Mixed Number Calculator
Convert an improper fraction to a mixed number, or a mixed number back to an improper fraction, with the decimal value.
How it works
improper → mixed: whole = ⌊|n| ÷ d⌋, remainder = |n| mod d · mixed → improper: (whole × d + numerator) ÷ d
A mixed number and an improper fraction are two ways of writing the same value. Going from improper to mixed, divide the top by the bottom: the quotient is the whole part and the remainder stays over the original denominator. Going back, the whole part is worth that many denominators, so multiply it by the bottom and add the numerator to rebuild the single top-heavy fraction.
Worked example
11/4 → mixed: 11 ÷ 4 = 2 remainder 3, so it’s 2 3/4 (2.75 as a decimal). Reversing it, 2 3/4 → improper: 2 × 4 + 3 = 11, giving 11/4 again.
Sources: Fraction — Wikipedia
Frequently asked questions
What makes a fraction "improper"?
Its numerator is at least as large as its denominator, so its value is 1 or more — like 11/4 or 7/7. That isn’t wrong, just top-heavy, and it converts cleanly to a mixed number.
How do I handle a negative mixed number?
The minus sign applies to the whole quantity: −2 3/4 means −(2 + 3/4) = −11/4. This calculator keeps the sign out front and works with the sizes underneath.
When should I prefer one form over the other?
Mixed numbers read naturally for measuring and everyday amounts (2 3/4 cups), while improper fractions are easier to multiply, divide and simplify inside longer calculations.
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This calculator is for educational purposes. Double-check important results before acting on them.