Adding and Subtracting Integers

The concepts of adding and subtracting integers are used on a daily basis. I know, I know, you say that you don't use it. Well, you use it more often than you think. Let's take a look into the "daily" shall we. Suppose you go online and purchase the book "Look Young Stay Young" by Johnny Capers using your credit card. After making your purchase, you owe the credit card for the total purchase price. Here's where negative numbers come into play. When you owe, that's a negative number. If the total purchase price was $21.76,  then that's negative $21.76 or -$21.76. Now let's look a different scenarios of making payments on the bill.
If you submit a payment for the entire amount you no longer owe anything.
-21.76 + 21.76 = 0  
                                  
If you submit a payment for more than you owe and there are no other charges on the card then they owe you.
-21.76 + 22.00 = 0.24

If you submit $10.76 then you still owe (not including interest).
-21.76 + 10.76 = -11

Now you want to buy a custom toddler pillow by Bobbleroos using that same credit card for a total purchase price of $18.26. Now you owe an additional $18.26.
-11 - 18.26 = -29.26

Now that you've seen integers in some "daily" transactions, let's talk a little more about some things that may help you in the classroom.
1) When the signs are the same you add the numbers and keep the same sign.
     20 + 10 = 30
     -20 - 10 = - 30
2) A negative sign and a subtraction sign are the same. When the signs are different           you subtract the numbers and take the sign of the "largest number" (technically the number furthest from zero).
    7 - 5 = 2
                                       -5 + 7 = 2
                                       -7 + 5 = -2
                                        5 - 7 = -2
Sometimes things can get tricky when multiple signs and parenthesis are used, so to eliminate confusion rewrite the problem with out unnecessary signs and parenthesis.To do this, whenever there are two signs beside each other replace the two with one sign. If the signs are the same use a "+" sign and if the signs are different use a "-" sign.

Example
-5 + (-9) - (-7)
The underlined signs below can be replaced
-5 + (-9) - (-7)
Becomes
 -5 - 9 + 7
Which is
-14 + 7 = -7

Another Example

3 + (+2) - (+5) - (-6) + (-3)

The underlined signs below can be replaced 

3 + (+2) - (+5) - (-6) + (-3)

Becomes

3 + 2 - 5 + 6 - 3

Which is

5 - 5 + 6 - 3 = 0 + 6 - 3 = 6 - 3 = 3

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