Reduce any fraction to lowest terms and add, subtract, multiply or divide two fractions — with the GCD and the LCM shown.
Reducing a fraction means dividing the top and the bottom by the same number until nothing else divides both. The fastest way to get there in a single move is the greatest common divisor: 12/18 has a GCD of 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, and the fraction is 2/3. Adding and subtracting is the opposite move — the two fractions first have to be rewritten over a common denominator, and the smallest one available is the least common multiple of the denominators. For 1/2 + 1/3 the LCM is 6, the fractions become 3/6 and 2/6, and the sum is 5/6.
Multiplication and division need no common denominator at all. Multiplying goes straight across — numerator times numerator, denominator times denominator — and dividing means multiplying by the reciprocal of the second fraction, so 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. Whatever the operation, the answer is reduced by its own GCD at the end using the Euclidean algorithm, and then shown in the two other forms people usually need: the mixed number, 15/8 = 1 7/8, and the decimal, 1.875. The decimal is marked as exact or approximate depending on the denominator — a reduced fraction terminates only when its denominator is built from 2s and 5s, which is why 3/8 ends and 2/3 does not.
Fractions turn up far outside homework. Recipes scale by them, tools and pipe fittings are sold in sixteenths of an inch, musical time signatures and note values are fractions, and any ratio simplified to lowest terms is easier to read and to compare. Screen aspect ratios are the same idea: 1920/1080 divided by its GCD of 120 is 16/9. Whole numbers between −1,000,000 and 1,000,000 cover all of that comfortably, and every step — the GCD found, the common denominator chosen, the final reduction — is printed so the reasoning can be copied into an exercise. Everything runs in your browser and nothing is uploaded.
Simplifying: divide the numerator and the denominator by gcd(a, b). Addition and subtraction: a/b ± c/d = (a × (L ÷ b) ± c × (L ÷ d)) ÷ L, where L = lcm(b, d). Multiplication: a/b × c/d = (a × c) ÷ (b × d). Division: a/b ÷ c/d = (a × d) ÷ (b × c). The result is always reduced by its own GCD at the end.
Divide the numerator and the denominator by their greatest common divisor. With 12 and 18 the GCD is 6, so 12/18 becomes 2/3, and no further cancelling is possible because 2 and 3 share no factor.
Because parts of different sizes cannot be added directly. Rewriting both fractions over the least common multiple of the denominators makes the parts the same size, and only then can the numerators be added.
It is a whole number written next to a proper fraction, such as 1 7/8 for 15/8. The tool shows it whenever the result is an improper fraction, since that form is easier to picture as a quantity.
Because that fraction has no exact decimal form. A reduced fraction ends as a decimal only when its denominator is made of 2s and 5s; 2/3 repeats forever, so the value shown is rounded and flagged with an approximation sign.
No. All the arithmetic runs in JavaScript on your device, with no requests to any server and nothing stored.
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