I have always heard that multiplication is fast adding of the same number. This made sense until we got to negative numbers. Why would two negative numbers become a positive number when they are multiplied if it is indeed just adding the same number? I have asked several people this and never got a straight answer. Please help me!
In: Mathematics
I think the other answers here cover to ELI5 part, so I’ll take it a step further and prove that (-a)*(-b)=a*b for any two numbers a and b. To do this I first show that (-a)*b=-a*b:
(-a)*b + a*b = (-a+a)*b = 0*b = 0,
so subtracting a*b on both sides gives (-a)*b=-a*b. Now since -(-x)=x for any number x, we get
(-a)*(-b)=-a*(-b)=-(-a*b)=a*b, and we’re done.
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