An integer is any whole number, whether it is negative or positive. Integers that are positive are just like the everyday counting numbers you have used up until now, but now we are going to put negative integers into the mix. Don't worry, there are a few simple rules that should clear everything up.
Adding Integers
When adding integers, you can use a few different strategies. The first is to create a "chip board" model that looks something like this:
This chip board has black chips and red chips. The black chips represent (+1) and the red chips represent (-1). So on this board, I have seven positive chips and 4 negative chips. I can create pairs of red and black chips to create what is called a "zero pair" because +1 and -1 together make 0. So I can arrange by board in pairs and and see how many I have left:
On this chip board I now have 4 "zero pairs" which represent a value of 0. I also have 3 (+1) chips floating around by themselves. Well, 0 + 3 = 3, so this board has a total value of +3.
You can also add integers by looking at a number line. If you are adding a positive, you move towards the right where the positive side of the number line is. If you are adding a negative, you move toward the left where the negatives are.
You can also add integers by looking at a number line. If you are adding a positive, you move towards the right where the positive side of the number line is. If you are adding a negative, you move toward the left where the negatives are.
Subtracting Integers
Subtracting integers can be a little more complicated, but it isn't too much of a challenge as long as you pay attention and remember what you're supposed to be taking away. Lets look at the following problem to help explain those rules:
7 - (-3)
7 - (-3)
When subtracting integers with a chip board, it is always best to start with just the first number on the board. If that number is positive, put that number of black chips on the board. If the number is negative, but that number of red chips on the board.
As you can see, we are supposed to be taking away 3 negative chips, but I don't have any negative chips on the board. To put negative chips on the board, we must add "zero pairs" to the board. This lets us put negative chips on the board WITHOUT changing the value of the board. Now I have added 3 "zero pairs" to the board, so that I have at least 3 negative chips to take away. The value of the board is still +7 because the "zero pairs" cancel themselves out and I only have 7 other positive chips on the board. Now that I have negative chips on the board, I can subtract them from the board. Once I have taken the three negative chips away from the board, I can tally the total value of my board. I now have the original 7 black chips and 3 more black chips left, for a total of 10 black cihps. This makes my value +10. So 7 - (-3) = 10 |
When subtracting integers, it can sometimes get confusing knowing which way on a number line you are going, so if you would like to use a number line, here are a few simple rules for doing so.
-Subtracting a negative means you are moving away from the negative side of the number line, so move to the right.
-Adding a negative means you are moving toward the negative side of the number line, so move to the left.
-Subtracting a negative means you are moving away from the negative side of the number line, so move to the right.
-Adding a negative means you are moving toward the negative side of the number line, so move to the left.
Multiplying and Dividing Integers
Unlike adding and subtracting, multiplying and dividing integers are really quite simple when you know the rules. You will divide or multiply the numbers just like you would normally. The only thing that may change is what sign you give your answer:
1. A positive times a postive will be a positive, just like normal multiplication you are used to.
2. A negative times a positive will be a negative. 3. A negative times a negtaive will be a positive. (Two negatives cancel each other out.) 1. A positive divided by a positive will be a positive. 2. A negative divided by a positive will be a negative. 3. A positive divided by a negative will be a negative. 4. A negative divided by a negative will be a negative. |
4 x 4 = 16
4 x -4 = -16 -4 x -4 = 16 16 / 4 = 4 -16 / 4 = -4 16 / -4 = -4 -16 / -4 = 4 |