Mixed Number Calculator
Add, subtract, multiply, or divide two mixed numbers (whole + fraction). Returns the result as a simplified mixed number or improper fraction.
Last updated: September 2026
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About this calculator
A mixed number combines a whole part and a proper fraction, like 2 ½ or 3 ¼. Under the hood, arithmetic on mixed numbers is easiest by first converting each mixed number to an improper fraction (numerator/denominator only): 2 ½ = (2 × 2 + 1) / 2 = 5/2. Do the operation on improper fractions, then simplify and re-express as a mixed number.
Rules: addition/subtraction requires a common denominator (a/b ± c/d = (a×d ± b×c) / (b×d)). Multiplication is direct: (a/b) × (c/d) = (a×c) / (b×d). Division inverts the second fraction: (a/b) ÷ (c/d) = (a×d) / (b×c). After each operation, divide both numerator and denominator by their greatest common divisor (GCD) to simplify. If numerator ≥ denominator, extract the whole part: numerator ÷ denominator gives the whole; the remainder over the original denominator is the fractional part.
Mixed numbers are the everyday human-readable form for fractional quantities: cooking recipes, US carpentry measurements, imperial units. Improper fractions are the algebra-friendly form. This calculator handles the conversion both ways so you never need paper.
How to use
Example — 2 ½ + 1 ¾. Convert to improper: 5/2 and 7/4. Common denominator 4: 10/4 + 7/4 = 17/4 = 4 ¼. Example — 3 ⅓ × 2 ½. Improper: 10/3 × 5/2 = 50/6. GCD(50, 6) = 2, simplify to 25/3. As mixed: 25 ÷ 3 = 8 remainder 1 → 8 ⅓. That is 3.33 × 2.5 = 8.33, matching.
Frequently asked questions
What is a mixed number?
A number written as a whole part plus a proper fraction, like 2 ½ (spoken "two and a half"). It equals the sum: 2 + ½ = 2.5. The alternative representation is an improper fraction (5/2), which has the same value but is written without a whole part.
When is a mixed number vs improper fraction better?
Mixed numbers are more human-readable for measurement and cooking ("1 ¾ cups flour"). Improper fractions are algebra-friendly because they eliminate special-case rules — 5/2 × 3 = 15/2 without needing to handle the whole part separately. Convert to whichever form the next step wants.
How do I simplify the result?
Divide both numerator and denominator by their greatest common divisor (GCD). GCD(6, 4) = 2, so 6/4 simplifies to 3/2. Once numerator/denominator share no common factors above 1, the fraction is in lowest terms. This calculator does that automatically.
Does the calculator handle negative mixed numbers?
Yes — enter a negative in the whole part. −2 ½ is treated as −(2 + ½) = −2.5. Subtracting a larger mixed number from a smaller one will produce a negative result; the calculator normalizes the sign so the fraction part is always positive relative to the whole.