Subtracting Positive and Negative Numbers

Subtracting
positive and negative numbers can also be tricky because there are several
rules to remember and follow.

Rule 1: Subtracting a positive number from a positive number—this is normal
subtraction.

Example 1: Don’t let all this talk of positive and negative numbers throw
you off track—if you see a positive number minus a positive number, subtract it
like normal! For example, if you see 5 – 3, subtract normally! 5 – 3 = 2.

Rule 2: Subtracting a positive number from a negative number—start at the
negative number, and count backwards the additional amount you’re subtracting.

Example 2: Let’s say we had the problem -5 – 3. This would be read as “negative
five minus three.” This can be thought of on a number line, which means we’re going
to start at the negative number (-5) and keep counting back the -3, arriving at
-8, like this:

The large red dot above the -5 shows that that’s where we’re starting our problem.
The red arrow shows that we counted backwards (subtracted) 3. The red circle around
the –8 shows that that’s our answer.

Thus, -5 – 3 = -8.

You can also think about these problems as addition problems—you add the numbers
together (5 + 3 = 8) and then, since both numbers have a minus sign in front of
them, you would add a negative sign in front of your answer, like this: -8. If this
makes more sense, you can do these problems like this—but only problems that are
written like this: -5 – 3. If there are any other signs (addition, subtraction,
etc) you need to follow the rule for that type of problem.

Rule 3: Subtracting a negative number from a negative number—when you see
the subtraction (minus) sign followed by a negative sign, turn the two signs into
a plus sign. Thus, instead of subtracting a negative, you are adding a positive.
So, – -5 becomes +5, and continue normally with the addition.

Example 3: Let’s say we had the problem -6 – -3. This would be read as “negative
six minus negative three.” This can be thought of on a number line, which means
we’re going to start at by changing the – -3 into +3, like this:

Now our problem reads -6 + 3, which we can solve as a normal addition problem on
the number line, like this:

The large red dot above the -6 shows that that’s where we’re starting our problem.
The blue arrow shows that we counted forward (added) 3. The blue circle around the
–3 shows that that’s our answer.

Rule 4: Subtracting a negative number from a positive number—when you see
the subtraction (minus) sign followed by a negative sign, turn the two signs into
a plus sign. Thus, instead of subtracting a negative, you’re adding a positive,
so you have a simple addition problem.

Example 4: Let’s say we had the problem 5 – (-3). This would be read as “five
minus negative three.” This would work the same way as the previous example, so
the – (-3) would change to a +3; therefore, your new problem would read 5 + 3, which
is a simple addition problem, resulting in 8.