Basic Mathematics for College Students

To perform this addition, we must know how to add positive and negative integers. In
this section, we develop rules to help us make such calculations.

2.2 Adding Integers 145

The Language of Mathematics In 1724, Daniel Gabriel Fahrenheit,a German

scientist, introduced the temperature scale that bears his name. The United

States is one of the few countries that still use this scale. The temperature

degrees Fahrenheit can be written in more compact form as 4°F.

 4

1 Add two integers that have the same sign.

We can use the number line to explain addition of integers. For example, to find
, we begin at 0 and draw an arrow 4 units long that points to the right. It
represents positive 4. From the tip of that arrow, we draw a second arrow, 3 units
long, that points to the right. It represents positive 3. Since we end up at 7, it follows
that. 4  3  7

4  3

− 8 − 7 − 6 − 5 − 4 − 3 − 2 − 1

Begin

4  3  7

End

01 2 34 5 6 7 8

4 3

To check our work, let’s think of the problem in terms of money. If you had $4 and
earned $3 more, you would have a total of $7.
To find on a number line, we begin at 0 and draw an arrow 4 units long
that points to the left. It represents. From the tip of that arrow, we draw a second
arrow, 3 units long, that points to the left. It represents. Since we end up at , it
follows that  4 (3) 7.

 3  7

 4

 4 (3)

 4  (3)   7

− 8 − 7 − 6 − 5 − 4 − 3 − 2 − 1

End Begin

01 2 34 5 6 7 8

− 3 − 4

Let’s think of this problem in terms of money. If you lost $4 and then lost
another $3 , overall, you would have lost a total of $7.

Here are some observations about the process of adding two numbers that have
the same sign on a number line.

• The arrows representing the integers point in the same direction and they
  build upon each other.


• The answer has the same sign as the integers that we added.
  These observations illustrate the following rules.

(3) (7)

(4)

Adding Two Integers That Have the Same (Like) Signs

1. To add two positive integers, add them as usual. The final answer is
   positive.


2. To add two negative integers, add their absolute values and make the
   final answer negative.