Add, subtract, multiply, or divide — always simplified.

How do you add or subtract fractions with different denominators?

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.

How do you multiply and divide fractions?

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.

How is a fraction simplified to lowest terms?

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.

What's a mixed number, and how is it different from an improper fraction?

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.

What happens with negative numbers or a zero denominator?

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.

Where does this come up outside of math class?

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.