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Multiplication is a way to do adding faster, and division is a way to do subtraction faster. Pretty cool if kids are being encouraged to realise that relationsh

by DougBTX 13y ago

Multiplication is a way to do adding faster, and division is a way to do subtraction faster. Pretty cool if kids are being encouraged to realise that relationship. It was only when I watched videos of those mechanical "fire control" computers on YouTube that I understood that integration is just a way of adding. Multiplication is adding the same number again and again, which is why integrating a constant (that number) is the same as multiplication. Cute.

betterunix 13y ago
Repeated addition is just one multiplication algorithm. I think a much better way to think of multiplication is as an operation on numbers that is related to addition by the distributive law. That law gives the "multiplication is repeated addition" algorithm, as well as the "shift and add" algorithm that most people learn in grade school. Of course, there are more efficient multiplication algorithms than either of those, which is why it is better to think of multiplication independently from addition. I would also point out that the repeated addition algorithm makes a lot of sense in base 1, but that shift and add makes far more sense in base 2 or higher. As for integration, I would say it is better to think of it as a limit involving both addition and multiplication.
philh 13y ago
> Multiplication is a way to do adding faster, and division is a way to do subtraction faster. Can you elaborate? If you need to do 13 + 13 + 13 + 13, you can do that as 13 x 4, which I guess is what you mean by the first part; but what analagous subtraction could you replace with a division?
- redblacktree 13y ago
  Not OP, but I'm guessing he means this: 52/13: 52 - 13 = 39 39 - 13 = 26 26 - 13 = 13 13 - 13 = 0 count the subtractions and you get 4. As long as we're sticking to integer division, this works out fairly well. Here, a calculation with a remainder: 54/13: 54 - 13 = 41 41 - 13 = 28 28 - 13 = 15 15 - 13 = 2 (smaller than 13, so this is our remainder) 54/13 = 4 with 2 reaminder

by DougBTX 13y ago

betterunix 13y ago

Repeated addition is just one multiplication algorithm. I think a much better way to think of multiplication is as an operation on numbers that is related to addition by the distributive law. That law gives the "multiplication is repeated addition" algorithm, as well as the "shift and add" algorithm that most people learn in grade school. Of course, there are more efficient multiplication algorithms than either of those, which is why it is better to think of multiplication independently from addition. I would also point out that the repeated addition algorithm makes a lot of sense in base 1, but that shift and add makes far more sense in base 2 or higher. As for integration, I would say it is better to think of it as a limit involving both addition and multiplication.

philh 13y ago

> Multiplication is a way to do adding faster, and division is a way to do subtraction faster. Can you elaborate? If you need to do 13 + 13 + 13 + 13, you can do that as 13 x 4, which I guess is what you mean by the first part; but what analagous subtraction could you replace with a division?

redblacktree 13y ago
Not OP, but I'm guessing he means this: 52/13: 52 - 13 = 39 39 - 13 = 26 26 - 13 = 13 13 - 13 = 0 count the subtractions and you get 4. As long as we're sticking to integer division, this works out fairly well. Here, a calculation with a remainder: 54/13: 54 - 13 = 41 41 - 13 = 28 28 - 13 = 15 15 - 13 = 2 (smaller than 13, so this is our remainder) 54/13 = 4 with 2 reaminder