We can multiply both sides of an equation by any number. The equality axiom is that a = a for any number a. This is the justification for multiplying both sides of an equation by a number.

 

The same logic applies to expressions. We can always multiply any expression by 1 without changing it, where we write 1 as a / a, with a ≠ 0. This is the justification for simplification by multiplying by the reciprocal.