Adding Integers

Remember in class we talked about "adding the opposite" whenever you see a subtraction sign.  We called it "add op."  For example, instead of solving the problem 32-78, we should look at it as 32 + (-78) or the problem 16 - (-32) as 16 + 32.  The reason why this works has to do with the direction you are going on a number line.  Subtracting (-2) means you are going to move two places to the right on the number line which is the same as adding positive 2.

The reason I suggest "add op" when you see subtraction because of two primary reasons.

1. When the work becomes more complicated with variables and various grouping symbols and you are expected to simpliy or solve, it becomes really easy to "lose the sign" meaning you have forgetten to include a negative sign as you are solving the problem.  "Add op" helps you to prevent this common error.
2. "Add op" allows you to make your problem/expression into all addition.  When you have all addition you can use the communitive and associative properties to group the work in ways that save time and allow you to do some mental math - essentially making the computation easier.

So you only have to worry about adding integers of the same sign or integers of opposite signs.  Adding integers of the same sign is simple if you think about positive and negative counters.  For example (-12) + (-13) can be viewed as 12 negative counters plus 13 negative counters, so when you add all the negative counters you will have 25 negative counters or (-25).  

So we can create a rule for adding integers of the same sign. RULE: Adding integers of the same sign will result in the sum with the sign of the addends. 3+4=7 OR (-3) + (-4) = (-7)

Adding integers with opposite signs becomes a little trickier.  Below are two videos that might help you understand. First is a video using a chip model.  The second video is from Khan Academy using a number line.

The second rule we can create then is RULE: When adding integers of opposite signs, subtract the absolute value of the addends (the numbers you are adding).  Give the difference the sign of the larger absolute value. I like to think of it as, "Do I have more negatives or more positives in my problem? If I have more negatives, my answer is negative.  If I have more positives, my answer is positive."