Sign Rules

OK. Maybe it's me, but here is what's in my son's Glencoe Pre-Algebra book (2008 ed.), section 2-2 (Adding Integers).

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Key Concept Number 1

Words:

To add integers with the same sign, add their absolute values.

The sum is:

- positive if both integers are positive
- negative if both integers are negative


Examples

-5 + (-2) = -7

6 + 3 = 9

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Key Concept Number 2

To add integers with different signs, subtract their absolute values.

The sum is:

- positive if the positive integer's absolute value is greater
- negative if the negative integer's absolute value is greater

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It seems to me that you can't make it much more complicated.


And he hasn't even gotten to subtracting integers, which states:

"To subtract an integer, add its additive inverse."

(Then use one of the rules above.)



It sounds like they are defining a foolproof method, but how about

4 + (-4) = ????

Neither integer is greater.

and how are these rules going to help when you get to variables, like

X +(3-2X) = ?????

You can't combine

X + (-2X)

because you don't know the absolute value of X?

Perhaps they will get new rules when they introduce variables.

And what about decimals? The sections only talk about integers!


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The simple rules I taught my son during the summer are:

1. When adding or subtracting, you often get two signs in a row, like:

5 + (-2)

If the signs are the same, combine them into a '+'

If the signs are opposite, combine them into a '-'

This works for numbers or variables. I told him that there is no difference between a sign and an operation, since: -5 is the same as (0 - 5).


2. When multiplying, you often get two signs that get multiplied together, like:

(-5)(-2)

Remember that this is the same as (-1)(+5)(-1)(+2) = (-1)(-1)(5)(2)

If the signs are the same, combine them into a '+'

If the signs are different, combine them into a '-'


3. When dividing, it's the same rule:

If the signs are the same, combine them into a '+'

If the signs are different, combine them into a '-'

[You just have to make sure that the signs are for factors. For (-3)/(-2+x), the sign in the denominator is a '+', not a '-'.]


The same rule applies to all three cases and for numbers or variables. It couldn't be easier. [I changed some flash cards to add minus signs to many of them.]


There are some things you have to watch out for and they need to understand variations, but it all boils down to one simple rule about combining signs.

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Things to feel comfortable about:

1. 5 = -(-5)

2. 2-5 = 2+(-5)

3. 5 = (+1)(+5)

4. -5 = (-1)(+5)

5. (-4)/(5) = (-1)(+4)/(+5) = -1(4/5) = 0 - 4/5


I told my son that there is a case where two positives equals a negative, and he said "Yeah, right!"

I'm sorry, I couldn't resist.