Adding Positive and Negative Numbers

Once you understand the basics of
positive and negative numbers, you can start to add them together. Sometimes
this seems tricky, because there are lots of rules to remember and follow. We’ll
go through them slowly so that you understand.

Rule 1: Adding positive numbers to positive numbers—this is normal addition.

Example 1: Adding positive numbers to positive numbers is what you’ve been
doing for a long time now; for example 5 + 2 is adding two positive numbers together.
You can calculate these problems normally, as you’ve been doing all along. Sometimes
you might see something look like this: +5 + 2 = 7; that simply means that the 5
is also positive. Don’t worry—you can go ahead and calculate it like you normally
would!

Rule 2: Adding positive numbers to negative numbers—count forward the amount
you’re adding.

Adding positive numbers to negative numbers can get tricky, because you need to
pay close attention to where the negative signs are placed in the problem.

Example 2: Let’s say we had the problem: -5 + 2. This would be read as “negative
five plus two.” This is most easily thought about on a number line. Instead of starting
at a positive number, you’re starting at a negative number, which is to the left
of zero on the number line. However, you’re adding two, so you would still count
forward two places to arrive at your answer, like this:

The large red dot above the -5 shows that that’s where we’re starting our problem.
The blue arrow shows that we counted forward (or added) 2. The blue circle around
the -3 shows us that that’s our answer.

Thus, -5 + 2 = -3.

Rule 3: Adding negative numbers to positive numbers—count backwards, as if you were
subtracting.

Example 3: Let’s say we had the problem: 5 + (-2). This would be read as “five plus
negative two.” This can also be thought of on a number line. Now, we are starting
at a positive number, but we’re adding a negative number, which means we’ll be moving
backwards (to the left) as if we were subtracting. We would count backwards two
places to arrive at the answer, like this:

The large blue dot above the number 5 shows that that’s where we’re starting our
problem. The red arrow shows that we counted backwards (subtracted) 2. The red circle
around the number 3 shows that that’s our answer.

Thus, 5 + (-2) = 3.

Rule 4: Adding negative numbers to negative numbers—ignore the addition sign, and
treat the problem like subtraction (counting backwards).

Example 4: Let’s say we had the problem -4 + -2. This would be read as “negative
four plus negative two.” This can also be thought of on a number line. First, you
have to ignore the plus sign, and recognize that the second negative number means
you are subtracting that number. Thus, you would think of this problem as “negative
four minus two.” Start at -4, then count backwards (subtract) 2 more. Then, your
answer will be -6. You would see it on a number line, like this:

The red dot above the -4 shows that that’s where we’re starting our problem. Then,
since we know we need to subtract 2, we count backwards (subtract) 2 more. The red
circle around the -6 shows that that’s our answer.

Thus, -4 + -2 = -6.