Adding and subtracting integers, for some reason, seems to be tricky for a lot of individuals, especially when negatives are involved.
One common mistake is to concern yourself with the number of negatives or number of positives, for that has no determination on the answer
in these types of problems. The steps below show you "how to" add and subtract integers. The observations below, should provide you
with some ideas that should prove helpful for future problems.
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There really are only two steps to adding and subtracting (notice they are "steps" not "rules").
1. Start with the first number
This seems obvious, right? Believe it or not, the first number sometimes tricks people into thinking the answer will be one thing or another.
Really, the first number is just your starting point. Don't worry about whether it is positive or negative.

Now that we have that down, lets look at the meat of the work - the second step.
2. If adding: move in the same direction, and the number of spaces the second number is from zero.
    If subtracting: move in the opposite direction, and the number of spaces the second number is from zero.
Here's what you have to do. Once you have your starting point (the first number), you have to move from that point a particular direction
as well as a number of spaces. The only question is, what direction, and how far. The answers to these questions lie in the operation (addition
or subtraction) and the second number.

In addition, you move in the SAME direction that the second number is from zero. If the second number is positive, its to the right of
zero (see number line). Therefore, we will move from the first number, toward the right. If the second number is negative, then it is to the left of zero.
Therefore, if adding a negative, we will move to the left of the first number. How far? Well, we move the number of spaces the second number is from
zero. If it is 5 spaces away, move 5 spaces.
EXAMPLES:
       1. 5 + 6 = 11
       Here, you start with 5. Then, since we are adding, we will move in the same direction 6 (the second number) is from zero.
       6 is to the right of zero, therefore we will start at 5 and move to the right. How far? Well, 6 is 6 spaces away from zero, therefore
       we will move 6 spaces to the right of 5. Where do we end up? 11.
       2. -3 + -5 = -8
      Here, you start with -3 (negative has no affect on anything at this point). Then, since we are adding, we will move in the same direction
      -5 is from zero. -5 is to the left of zero, therefore we will move from -3 (the starting point) to the left. How far? Well, -5 is 5 spaces away from
      0, so we will move 5 spaces to the left of -3. Where does that leave us? -8.

In subtraction, you move in the OPPOSITE direction that the second number is from zero (subtraction is the inverse of addition). If the second number
is positive (to the right of zero), the we will end up moving to the left (opposite of right). If the second number is negative (to the left of zero), then we
will move to the right (opposite of left).
EXAMPLES:
      3. 3 - 6 = -3
      Here, you start with 3 (the first number). Since we are subtracting, we are going to move in the OPPOSITE direction that 6 (the second number) is
      from zero. Since 6 is to the right of zero, then we will move to the left. How far? Well, 6 is 6 spaces from zero. Therefore, we will start at 3 and move
      6 spaces to the left. Where do we end up? -3.
      4. -6 - -9 = 3
      This is usually the trickiest of the problems. Here, we start with -6 (the first number). Since we are subtracting, we are going to move in the
      opposite direction -9 (the second number) is from zero. -9 is to the left of zero, therefore we will start at -6 and move to the right. How far?
      Well, -9 is 9 spaces away from zero, so we will start at -6 and move 9 spaces to the right. Where does that leave us? 3.


There are a few observations that can be made here.

1. When we add a negative or when we subtract a positive, we end up moving to the left of the first number (move in the negative direction).
     Therefore, adding a negative provides the same result as subtracting a positive.
     - If the operation and the sign of the second number are different, the answer will be less than the first number.
     - To add a negative is to get "more negative". To subtract a positive is to get "less positive". These are essentially the same.

2. When we add a positive or when we subtract a negative, we end up moving to the right of the first number (move in the positive direction).
     Therefore, adding a positive provides the same result as subtracting a negative.
     - If the operation and the sign of the second number are the same, the answer will be more than the first number.
     - To add a positive is to get "more positive". To subtract a negative is to get "less negative". These are essentially the same.


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