This is not a proof, however a demonstration for a curious kid why negative times negative is positive. It may be helpful to think that when dealing with the numbers ‘-’ or ‘+’ signs are identical to ‘-1 times’ or ‘+1 times’. Here is an example:

-5 = ‘-1 times’ 5

A number plus a negative number can result zero. Lets take the number ‘1’ that is ‘+1’, then take ‘-1’. It could have been any other number. The MAIN assumption is:

1 -1 = 0

Without losing the effect we can times the equation by ‘-’ or ‘-1’ then:

-1 -(-1) = 0

Since both equations are the same, that means:

-1 -(-1) = 1 -1

that means:

-(-1) = 1

it shows:

‘-’ times ‘-’ is plus

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This approach is also helpful to show why ‘+’ times ‘-’ is ‘-’

Let us safely assume ‘1’, which is ‘+1’, times a number results in the number, i.e. ‘1 times’ 10 is 10. Then ‘1 times’ ‘-1’ is ‘-1’ . That is:

‘+1 times’ -1 = -1

That shows: ‘-’ times ‘+’ results ‘-’

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hence, 1 * (-1) = (-1)

also, -1 * a = -a, ”here ‘a’ is any number”

hence, -1 * (-1) = – (-1)

Negative of +1 = -1

negative of (-1) = 1, because a number plus the negative of the

number adds up to zero, for instance when -1 + x = 0, that means x=1

From above, (-1) * (-1) = – (-1) = negative of (-1) = 1

That shows (minus * minus ) yields plus

]]>The reasons for this we need not discuss.

OK, that’s the version I tell my students. And I tell them about both of you as well–my fine sons! One of these days I’ll try to go over Dan’s explanation with them. But he is right. I like yours better, Jeff!

Ogden Nash? How did you come up with that?

]]>The reason for this, we needn’t discuss.

– Ogden Nash

Actually, I’m not sure that’s the exact quote either, nor even the right source. Like Yogi Berra, Nash didn’t actually say half the things he said. But at least the rhythm is a little closer to matching and I’ve found it cited that way at least once on-line. I just wouldn’t want your readers to think that your brother recites couplets where one line has three more syllables than the other. :-)

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