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Mixed Number Calculator

Pick a direction. Enter an improper fraction to get the equivalent mixed number, or enter a mixed number to get the equivalent improper fraction, simplified, with the decimal value.

e.g. 9

Cannot be 0. · e.g. 4

Improper to mixed

Mixed number

2 1/4

9/4 as a mixed number

Improper (simplified)9/4
Whole part2
Fraction part1/4
Decimal2.25

Divide the numerator by the denominator. The quotient is the whole part; the remainder over the original denominator is the fraction part.

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Examples

9/4 → mixed number

= 2 1/4 · decimal 2.25

2 1/3 → improper

= 7/3 · decimal 2.333…

10/4 → mixed (simplified)

= 2 1/2 · decimal 2.5

How it works

Mixed numbers and improper fractions express the same value two different ways. The calculator runs the appropriate conversion and simplifies the fraction part by dividing numerator and denominator by their greatest common divisor.

Improper to mixed · n/d = ⌊n/d⌋ + (n mod d)/d

Mixed to improper · w n/d = (w · d + n) / d

Fraction part is reduced by dividing by gcd(n, d).

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Frequently asked questions

A mixed number combines a whole number with a proper fraction, like 2 1/3. It means the same value as 2 + 1/3 (which equals 7/3 as an improper fraction). Mixed numbers are easier to read in everyday measurements; improper fractions are easier to compute with.

Divide the numerator by the denominator. The quotient is the whole-number part; the remainder over the original denominator is the fraction part, simplified to lowest terms. For 9/4: 9 ÷ 4 = 2 remainder 1, so 9/4 = 2 1/4.

Multiply the whole number by the denominator, then add the numerator. Put the result over the denominator. For 2 1/3: 2 × 3 + 1 = 7, so 2 1/3 = 7/3. The calculator also simplifies the result.

Convert to an improper fraction first, then divide. For 2 1/3, the improper form is 7/3, which is 2.333… as a repeating decimal. The calculator shows the decimal alongside the fraction so you can check the answer quickly.

Yes. A negative sign applies to the whole value, so -2 1/3 means -(2 + 1/3) = -7/3. Enter the negative sign on the whole part (or the numerator if the whole part is 0), and the calculator handles the rest.

A fraction with denominator 0 is undefined. The calculator flags the input and returns no answer. Denominators must be nonzero integers.