Both directions, simplified
Converts a mixed number into an improper fraction and the other way round, pulling out the whole part and simplifying the result.
Mixed notation reads well — you can see at a glance that it is a bit over three. Improper notation calculates well: adding, multiplying and dividing are easier with a single fraction than with a whole number plus a fraction.
So school work bounces between the two constantly: convert to improper before working, pull the whole part back out for the answer. Both directions live here.
What this calculator shows
- The converted value in the direction you chose
- The simplified form when numerator and denominator share a factor
- The whole part, the remainder and a decimal for checking
What to keep in mind
- The sign belongs to the whole number: −3 2/5 means minus three-and-two-fifths, not minus three plus two fifths.
- The fractional part of a mixed number is normally below one; entering a larger numerator simply increases the whole part on conversion.
FAQs
How do I do it in my head?
Whole times denominator plus numerator. Reversing it is division with remainder: the quotient is the whole part, the remainder the new numerator.
Why bother with improper fractions?
To avoid mistakes. You cannot multiply mixed numbers by multiplying whole parts and fractional parts separately — they must be converted first.
How are negatives handled?
The minus applies to the whole quantity. −2 3/4 is −(2 + 3/4) = −11/4, which is how this calculator reads it.
Why does the result sometimes simplify?
Because conversion can create a common factor. 2 2/4 becomes 10/4, which reduces to 5/2. Both forms are shown on separate lines.
Worked example
Three and two fifths
Input: 3 2/5
Output: 17/5
Note: 3 × 5 + 2 = 17, denominator unchanged. Going back, 17 ÷ 5 gives 3 with a remainder of 2.