Algebraic Properties of Equality
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Please share your thoughts about whether to merge this page with Mathematical Properties. 
The equal sign that depicts the fact that both sides of it are equal is a very strange symbol with many properties. It tells you various traits of each side, and it allows you to manipulate each side in specific ways. Here are the different properties of that sign:
Property  Definition  Example 
Reflexive  For all a, a=a  
Symmetric  If a = b, then b = a  
Transitive  If a = b & b = c, then a = c  If 8 = (4)(2) and (4)(2) = (2)(4), then 8 = (2)(4) 
Substitution  If a = b, then one can replace a with b.  
Subtraction  You can subtract one number from both s
 
Multiplication  You can multiply both
 
Division  You can divide both sides of
