4.4 Multiplication and Division of Decimalsfaculty.ccbcmd.edu/~lwalte19/Math081C4S4Text.pdfCCBC Math...

CCBC Math 081 Multiplication and Division of Decimals Section 4.4 Third Edition 16 pages

298

4.4 Multiplication and Division of Decimals

In this section, we’ll consider the operations of multiplication and division of decimal numbers.

While we could do all of these calculations on a calculator, it is important to understand how to

do them by hand as well. We will also review order of operations and a few applications.

Multiplication of Decimals

Multiplying decimals is very much like multiplying whole numbers. However, unlike adding

and subtracting decimals, we do NOT need to line up the decimal points when multiplying

decimal numbers. So, where does the decimal point go in the product (answer)?

Example 1: Multiply 5.6 0.007

5.6 digits to the right of the decimal point.

0.007 + digits to the right of the decimal point.


1

3

4

Put the decimal point here so that there are 4 digits to the right of the decimal point.

Answer: 5.6 0.007 = 0.0392

Practice 1: Multiply 8 23 0 005. . Answer: 0.04115

Watch It: http://youtu.be/E9PH58wMovQ

STEPS TO PLACING THE DECIMAL POINT IN THE PRODUCT

1. Count the number of digits to the RIGHT of the decimal point in the first number.

2. Count the number of digits to the RIGHT of the decimal point in the second number

3. Add these two counts.

4. In the answer, place the decimal point so that there are as many digits to the right of the

decimal point as there are the sum total of the number of digits to the right of the decimal

in the two factors.

http://youtu.be/E9PH58wMovQ


299

Example 2: Multiply 34.5 0.13



1035 3

1

2

45

4.485 digits to the right of the decimal point

0

3

Put the decimal point here so that there are 3 digits to the right of the decimal point.

Answer: 34.5 0.13 = 4.485

Practice 2: Multiply 0 12 39 7. . Answer: 4.764

Watch It: http://youtu.be/SWGkjkQVFiI

Example 3: Multiply –9.16 8

The rules for multiplying signed numbers are the same whether we are multiplying integers,

fractions, or decimals. In this problem, we are multiplying a negative number with a positive

number; thus, the product (answer) is a negative number.


8 + digits to the right of the decimal point.


2

0

2

Put the decimal point here so there are 2 digits to the right of the decimal point.

Answer: –9.16 8 = –73.28

Practice 3: Multiply 3.15 ( 6) Answer: 18.9

Watch It: http://youtu.be/BSvYTqdVoFc

http://youtu.be/SWGkjkQVFiI

http://youtu.be/BSvYTqdVoFc


300

Example 4: Calculate the area of the given rectangle.

Remember that the area of a rectangle can be found by multiplying its length L by its width W.

Area = L W



50 100

1

1

0

10.50 digits to the right of the decimal point

2

210.5 m (Don't forget squared units for area.)

Practice 4: Calculate the area of the given rectangle. Answer: A = 5.92 cm2

Watch It: http://youtu.be/XhstK-9Iwf4

2.5 m

4.2 m

4.2 m

2.5 m

1.6 cm

3.7 cm

3.7 cm

1.6 cm

http://youtu.be/XhstK-9Iwf4


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Division of Decimals

Let’s review terminology used in division problems:

Divisor: The divisor is the number outside of the division sign.

Dividend: The dividend is the number inside of the division sign.

Quotient: The quotient is the answer.

Dividing decimals is very much like dividing whole numbers. However, if the divisor has a

decimal point, we will have to move it all the way to the right end of the number to make it a

whole number. Then, we must move the decimal point in the dividend by the same number of

places to the right. Once the decimal point is in the proper place in the dividend, we can put the

decimal point in the proper location in the quotient (answer). The decimal point in the quotient

will be directly above the decimal point in the dividend.

PARTS OF A DIVISION STATEMENT

Dividend Divisor Quotient

8 2 4

DividendQuotient

Divisor

84

2

Quotient

Divisor Dividend

42 8

DIVIDING DECIMALS

1. Move the decimal point in the divisor all the way to the right end of the number to make it a

whole number.

2. Move the decimal point in the dividend by the same number of places to the right.

3. Put the decimal point in the quotient (answer) directly above the decimal point in the

dividend.

4. Use long division method to divide.


302

Example 5: Divide. 78.06 by 3.

The number 78.06 is the dividend so it is placed inside of the division sign. The number 3 is the

divisor so it is placed outside of the division sign.

.

3 7 8.06 Since there is no decimal place in the divisor, the decimal gets moved

straight up into the quotient. Then divide as you would whole numbers.

2 .

3 78.06

6

18

26.

