every mode, rather than returning a misleading or infinite-looking result.

Yes - a numerator, a denominator, or both can be negative, and this calculator normalizes the result so the negative sign always ends up on the numerator rather than the denominator, matching standard mathematical convention. For example, both 6/-8 and -6/8 simplify to -3/4, while -6/-8 (two negatives) simplifies to the positive 3/4, since dividing a negative by a negative gives a positive result.

This calculator treats every decimal input to a fixed precision of 4 decimal places rather than detecting that a decimal repeats forever, so 0.3333 becomes 3333/10000 (which does not reduce further, since 3333 and 10000 share no common factor) - not the exact 1/3 a repeating-decimal-aware tool might return. For an exact result from a known repeating decimal like 1/3, use Fraction to Decimal in reverse, or enter the fraction directly in whichever mode you need.

They start from different places, even though the arithmetic that reduces the numbers ends up the same either way. Ratio Calculator's Ratio to Fraction mode is built for someone who already has a ratio (like a 16:9 screen size) and wants it rewritten with a division line instead of a colon; this calculator's Simplify mode is built for someone who already has a fraction (like 8/12 from a recipe or a measurement) and wants it reduced to its smallest equivalent. If your starting point is a colon-separated ratio, reach for Ratio Calculator; if it's already a fraction, this Simplify mode is the more direct fit.

Partly - you cannot enter a mixed number, but the result shows one. Every mode takes input as a plain numerator over a denominator, with no field for a whole-number part, so a value larger than 1 must be entered as an improper fraction (use 11/4, not "2 and 3/4"). When an answer comes out as an improper fraction, though, the calculator displays the mixed-number form on a line beneath it, so 9/2 is also shown as 4 1/2. Entering mixed numbers directly is a possible future addition.

This calculator rejects it, the same way it rejects a zero denominator - dividing by zero is undefined whether the zero appears directly as a denominator or as the value of an entire fraction you are dividing by (such as 0/5, which equals zero even though neither of its own numbers is a zero denominator). Division by any fraction whose numerator is 0 is always treated as invalid input, not as an error to silently work around.

Yes - a fraction where the numerator is larger than the denominator, such as 9/2, is called an improper fraction, and every mode accepts and returns improper fractions. The improper form is the primary result because it is easier to keep using in further calculations; when a result is improper, the equivalent mixed number (for 9/2, that is 4 1/2) is shown on a line beneath it as well, since the two forms represent exactly the same value.

Find the smallest number both denominators divide into evenly - the least common denominator - then rewrite each fraction over it and add the numerators. For 1/4 + 1/6, list the multiples of 4 (4, 8, 12, 16) and of 6 (6, 12, 18); the smallest shared value is 12, so 1/4 becomes 3/12, 1/6 becomes 2/12, and 3/12 + 2/12 = 5/12. This calculator reaches the same answer by cross-multiplying the denominators instead, which always works but can produce larger intermediate numbers before the result is reduced.