FOR THE STUDENT OF MATHEMATICS
DEMONSTRATION CLUB FILE XXV


PURPOSE: To demonstrate that for real number x, real number y, real number w ≠ 0 and real number z ≠ 0:

                    XXV.     If x = y and w = z then x / w = y / z.

is true for w ≠ 0 and z ≠ 0



DEMONSTRATION:     STATEMENTS                                       REASONS



            1.       x / w = x / w   for w ≠ 0                     1.   Property XII   Reflexive:   p = p

            2.     x = y and w = z   for w ≠ 0 and z ≠ 0   2.   Given ( from the hypothesis. )

            3.     x / w = y / z   for w ≠ 0 and z ≠ 0         3.   Property XVIII   Substitution of y for x and z for w on RHS


RHS indicates the right hand side of an equality in Reason #3.

Equal's divided by equal's are equal's.     [ ='s ÷ ='s are ='s ]

What about:   "Equal's multiplied by equal's are equal's."   ? So!

    Property XXVa.     If x = y and w = z then x w = y z.


Would you like to demonstrate Property XXVa. ?

Properties:     List #1 Link     List #2 Link     List #3 Link     List #4 Link     List #5 Link   and   Demonstrations

Copyright © 2009 with all rights reserved by William V. Thayer         Assisted by Peter Rankin, Demo Club Member