Both directions, simplified
Convert a mixed number to an improper fraction and back: 3 2/5 becomes 17/5, with the whole part, the remainder, the simplified form and a decimal for checking.
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.
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 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. How do you convert a mixed number to an improper fraction? Multiply the whole number by the denominator, add the numerator, and keep the denominator. For 3 2/5: 3 × 5 = 15, plus 2 is 17, so the answer is 17/5. The calculator shows the result, its simplified form and a decimal to check it against.
How do you turn an improper fraction back into a mixed number? Divide the numerator by the denominator: the quotient is the whole part and the remainder is the new numerator over the same denominator. 17 ÷ 5 is 3 remainder 2, so 17/5 is 3 2/5. Pick the second direction and the calculator does the division for you.
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.
