If w have a factor and we want to get the largest unit factor less than it, Why we use this equation to get the least denominator: (numerator+denominator-1/numerator) ? I don't understand it
(den+num-1) / num = (den - 1)/num + 1
in integer division gives the next largest integer to the ratio den/num. Note that when this ratio is already an integer, i.e., den is an integer multiple of num, then the formula returns exactly this integer.
That is, this formula is the (always exact) integer variant of the floating point formula
fceil(den/(double)num)