When adding two numbers such as 3 + 5, we assume that both the 3 and 5 are positive as we generally don't include a sign for positive numbers. If we do include the sign for positive numbers we would rewrite the equation as:
(+3) + (+5) = (+8)
When we are adding negative numbers we do include the sign to distinguish it from positive numbers.
Adding Negative Numbers to Positive Numbers
Lets look at another example which involves adding a negative number to a positive number:
4 + (-2)
In order to solve this problem lets look at a number line. The first number is a positive 4 so we start at 0 and move 4 steps in the positive direction:
With the negative 2 we then go backwards 2 spaces:
We now have arrived at our answer of 2.
4 + (-2) = 2
You may have noticed that 4 + (-2) gives us the same answer as 4 - 2. This is true as subtraction is the same as adding a negative number. Knowing this, we can easily solve problems where you are adding a negative number to a positive number through use of subtraction. Here is how you do it.
First find out which of the two values have the larger absolute value. This will determine the sign of the answer. Let's take the problem (-3) + 1 for example. In this problem, the -3 has an absolute value of 3 while the 1 has an absolute value of 1. Since 3 > 1 we know that our answer will be negative since the 3 was negative in our problem.
The next step is to subtract the smaller number from the larger number as if they didn't have signs.
3 - 1 = 2
We now can combine this answer with the knowledge that our answer is negative to get our result:
(-3) + 1 = -2
More Examples:
6 + (-7) = -1
(-4) + 1= -3
9 + (-5) = 4
Adding Two Negative Numbers
Now that we have looked at adding a negative and positive number together, let's look at how to add two negative numbers together. Let's look at the following example:
(-2) + (-3)
First lets plot the (-2) on the number line:
Remember that since we are dealing with a negative, we go backwards. Next we plot the (-3):
We go three more steps backwards to arrive at our answer of (-5).
The general rule of thumb is that when you are adding two negative numbers, simply add the two numbers as if they are not negatives and then make the answer negative.
More Examples:
(-4) + (-2) = -6
(-1) + (-7) = -8
(-20) + (-5) = -25