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Adding and Subtracting Negative Numbers

You're in luck! Adding and subtracting with negative numbers is very easy! In fact, if you know how to add and subtract, you already know how to do it with negative numbers - but we'll show you the tricks here anyway.

A Quick Example of Each Type of Problem:

Adding a positive number and a negative number:
Example: 5 + -2 [Note: This is sometimes shown as: 5 + (-2) ]
The great thing about these kind of problems is that all you have to do is subtract. Why? Because you're adding a negative number, which is the same as subtraction! So you could actually rewrite the problem as: 5 - 2, and you can do that one easily!
Adding a negative number and another negative number:
Example: -2 + -3
Here, we will do the same as above. This time we're starting with a negative number, but that doesn't change our strategy! We can rewrite the problem as -2 - 3, and since a negative minus another number is always going to stay negative (since we aren't adding any positive numbers), we can take write: -2 - 3 = -5
Subtracting a negative number from another negative number:
Example: -4 - (-7).
So let's see what's going on here. You start with -4. Then you're subtracting a negative 7. Sound confusing? It really isn't! There's only one thing extra to remember: two negatives make a positive. Using that rule, we can rewrite the problem as: -4 + 7, which equals 3.
Subtracting a negative number from a positive number:
Example: 9 - (-2)
There's nothing new here at all. If you read the above rule that two negatives make a positive,then you already know that you can rewrite this as 9 + 2, which is, of course, 11.

And that does it for the examples! But in case there is any confusion, here are some more detailed explanations of how to perform the operations on negative numbers.

What is actually happening on these problems? Let's take a closer look. When you start with a positive number, then add a negative number, we can treat this as having $50 but owing somebody $20. As far as your total amount is concerned, the $20 is a negative amount to you. Regardless of how much you actually have, the $20 is still in the negative direction.

For instance, if you have $0 and you owe $20, your total value is negative twenty dollars. So, in these cases, it works like a standard subtraction problem: 50 + (-20) is the same as 50 - 20 = 30.

Here is a table that you can refer to:
(Postive Number) + ( Positive Number) = Postive Number + Postive Number
(Postive Number) + (Negative Number) = Postive Number - Positive number
(Negative Number) + (Positive Number) = (Negative Number) + (Positive)
Note: This can also be rewritten as: Postive Number - Postive Number
(Negative Number) - (Negative number) = Negative Number + Positive Number
Note: Or can be written (+number) - number.

Examples of these:
1. 7 + 8 becomes 7 + 8 (= 15)
2. 5 + (-6) becomes 5 - 6 (= -1)
3. -4 + 8 stays -4 + 8 (or can be rewritten as 8 - 4) (= 4)
4. -5 - (-8) becomes -5 + 8, and can be rewritten as 8 - 5 (=3)

Once you can see that using a negative number in addition and subtraction is no different than normal subtraction, the entire process is incredibly easy!

One thing to note: If you are subtracting a negative number from another negative number, the answer could be positive. But if you are ADDING a negative number to another negative number the answer will always be negative. Example 1: -3 - (-5) turns into -3 + 5 which is +2. Example 2: -3 + (-5) is just -3 - 5, which equals -8!

Next up... Multiplying and Dividing with Negative Numbers!
(Hint: Multiplying and Dividing is actually easier than adding and subtracting!)

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