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This is targeted for elementary kids. One way to think is that add any number to itself zero times... Just wondering if there is a better way...

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similar question: math.stackexchange.com/questions/9703/… –  PEV Feb 2 '11 at 17:55
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up vote 10 down vote accepted

Apples in bags.

Multiplying zero: you have a bunch of empty bags with no apples in them. You take 5 bags. How many apples do you have?

Multiplying by zero: you have many bags on the table, each with 5 apples in them. You don't take any bags, how many apples do you have?

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The area of a "rectangle" with sides 0 and $x$ is zero.

I really don't this any such analogy will be of much help...

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Suppose I have no apples, and I decide to look through all apples I have, and give you two for every one I have.

Then the total number of apples I give you is 0*2. But looking it at another way, I just start looking through all apples, and immediately stop because I found none; I haven't given you anything yet, and now I'm done.

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