Reduce fractions to their simplest form, convert to mixed numbers, and find the decimal.
Simplifying a fraction means finding its irreducible form by dividing the numerator and denominator by their Greatest Common Divisor (GCD), computed here with the Euclidean algorithm. The resulting fraction represents exactly the same value, just written with the smallest possible integers, it is irreducible when the GCD equals 1. Besides reducing, the tool classifies the fraction (proper, improper or whole), converts improper fractions to a mixed number (a whole part plus a proper fraction) and computes the exact decimal by long division, detecting and marking the part that repeats: 1/3, for example, appears as 0.[3], and 1/7 as 0.[142857]. All the arithmetic uses BigInt (arbitrary-precision integers), so there is no rounding error and no practical size limit for the numerator and denominator. The sign is normalized to the numerator, keeping the denominator always positive, and each step (GCD found, division, result) is shown. Everything runs locally in your browser.
Reducing a fraction means dividing both terms by the same number, the largest possible, which is the GCD. To find it, the Euclidean algorithm divides the larger by the smaller, keeps the remainder and repeats with the divisor and remainder until the remainder is zero; the last nonzero divisor is the GCD. Dividing the numerator and denominator by it reaches the irreducible form in one shot.
With the fraction reduced, the tool does two more things. If it is improper (numerator ≥ denominator), it splits off the whole part (the quotient of the division) from the remainder, forming the mixed number. And it computes the decimal by long division, watching the remainders: when a remainder repeats, the digits enter a cycle, and that block is marked in brackets.
Example 1, reduce with an exact decimal: 18/24. The GCD(18, 24) = 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Since the reduced denominator (4) has only the factor 2, the decimal is finite: 0.75.
Example 2, improper with a repeating decimal: 7/3. The GCD is 1, so the fraction is already irreducible; being improper, it becomes the mixed number 2 1/3. In the division, the remainder 1 reappears, so the decimal is 2.333…, shown as 2.[3], where [3] is the block that repeats forever.
There is an elegant rule for telling, without dividing, whether the decimal will terminate: a reduced fraction has a finite decimal exactly when its denominator's only prime factors are 2 and 5. That is why 3/4 (denominator 4 = 2²) terminates, but 1/3 and 1/7 do not. The bracket notation keeps the repeating decimal exact: 0.[3] is 1/3 with no approximation.
Using BigInt instead of floating point guarantees that huge numerators and denominators reduce without error, something an ordinary calculator would fail at. Simplifying fractions is essential to compare fractions, add measurements in recipes and woodworking, express probabilities and ratios in their cleanest form and check work on tests and problem sets.
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
<iframe
src="https://jkit.tools/embed/en-US/fraction-simplifier"
width="100%"
height="600"
style="border:0"
loading="lazy"
title="Fraction Simplifier"
></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
Simplifying means dividing both the numerator and denominator by their Greatest Common Divisor (GCD) until no integer greater than 1 divides both. The resulting fraction is equivalent but in its most reduced form.
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