Once you understand
adding negative numbers, subtraction with negative numbers becomes very simple. The most important thing to remember about subtracting negative numbers is that subtracting is simply adding the negative of a number.
Subtracting a Positive Number From a Negative Number
Let's take a look at the following problem:
(-8) - 3
Another way to look at this problem is that we are adding -8 to -3. We can rewrite this problem as
(-8) + (-3)
Now since both numbers are negative, we can add the 8 and 3 to get 11 and we know the answer is negative since both addends are negative so we get our answer of -11.
(-8) - 3 = (-8) + (-3) = -11
It is interesting to note that this holds true when subtracting a positive number from a positive number. If you have the problem 4 - 2, it can be written as 4 + (-2).
Subtracting a Negative Number From a Positive Number
Now lets look at another problem:
9 - (-5)
Understanding this problem takes a little bit different way of thinking. When dealing with subtraction we think of taking things away, but how can we take away something that is not there? Lets say you borrow $5 from a friend to buy lunch but you get too busy to eat and pocket the $5 instead. Well you can write that down as having $-5 in your checkbook to remind you that need to pay your debt back. The next day you do a favor for your friend and they decide to forgive your debt. When you go back to balance your check book, you need to take away or subtract that debt. Essentially what you are doing is removing the $-5. If you had $9 to start and you are removing $-5, you are basically adding that $5 to the $9 you had to start.
Anytime you are subtracting a negative, you convert it to adding a positive. Another way to put it is two negatives make a positive:
-(-3) = 3
-(-5) = 5
-(-(-3)) = -3 * the two inside negative signs make a positive 3, but there is still an outer negative sign.
Going back to our original problem:
9 - (-5) = 9 + 5 = 14
Here are some more examples:
3 - (-6) = 9
4 - (-2) = 6
0 - (-8) = 8
Subtracting a Negative Number From a Negative Number
Now lets look at one final example:
-3 - (-5)
This problem is done the exact same way as in the previous section. We know that two negative signs next to each other turn the number positive so we can think of our problem as:
-3 - (-5) = -3 + 5
We now use our rules to solve the addition problem, or simply use the commutative property of addition and rearrange so that our problem is:
-3 - (-5) = -3 + 5 = 5 + (-3)
Going back to our first example, we know that adding a negative is the same as subtracting a positive so
-3 - (-5) = -3 + 5 = 5 + (-3) = 5 - 3 = 2
We get our final answer of 2.