Proof: Division Property of Equality
Let's prove the following theorem:
if a = b, then a / c = b / c
This theorem is the division equivalent of the Multiplicative Property of Equality.
Proof:
Given
| 1 | a = b |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | a ⋅ (1 / c) = b ⋅ (1 / c) | if a = b, then a ⋅ (1 / c) = b ⋅ (1 / c) |
| 2 | a / c = a ⋅ (1 / c) | a / c = a ⋅ (1 / c) |
| 3 | b / c = b ⋅ (1 / c) | b / c = b ⋅ (1 / c) |
| 4 | a / c = b ⋅ (1 / c) | if a / c = a ⋅ (1 / c) and a ⋅ (1 / c) = b ⋅ (1 / c), then a / c = b ⋅ (1 / c) |
| 5 | a / c = b / c | if a / c = b ⋅ (1 / c) and b / c = b ⋅ (1 / c), then a / c = b / c |
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