CalcRover

Mixed Number Calculator

Do arithmetic on mixed numbers like 2 1/2 + 1 2/3 and see every step: converting to improper fractions, the operation itself, reducing by the GCF, and converting back. Set a whole part to 0 for a plain fraction.

For a plain fraction, set the whole part to 0. Negative? Put the minus on the whole part.

Mixed number arithmetic

The reliable route is always the same: convert each mixed number to an improper fraction (whole × denominator + numerator over the same denominator), do the fraction arithmetic, then convert the answer back. Adding whole parts and fraction parts separately works for addition but breaks on subtraction with borrowing — improper fractions never break.

For multiplication and division the conversion isn't optional: 2 1/2 × 1 1/2 is NOT 2×1 + 1/2×1/2. Convert first: 5/2 × 3/2 = 15/4 = 3 3/4.

a b/c = (a×c + b)/c
compute as fractions → reduce → back to mixed

Worked examples

Example 1: 2 1/2 + 1 2/3

Add two mixed numbers.

  1. To improper fractions.
    2 1/2 = 5/2; 1 2/3 = 5/3
  2. Common denominator 6.
    15/6 + 10/6 = 25/6
  3. Back to mixed.
    25/6 = 4 1/6

4 1/6.

Example 2: subtraction with borrowing

3 1/4 − 1 3/4 — the fraction part doesn't subtract cleanly.

  1. To improper fractions (no borrowing needed this way).
    13/4 − 7/4
  2. Subtract and reduce.
    6/4 = 3/2 = 1 1/2

1 1/2 — improper fractions sidestep the borrowing headache entirely.

Example 3: scaling a recipe

A recipe uses 3 3/4 cups of flour; you're doubling it.

  1. Convert and multiply.
    15/4 × 2 = 30/4
  2. Reduce and convert back.
    30/4 = 15/2 = 7 1/2

7 1/2 cups of flour.

FAQ

What's the difference between a mixed number and an improper fraction?+

Same value, two notations: 7/2 (improper) is 3 1/2 (mixed). Mixed reads naturally for measurements and cooking; improper computes cleanly. This calculator shows both forms plus the decimal.

How do I enter a negative mixed number?+

Put the minus on the whole part: −2 1/3 means −(2 + 1/3) = −7/3. A minus on the fraction part isn't standard mixed-number notation, so the calculator rejects it.

How do I enter a whole number or a plain fraction?+

Whole number: set the fraction part to 0/1 (e.g. 2 0/1 = 2). Plain fraction: set the whole part to 0. The plain-fraction case is exactly our fraction calculator.

Why does my teacher want the answer as a mixed number?+

Convention: measurements and word-problem answers read better mixed (1 1/2 cups), while algebra prefers improper (3/2) because it multiplies cleanly. Both are correct — match the context.

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