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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/yFor mathematically inclined people who wish to cover all bases for the assumptions that x>=y>0If 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.
Reflecting a point P, in the x axis is finding another point Q such that they both have the same x-coordinate and that the y-coordinate of Q is the additive inverse of the y-coordinate of P. Thus, is P is 4.5 above the x-axis, then Q is 4.5 below it and if P is below, then Q is above by the same distance.Reflection in the y-axis is similar except that now it is the y-coordinate that remains the same and the x-coordinate that changes. If P was to the left then Q is to the right (and conversely).
Suppose x and y are two rational number.Then x = p/q and y = r/s where p, q, r and s are integers, with q and s being non-zero. Then x - y = p/q - r/s = pq/qs - qr/qs = (pq - rs)/qs. The signs of x and y do not matter, in so far as their signs will be used to determine the signs of p,q, r and s.
Starting with an arbitrary point (p,q) y = q + 26/ln(2)*ln(x/p)