Algebraic Properties of Equality

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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 sides

Multiplication You can multiply both sides by a same number

Division You can divide both sides by a same number different from zero