Basic Mathematics for College Students

4.4 Dividing Decimals 365

WHYIn part a, the divisor is positive and the dividend is negative. In part b, both Now TryProblems 51 and 55
the dividend and divisor are negative.

Solution
a.First, we find the absolute values: and.
Then we divide the absolute values, 104.483 by 16.3, using the methods of
this section.

Since the signs of the original dividend and divisor are unlike, we make the

final answer negative. Thus,

Check the result using multiplication.

b.We can use the rule for dividing a decimal by a power of 10 to find the
quotient.

Since the divisor 0.1 has onedecimal place, move the decimal

point in 38.677 oneplace to the right. Since the dividend and

divisor have like signs, the quotient is positive.

38.677

0.1

386.77

104.48316.36.41

Move the decimal point in the divisor and the dividend

one place to the right.

Write the decimal point in the quotient (answer)

directly above the decimal point in the dividend.

Divide as if working with whole numbers.

6.41

(^163) 1044.83
 978
66 8
65 2 0
163
 163
0

0 104.483 0 104.483 0 16.3 0 16.3

 

7 Use the order of operations rule.

Recall that the order of operations rule is used to evaluate expressions that involve
more than one operation.

EXAMPLE 9

Evaluate:

StrategyWe will evaluate the expression above and the expression below the
fraction bar separately. Then we will do the indicated division, if possible.

WHYFraction bars are grouping symbols. They group the numerator and
denominator.

Solution

In the numerator, do the addition.

Do the division indicated by the fraction

bar. The quotient of two numbers with

unlike signs is negative.

 3.153



1.2612

0.4

In the numerator, do the multiplication.

 (^) In the denominator, do the subtraction.

0.7020.5592

0.4

0

1

.70

1

20

 0.5592

1.2612

0.3

1

51

 2

0.702

2(0.351)0.5592

0.2  0.6

2(0.351)0.5592

0.20.6

Self Check 9

Evaluate:

Now TryProblem 59

2.77563(0.63)

0.41.2

3.153

4 12.612

 12

6

 4

21

 20

12

 12

0