>>14331861You're correct OP, it doesn't make sense the way they teach it in school.
But because it's practical people just take it for granted without thinking more about it.
It can make sense if we go back down to the definitions and clarify what we mean.
I'll define x×y to be adding a x, y times.
So for example 4×3 is 4 + 4 +4 which is 12.
Something to note is that, by default, this definition only makes sense if y is a positive whole number.
If you want to use multiplication with any other kind of y, you'll need to clarify what you mean.
For example what if y is negative, what does it mean to add x a negative number of times?
What does it mean to do something a negative number of times.
The only based answer is that it's nonsensical. Done. -3 × 4 = -3 + -3 + -3 = -12 but 4 × -3 is nonsensical.
Another answer is that doing something -1 time is like doing the opposite one time.
Putting on a pair of socks -1 times is like removing a pair of socks one time.
What's the opposite of adding a number? Subtracting a number.
So adding a copy of x minus 3 times means subtracting a copy of x 3 times.
So 4 × -3 = -4 - 4 - 4 = -12.
Doesn't matter if the left number is negative either.
So -4 × -3 = -(-4) - (-4) - (-4) = 12.
