Division Property of Equality

For any numbers \(a\), \(b\), and \(c\) where \(c \ne 0\)

if 

$$a = b$$

then

$${a \over c} = {b \over c}$$

In words: When each side of the equation is divided by the same nonzero number, the meaning of the new equation remains true and the same. 

Example 1:

$$\eqalign{
   15 &= 15  \cr 
   {{15} \over \color{red}{5}} &= {{15} \over \color{red}{5}}  \cr 
   3 &= 3 \cr} $$

Example 2:

$$\eqalign{
   27 &= 27  \cr 
   {{27} \over {\color{red}{- 3}}} &= {{27} \over {\color{red}{ – 3}}}  \cr 
    – 9 &=  – 9 \cr} $$