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by emilgouliev
2481 days ago
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you don't need to invoke a concept of area to justify this. you can just think of a grid of dots. since multiplication is repeated addition, each row represents one step of the repeated addition. 2x3 = 3 + 3 ... ... 3x2 = 2 + 2 + 2 .. .. .. since rotation doesn't change the number of dots, we expect 2x3 and 3x2 grid of dots to contain the same number of dots, which proves that multiplication is commutative. |
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