Multiply by breaking up a factor.
a)7×9
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My friend and I were discussing some mathematical philosophy and how the number systems were created when we reached a question. Why can we multiply two different numbers like this?
Say we had to multiply 13×34. One may break this up like (10+3)×(30+4). Applying distributive property here will give us the answer of 442. We can also choose to multiply this as (6+7)×(22+12). Intuitively, we can hypothesize that this should give us the same answer as 13×34. How can we prove that our answer will be equal regardless of how we break up the numbers?
surendradm:
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