Lesson 101:  Adding Signed Numbers

Of course you already know how to add positive numbers.  In later math, you'll need to work a lot with negative numbers.  This lesson shows you how.

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.

Many students feel uncomfortable with negative numbers.  They can sometimes be hard to relate to.  How can you have negative 3 apples?  Just think of negative as opposite.  If you have -3 apples, instead of having them, you owe them.  Don't worry too much about finding real world analogies to every single arithmetic problem that you encounter.  Just learn the rules for how to handle them.  Later they will all make more sense.

Very often we have to add negative and positive numbers.  There are a few ways to do it.  Before we do anything else, let's take a look at a partial number line with positives, negatives and zero: 
....-5....-4....-3....-2....-1.....0.....1.....2.....3.....4.....5.....

It's important to just see how it works.  As we move to the left of zero, we are getting deeper and deeper into negative territory.

Let's say we want to add -4 + 1.  All we do is start at -4, and then move 1 to the right on our number line.  Adding means move to the right.  We get -3.  Let's say we want to add -4 + 7.  We start at -4, and move 7 numbers to the right.  We get positive 3.  This is easy with small numbers, but when we work with larger numbers, it's not practical to count on a number line. 

Here is what we do when we need to add a negative and a positive number.  Recall the lesson on absolute value.  Ignore the signs of the numbers.  Just look the absolute value (positive versions) of each number.  Then subtract the smaller number from the larger.  Here we'll do 7 - 4 to get 3.  Then give the answer the sign of whichever of the two numbers had the greater absolute value.  In this case, 7 was bigger, and 7 was positive, so our answer will be positive.

Here is a much easier way to think about it.  We're starting at -4, and adding 7.  We know that we will end up in positive territory.  It will take us 4 just to get to 0.  Then we have to add 3 more, since we're adding 7.  That puts us at +3.  What we really did was find the difference between 7 and 4, and then made our answer positive.

Here is how I like to teach how to do these problems.  Think of positive numbers as money that you have, and negative numbers as money that you owe.  To add -5 + 7, think of that as you owe 5, but have 7.  After paying what you owe, you have 2, so we'll write that as positive 2.   To add 4 + -9, think of that as you have 4, but owe 9.  You can pay back 4, but you'll still owe 5, which we'll write as -5.  Practice doing problems like this until you feel comfortable.

Sometimes we need to add two negative numbers together, like (-4) + (-7).  In this case, all we do is add the absolute values (positive versions) of the two numbers, and make the answer negative.  We get -11.  Think about why this makes sense.  You owe $4, and you also owe $7.  You owe a total of $11, which we can write as -11.  You're getting deeper into debt...you're adding up your debts.

In the next lessons, you'll learn how to subtract, multiply, and divide signed numbers.

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