This mixed number calculator adds, subtracts, multiplies and divides mixed numbers — converting to improper fractions, computing exactly, and simplifying back to both mixed and improper forms.

First number


Second number

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Convert, Compute, Convert Back — Exactly

Mixed numbers are display format; improper fractions are the working format (whole × denominator + numerator over denominator). General fraction arithmetic beyond mixed inputs lives on our Fraction Calculator. Part of our Math Calculators collection.

Worked Examples (Verified)

  • 2⅓ + 1¾ (defaults): 7/3 + 7/4 = 28/12 + 21/12 = 49/12 = 4 1/12 (≈ 4.0833)
  • A genuine curiosity in the same inputs: 2⅓ × 1¾ also equals 49/12 — sum and product coincide whenever (a−1)(b−1) = 1, and 4/3 × 3/4 = 1 exactly. Try other pairs to watch them diverge
  • Subtraction with borrowing made invisible: 3 1/4 − 1 3/4 → 13/4 − 7/4 = 6/4 = 1½ — the improper route never borrows; it just subtracts
  • Division: 2⅓ ÷ 1¾ = 7/3 × 4/7 = 28/21 = 1⅓ — reciprocal flip, then the multiplication pipeline

Where Mixed Numbers Live

  • Recipes and carpentry measure in mixed numbers (2⅓ cups, 5⅜ in) — and both punish sloppy conversion; measure twice in either format.
  • Math curricula introduce them early because wholes carry intuition; algebra abandons them because improper fractions compute cleanly. Fluency is translating without thinking.
  • Results simplify by GCD (our GCF Calculator's day job) — 49/12 is already fully reduced since 49 = 7² shares nothing with 12.

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Frequently Asked Questions

How do you add mixed numbers?

Convert both to improper fractions (whole × denominator + numerator), find a common denominator, add, simplify, and convert back. 2⅓ + 1¾ = 7/3 + 7/4 = 49/12 = 4 1/12. Adding wholes and fractions separately also works but borrowing/regrouping makes it error-prone — the improper route is mechanical.

How do you multiply mixed numbers?

Never multiply part-by-part: convert to improper first. 2⅓ × 1¾ = 7/3 × 7/4 = 49/12 = 4 1/12. The common mistake (2×1 + ⅓×¾ = 2¼) misses the cross terms — exactly the (a+c)(b+d) expansion error algebra teachers hunt for.

How do you turn a mixed number into an improper fraction?

Multiply the whole part by the denominator and add the numerator; keep the denominator: 2⅓ → (2×3+1)/3 = 7/3. Backwards: divide numerator by denominator — quotient is the whole, remainder the new numerator (49 ÷ 12 = 4 r 1 → 4 1/12).

Can results be negative or improper-only?

Yes: subtraction can cross zero, and this calculator presents the mixed form with the sign on the whole (−1 3/4 means −(1¾)) plus the reduced improper fraction and decimal to remove all ambiguity. A zero numerator simply prints the whole number.

Why simplify fractions?

Reduced form is the canonical answer: 6/4 and 1½ and 3/2 are the same number, but simplest terms compare instantly and are what measurements, answer keys, and recipes use. Reduction divides out the GCD of numerator and denominator.

Is this mixed number calculator free?

Yes — free, instant, no sign-up.