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PROOF 04

Prove.

a ÷ (b/c) = a × (c/b)

On the rationals ℚ.

What you may use

A1(ab)c = a(bc)
associativity of multiplication
A2ab = ba
commutativity of multiplication
A3a × 1 = a
multiplicative identity
A4if a ≠ 0 then a·a⁻¹ = 1
existence of multiplicative inverses
Ea = b ⟹ apply the same operation to both sides
properties of equality

Nothing outside this list may be cited.

Definition D1

When c has a multiplicative inverse, b/c denotes b · c⁻¹.

Proof.

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