What is the improper fraction as a mixed number?

Answer 1

Given an improper fraction of the from x/y where x and y are integers and x>=y>0,let x = q*y + r [q is the quotient and r the remainder when x is divided by y].

Then x/y = (q*y + r)/y = q + r/y

For mathematically inclined people who wish to cover all bases for the assumptions that x>=y>0

If y is negative, then the numerator and denominator of the fraction can be multiplied by -1 to give an equivalent fraction; except that now y > 0.

If 0 < x < y then q = 0 so that x/y is a proper fraction and so there is no mixed number.

If x < 0 then swap with -x (which will be >0), calculate the mixed number and put a negative sign in front of the answer.