Basic Mathematics for College Students

4.2 Adding and Subtracting Decimals 335

3 Add and subtract signed decimals.

To add signed decimals, we use the same rules that we used for adding integers.

Adding Two Decimals That Have the Same (Like) Signs

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


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

Adding Two Decimals That Have Different (Unlike) Signs

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

value from the larger.

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


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

EXAMPLE (^4) Add:
StrategyWe will use the rule for adding two decimals that have the same sign.
WHYBoth addends, and are negative.
SolutionFind the absolute values: and
Add the absolute values, 6.1 and 4.7, to
get 10.8. Then make the final answer
negative.

6.1(4.7)10.8

0 6.1 0 6.1 0 4.7 0 4.7.

6.1 4.7,

6.1(4.7)

Self Check 4

Add:

Now TryProblem 35

5.04(2.32)

EXAMPLE (^5) Add:
StrategyWe will use the rule for adding two integers that have different signs.
WHYOne addend is positive and the other is negative.
SolutionFind the absolute values: and
Subtract the smaller absolute value from
the larger: 12.9 5.35 7.55. Since the
negative number, 12.9, has the larger
absolute value, make the final answer
negative.
12.9
8
0
10
5.3 5
7.5 5

5.35(12.9)7.55

0 5.35 0 5.35 0 12.9 0 12.9.

5.35(12.9)

Self Check 5

Add:

Now TryProblem 39

21.416.75

The rule for subtraction that was introduced in Section 2.3 can be used with
signed decimals:To subtract two decimals, add the first decimal to the opposite of the
decimal to be subtracted.

EXAMPLE (^6) Subtract:
StrategyWe will apply the rule for subtraction: Add the first decimal to the
opposite of the decimal to be subtracted.
WHYIt is easy to make an error when subtracting signed decimals. We will
probably be more accurate if we write the subtraction as addition of the opposite.

35.65.9

Self Check 6

Subtract:

Now TryProblem 43

1.182.88

6.1

 4.7

10.8