Proof: Multiply by Inverse 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(1 / b) ⋅ a = a ⋅ (1 / b)	(1 / b) ⋅ a = a ⋅ (1 / b) (Commutative Property of Multiplication)
2	a ⋅ (1 / b) = a / b	a ⋅ (1 / b) = a / b (division_theorem)
3	(1 / b) ⋅ a = a / b	if (1 / b) ⋅ a = a ⋅ (1 / b) and a ⋅ (1 / b) = a / b, then (1 / b) ⋅ a = a / b (Transitive Property of Equality)

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