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.
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.
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.