Enter two fractions and an operation to get the result as a simplified fraction, decimal, and mixed number, or simplify a single fraction below.
Reduce any fraction to its lowest terms.
Multiplying the two denominators together always produces a common denominator, just not always the smallest one. Adding 2/4 and 1/6 cross-multiplies to (2×6 + 1×4)/(4×6) = 16/24 — a valid common denominator of 24, even though the lowest common denominator here is actually 12. It does not matter: simplifying 16/24 by its GCD of 8 (found the same way the Factor Calculator finds any number's factors) lands on exactly 2/3, the same answer a lowest-common-denominator approach would give. The numbers along the way are occasionally bigger than strictly necessary; the final answer is identical either way, which is why this calculator can skip finding the LCD and still always be exact.
This page's own default inputs, 1/2 and 1/3, run through every operation this tool offers: addition gives 5/6, subtraction gives 1/6, multiplication also gives 1/6 (a coincidence of these particular numbers, not a rule), and division gives 3/2. Division and multiplication share one instinct worth remembering: dividing by a fraction smaller than 1 always makes the result larger, precisely because dividing by 1/3 is the same as multiplying by its reciprocal, 3.
3/4, the ratio 3:4, and 75% all describe the exact same relationship between two quantities — only the notation changes. The Ratio Calculator works in the colon notation directly, and the Percentage Calculator converts to and from the hundredths notation; all three tools agree on the same underlying answer to the same underlying question, just written differently.
Fractions need a common denominator before you can add or subtract their numerators. This calculator uses cross-multiplication so you never have to find the lowest common denominator by hand: a/b ± c/d = (a×d ± c×b) / (b×d). Adding 1/2 + 1/3: (1×3 + 1×2) / (2×3) = 5/6.
Multiplying is the most direct fraction operation — multiply numerators together and denominators together: (a/b) × (c/d) = (a×c)/(b×d). Dividing flips the second fraction and multiplies: (a/b) ÷ (c/d) = (a×d)/(b×c). So 1/2 ÷ 1/3 becomes 1/2 × 3/1 = 3/2.
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. 8/12's GCD is 4, so it reduces to 2/3 — the same value, smaller numbers. This calculator finds the GCD using the Euclidean algorithm and applies it automatically to every result, including the outputs of the add/subtract/multiply/divide tool above.
An improper fraction has a numerator at least as large as its denominator, like 7/2. A mixed number writes the same value as a whole number plus a proper fraction — 7/2 becomes 3 1/2 (3 whole plus a remaining 1/2). Both are mathematically identical; mixed numbers are usually easier to picture (like "three and a half"), while improper fractions are easier to keep multiplying or dividing further without converting back and forth.
A negative numerator or denominator works normally — the sign carries through to the result correctly. A zero denominator is undefined in ordinary arithmetic (division by zero), so this calculator can't produce a meaningful result for that input; double-check your denominator if the result looks blank or unexpected.
Cooking measurements (combining 1/3 cup and 1/4 cup), woodworking and construction (adding 3/8" and 5/16"), and splitting recipes or materials all reduce to the same fraction arithmetic here. For unit-based cooking conversions specifically, the Unit Converter's cooking category handles cup/tablespoon/teaspoon conversions directly.
Worked example: 3/4 + 5/6: cross-multiply to (3×6 + 5×4)/(4×6) = (18+20)/24 = 38/24, which simplifies (GCD 2) to 19/12 — an improper fraction equal to the decimal 1.583..., or the mixed number 1 7/12.
Finding that GCD of 2 by hand is exactly what the GCF Calculator automates for any pair of numbers, and the least common denominator this page finds via cross-multiplication is precisely what the LCM Calculator computes directly, without the extra simplification step afterward.
For proportions expressed as a:b rather than a/b, use the Ratio Calculator. For anything involving exponents, logs or trigonometry, the Scientific Calculator handles it. Working on geometry homework? See the Area Calculator, Triangle Calculator and Slope Calculator. To reduce a fraction in one step, find the GCF of numerator and denominator; for a common denominator use the LCM Calculator.