How this calculator works
For an improper fraction, reduce it and divide the numerator magnitude by the positive denominator. The quotient is the whole part and the remainder is the fractional numerator. Place a negative sign before the whole mixed number. For the reverse direction, multiply the whole magnitude by the denominator, add the numerator and apply the whole part sign.
Formula
For n/d: whole magnitude = floor(|n|/|d|), remainder = |n| mod |d| after reduction. A signed mixed number converts to sign × (|w|d + n)/d.
Worked example
17/5 becomes 3 2/5, and -17/5 becomes -3 2/5. In the other direction, 3 2/5 gives (3 × 5 + 2)/5 = 17/5.
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Frequently asked questions
What does -3 2/5 mean?
The minus sign applies to the entire mixed number, so it means -(3 + 2/5), or -17/5. It does not mean -3 + 2/5.
How is a negative fraction smaller than one shown?
For example, -1/2 is shown as -0 1/2 so its sign is retained. To enter that value in the reverse direction, use the fraction calculator because a numeric zero whole part has no retained sign.
What does a proper fraction show?
The whole part is zero with the fraction left over, so 3/4 is shown as 0 3/4. The sign is kept in front of the whole part.