Basic Mathematics for College Students

In terms of money, if you lost $4 and then won $3, overall, you have lost $1
.
Here are some observations about the process of adding two integers that have
different signs on a number line.

• The arrows representing the integers point in opposite directions.


• The longer of the two arrows determines the sign of the answer. If the longer
  arrow represents a positive integer, the sum is positive. If it represents a
  negative integer, the sum is negative.
  These observations suggest the following rules.

(1)

(4)

2.2 Adding Integers 147

 4  3   1

− 8 − 7 − 6 − 5 − 4 − 3 − 2 − 1012345 6 7 8

End

Begin

–4

3

Adding Two Integers That Have Different (Unlike) Signs

To add a positive integer and a negative integer, subtract the smaller absolute

value from the larger.

1. If the positive integer has the larger absolute value, the final answer
   is positive.


2. If the negative integer has the larger absolute value, make the final
   answer negative.

EXAMPLE (^2) Add:
StrategyWe will use the rule for adding two integers that have different signs.
WHYThe addend 5 is positive and the addend is negative.
Solution
Step 1To add two integers with different signs, we first subtract the smaller
absolute value from the larger absolute value. Since , which is 5, is smaller than
, which is 7, we begin by subtracting 5 from 7.
Step 2Since the negative number, , has the
larger absolute value, we attach a negative sign
to the result from step 1. Therefore,
Make the final answer negative.

5 (7) 2



 7

7  5  2

0  70

050

 7

5 (7)

Self Check 2

Add:

Now TryProblem 31

6 (9)

The Language of Mathematics A positive integer and a negative integer are

said to have unlikesigns.





arrow, 3 units long, that points to the right. It represents positive 3. Since we end up at
 1 , it follows that  4  3  1.