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Lesson 102a: Subtracting Signed Numbers
In the last lesson you learned how to add signed numbers. In this lesson you'll learn how to subtract, them. This is one of the most important lessons on the site. Be sure you understand it.
Don't forget to watch the embedded YouTube video clip for this lesson at the bottom of the page.
Download or view a PDF file of practice exercises for this topic.
Subtracting signed numbers can be a bit tricky. Let's look at how to do 4 - 7. We start at 4 on a number line, and then move 7 to the left, since we're subtracting. We end up on -3. Here is the rule that we use: Convert the problem into 4 + (-7). That is really all subtracting is. It's just adding the negative version of the second number. We learned how to do this addition in the last lesson. We'll subtract the absolute values of the numbers, and get 3. Then we'll take the sign of the number with the greater absolute value. That's 7, and it's negative, so we'll make our answer negative and get -3.
To summarize the suggested procedure for subtracting signed numbers:
1) Leave the first number alone.
2) Change the subtraction operation to addition.
3) Change the sign of the second number
Let's do -3 - 6. Again, convert it to an addition problem: -3 + (-6). As we learned in the last lesson, when we add two negatives, we just add the absolute values and make the answer negative. The answer is -9.
Here is where it gets a little tricky. Let's do 9 - (-4). There is a simple rule. When you subtract a negative, just add the positive version. We'll convert the problem to 9 + (+4). We just add this as we learned a long time ago, and get 13. You could think of the rule as two negatives make a positive. Let's try one more.
What is -8 - (-3)? Remember, instead of subtracting a negative, we'll add a positive. The problem then becomes -8 + 3. We learned how to do that in the last lesson. We have a negative number and positive number. Think of it as owing 8, but having 3. You'll still owe 5, which we'll write as -5. All of this can be tricky. Just make up lots of problems for yourself, and practice. Before long it will be very easy for you. You will have much more practice with these concepts as we learn more math.
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