Basic Mathematics for College Students

336 Chapter 4 Decimals

SolutionThe number to be subtracted is 5.9. Subtracting 5.9 is the same as adding

its opposite,

Change the subtraction to addition.

Change the number being

subtracted to its opposite.

3

1

5

1

.6

 5.9

41.5

Use the rule for adding

two decimals with the

same sign. Make the

final answer negative.

35.65.935.6(5.9)41.5

5.9.

EXAMPLE (^7) 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.
SolutionThe number to be subtracted is Subtracting is the same as
adding its opposite, 16.2.
Add...

... the opposite

8.37(16.2)8.3716.27.83

Use the rule for adding

two decimals with

different signs. Since

16.2 has the larger

absolute value, the final

answer is positive.

16.2. 16.2

8.37(16.2)

Self Check 7

Subtract:

Now TryProblem 47

2.56(4.4)

EXAMPLE (^8) Evaluate:
StrategyWe will perform the operation within the parentheses first.
WHYThis is the first step of the order of operations rule.
SolutionWe perform the addition within the grouping symbols first.
Perform the addition.
Add the opposite
of 10.7.
Perform the addition.^12
1
.2
12
10. 7

1. 5

 1.5

 12.210.7

14

3

.5

15

3. 8

10. 7

12.2(14.53.8)12.2(10.7)

12.2(14.53.8)

Self Check 8

Evaluate:

Now TryProblem 51

4.9(1.25.6)

4 Estimate sums and differences of decimals.

Estimation can be used to check the reasonableness of an answer to a decimal addition

or subtraction. There are several ways to estimate, but the objective is the same: Simplify

the numbers in the problem so that the calculations can be made easily and quickly.

EXAMPLE 9

a.Estimate by rounding the addends to the nearest ten:

b.Estimate using front-end rounding:

StrategyWe will use rounding to approximate each addend, minuend, and

subtrahend. Then we will find the sum or difference of the approximations.

WHYRounding produces numbers that contain many 0’s. Such numbers are

easier to add or subtract.

381.7757.01

261.76432.94

Self Check 9

a.Estimate by rounding the

addends to the nearest ten:

526.93 284.03

b.Estimate using front-end

rounding:

Now TryProblems 55 and 57

512.3336.47







^16

5

.2

1

0

10

8.37

7.83

11