Crazy Idea: Negative Numbers

I’ve been thinking a little bit about adding and subtracting negative numbers.  Here’s my idea.

You have 4, which everybody understands, and then you have –4, which I am going to call “anti-four”.  It is defined as the number that annihilates 4 so that

4 + (-4) = 0

In my scheme there is no such thing as subtraction, but only the addition of annihilators.

The subtraction of annihilators is merely the addition of an anti-anti-number.

4 – (-4) = 4 + (-1)*(-4)

Which means you have to define the anti- operator to be multiplication by (-1).

By reducing subtraction to the addition of the anti-operator times a number, you are helping to remove some of those rules like:  subtracting a negative number is adding a positive and adding a negative number is like subtracting a positive (which seems silly).

What this helps clear up is difficulty around adding and subtracting, since there is only adding.  And it helps give a name to anti-four such that the basis could some day be laid for anti-matter in physics which annihilates its counterpart when they interact.

This also helps clear up confusion that may occur in accounting where all is summing, just sometimes you sum debits (anti-income) and sometimes you sum credits and similarly you can take away credits and take away debits.

Just wanted to get this off my chest.

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  • Taylor Jacobsen  On February 11, 2012 at 11:34 pm

    I like this, John. I think I’ve heard this before, or at least thought of it and used it with some kids. I think I may have used it the other way around. Students usually understand subtraction, so when a negative number pops up I help them see that 3 + (-4) is actually the same as 3 – 4. I like the idea of thinking of negative numbers as anti-numbers. Students always get frustrated with negatives because they aren’t “real.” I can’t show them -4 of something. This is where money helps and talking about owing money or something.

    You still have to deal with “a negative multipled by a negative is a positive, while a negative multiplied by a positive is a negative.” But if they could get this, your 6th paragraph would be a good way to understand subracting a negative. Interesting. Do you think this would be a way to start teaching negatives, or something to add after they already have an idea?

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