Pre Algebra Period 2 (Tuesday)

Absolute Value 1-4
ABSOLUTE VALUE IS ALWAYS POSITIVE!
(except zero because zero has no sign)
Absolute value is a DISTANCE concept and that is why it can't be negative.

On the other hand, every integer has an ADDITIVE INVERSE which will be its OPPOSITE SIGN (except zero which has no sign - neutral)

Adding Integers 1-5
Three ways to understand adding integers:
1. positive negative sketch - make positive numbers positive signs and make negative numbers negative signs. Then match up all the positives with the negatives by box them in. Whatever is left, is the answer and the sign of the answer.

2. number line - draw the arrows and see where you end up

3. Who wins and by how much?
Different signs: Put the winner on top and take the difference
Take the DIFFERENCE (subtract) and keep the BIGGER (absolute value)number's SIGN
I say: 2 teams came to play: the positive team and the negative team
If you have 10 + (-15) then the positive team scored 10 while the negative team scored 15
Who won?
The negative team (so keep that sign)
By how much?
5 points
Answer: -5

Same sign: Just add and keep the sign you have
I say: only one team came to play so, of course, they won!
You would just add up the scores because all the players are on the same team!
Example: -5 + (-10), so just the negative team came to play
Therefore, the negative team won and you just add up their scores
Answer: -15

Additive inverses: the sum of additive inverses (same number with opposite signs) is always zero.
I say: it's a tie and no one wins! The answer would be zero!
Example: -5 + 5 = 0
-x + x = 0

Again, the rules are:
SAME sign: Just ADD them and KEEP the sign
DIFFERENT signs: Take the difference (SUBTRACT) and take the BIGGER number's SIGN.

MORE THAN 2 ADDENDS:
When adding a lot of addends, here's a good strategy:
1) SEE IF ANY ARE ADDITIVE INVERSES AND JUST CROSS THEM OUT BECAUSE ADDING INVERSES ALWAYS GIVES YOU ZERO!
What justifies crossing them out? The Identity Property of Addition
2) Add the positives to the positives
Add the negatives to the negatives
What justifies changing the order and grouping the addends this way?
The Commutative (order) and Associative (grouping) Properties of Addition

3) Finally, add the positive sum to the negative sum at the end and
see who wins and by how much
Usually, you will make less silly mistakes this way than just going left to right!

Adding integers with variable expressions:
Just substitute in for the variable, putting the substituted number into
( ),then evaluate using the integer rules.
(I say plug and chug!)
y + 5 where y = -12
(-12) + 5 = -7