FOR THE STUDENT OF MATHEMATICS
DEMONSTRATION CLUB FILE XXIII


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

                    XXIII.     If x = y then x / z = y / z.

is true for   z ≠ 0.



DEMONSTRATION:     STATEMENTS                                       REASONS



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

                            2.     x = y                                     2.     Given from the hypothesis.

                            3.     x / z = y / z   for   z ≠ 0          3.     Property XVIII   Substitution of y for x



Dividing the same quantity into both sides of an equality results in an equality.

Can you find another demonstration for this property based on Property XXI and Definition 2. for Division?




Would you like to demonstrate Property XXIV. ?

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