Zero Times Any Number

We are told that 0 times any number is 0 but why is the answer 0?

 

why is the answer 0?

if I say I will give you $1000000 ZERO times, how much you will get?

 

If you are going to give me a certain amount of money zero times, then I will get no money from you.

 

Do you know the "distributive law"? For a, b, and c any three numbers, a(b+ c)= ab+ ac. In particular, if c= 0, a(b+ 0)= ab+ a0.

But b+ 0= b so a(b+ 0)= ab. We have ab= ab+ a0. Subtracting ab from both sides, a0= 0.

 

Yes, I know this law.

 

Then you have your answer!

 

Thanks.

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