Proof: Proportion Product
Let's prove the following theorem:
if a / b = c / d, then d ⋅ a = b ⋅ c
Proof:
Given
1 | a / b = c / d |
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# | Claim | Reason |
---|---|---|
1 | (b ⋅ d) ⋅ (a / b) = (b ⋅ d) ⋅ (c / d) | if a / b = c / d, then (b ⋅ d) ⋅ (a / b) = (b ⋅ d) ⋅ (c / d) |
2 | (b ⋅ d) ⋅ (a / b) = d ⋅ a | (b ⋅ d) ⋅ (a / b) = d ⋅ a |
3 | (b ⋅ d) ⋅ (c / d) = b ⋅ c | (b ⋅ d) ⋅ (c / d) = b ⋅ c |
4 | d ⋅ a = b ⋅ c | if (b ⋅ d) ⋅ (a / b) = (b ⋅ d) ⋅ (c / d) and (b ⋅ d) ⋅ (a / b) = d ⋅ a and (b ⋅ d) ⋅ (c / d) = b ⋅ c, then d ⋅ a = b ⋅ c |
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