If multiplication is just repeated addition, then why when 2 negatives get multiplied they become a positive?
In: Mathematics
I actually tried to explained this idea to an actual 5 year old (okay, 6 year old) with: temperature and time travel!
Multiplication is repeated addition. A x B is B plus B plus B … A times. You can see it as having a machine that do “plus B” to the temperature of the house, every second, and you wait A seconds to get the right result.
Let’s do 3 x 4. It’s “plus 4”, “plus 4”, “plus 4”: so plus 12. Okay, it’s getting warm.
Let’s do 3 x -4. It’s “minus 4”, “minus 4”, “minus 4”: so minus 12. Okay, cool.
Now, what if we rewind time. Instead of waiting A seconds, we go back A seconds early. This is what happen with a negative A.
Let’s do -3 x 4. It’s undo “plus 4”, undo “plus 4”, undo “plus 4”: so undo plus 12, aka. minus 12. Okay, the revert if getting warm is getting cool!
Let’s do -3 x -4. It’s undo “minus 4”, undo “minus 4”, undo “minus 4”: so undo minus 12, aka. plus 12. It’s getting warm!
The only issue with that explanation is that it feel like multiplication is not symmetric, even though it works perfectly fine either way.
A bunch of mathematicians, such as [this guy](https://www.maa.org/external_archive/devlin/devlin_06_08.html), are adamant that multiplication is in fact not repeated addition, but that multiplication makes for a shortcut for doing repeated addition.
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