3 78.06

6

18

18

00

26.0

3 78.06

6

18

18

00

0

06

26.02

3 78.06

6

18

18

00

0

06

6

0

Answer: 78.06 ÷ 3 = 26.02

Practice 5: Divide 11 12 4. Answer: 2.78

Watch It: http://youtu.be/fq4U1ffpjUA

http://youtu.be/fq4U1ffpjUA


303

Example 6: Divide. 496 ÷ 6.2

Since we have a decimal point in the divisor, we need to follow the steps below to move the

decimal point to the correct place in the quotient:

6.2 496 Write as a long division problem.

6.2 496.0 Place the decimal. (Remember 496 = 496.0)

.

62. 4960. Move the decimal to the end of the divisor. Move the decimal the same number of spaces in the dividend. .

62. 4960. Place the decimal of the quotient directly above the decimal in the dividend.

62. 4960.

-

8 .

Divide using long division.

496

00

Remember that every digit in the dividend must have an answer in the

quotient (if possible) up to the decimal point.

80.

62. 4960.

- 496

00

- 0

0

Answer: 80

Practice 6: Divide 35 0 05. Answer: 700

Watch It: http://youtu.be/QPVF-nUyejg

http://youtu.be/QPVF-nUyejg


304

Example 7: Divide 50.86 by 7 and round off your answer to the nearest hundredth.

.

7 50.86 Write as a long division problem. Since there is no decimal place in the divisor, place the decimal in the answer directly above the

decimal in the dividend.

.

7 50.86 To round to the hundredths place, we will need to know the digit of the thousandths place in the answer. Therefore we will need to

0

place a 0 to the right of the divisor in the thousandths place.

7.

7 50.86

- 49

1 8

0

7.2

7 50.86

- 49

1 8

- 1 4

4 6

0

7.26

7 50.86

- 49

1 8

- 1 4

46

- 42

40

0

7. 265

7 50.860

- 49

1 8

- 1 4

46

- 42

40

- 35

5

Since we are rounding the answer to nearest hundredth, the 5 (which is 5 or greater) in the third decimal

place is an indication to “bump” the 6 in the hundredths place to make it 7.

Answer: 50.86 ÷ 7 ≈ 7.27

Practice 7: Divide 51 2 3. Note: Round your answer to the nearest hundredth.

Answer: 17.07

Watch It: http://youtu.be/AcMb_kvVa2Q

http://youtu.be/AcMb_kvVa2Q


305

Example 8: Convert the fraction 9

8 to a decimal. Round to one decimal place.

We can think of the fraction 9

8 as 9 8 . Set up the division problem as 8 9 .

Since we need to round the answer to one decimal place, we need to have 2 decimal places in the

quotient. So, we write the division as8 9.00 .

1.12

8 9.00

- 8

1 0

- 8

20

-16

4

Since we are rounding the answer to one decimal place, the 2 (which is less than 5) in the second

decimal place is an indication to leave the 1 in the tenths place unchanged.

Answer: 9

8 rounded to one decimal place is 1.1

Practice 8: Convert the fraction 6

11

to a decimal. Round your answer to one decimal place.

Answer: 1.8

Watch It: http://youtu.be/5EJR-W8JqGI

http://youtu.be/5EJR-W8JqGI


306

Example 9: Convert the fraction 3

4 to a decimal.

We can think of the fraction 3

4 as 3 4 . Set up the division problem as 4 3 .

To begin the division, we need to put some zeros in the problem. We will begin with three zeros

and add more if necessary. So, we write the division as 4 3.000 .

0.750

4 3.000

- 28

2 0

- 20

00

- 0

0

Answer: 3

4 is 0.75

Practice 9: Convert the fraction 4

5

to a decimal. Answer: 0.8

Watch It: http://youtu.be/kWTaFHEFg2M

Now that we have studied how to add, subtract, multiply, and divide decimal numbers, we can

evaluate expressions using order of operations.

Example 10: Evaluate 2

5.1 4.7

2

5.1 4.7 Using Order of Operations, compute inside the parentheses.

5.1

- 4.7

0.4

=2(0.4) Now square 0.4 by multiplying 0.4 by 0.4:

0.4 1 digit to the right of the decimal

0.4 +1 digit to the right of the decimal

0.16 2 digits to the right of the decimal

= 0.16

Answer: 2

5.1 4.7 0.16

http://youtu.be/kWTaFHEFg2M


307

Practice 10: Evaluate 212.5 0.3 Answer: 12.41

Watch It: http://youtu.be/_oOXk__bCh0

Example 11: Evaluate 16.98 12.4 2

16.98 12.4 2 = Using Order of Operations, divide first:

6.2

2 12.4

- 12

0 4

- 4

0

16.98 6.2 Now add, lining up at the decimal point (and inserting a 0):

16.98

6.2

23.18

0

Answer: 16.98 12.4 2 23.18

Practice 11: Evaluate 0.5 7.25 0.1 Answer: 0.225

Watch It: http://youtu.be/MYFFjH-fh9w

http://youtu.be/_oOXk__bCh0

http://youtu.be/MYFFjH-fh9w


308

Now let’s review some geometry applications but here, our data will consist of decimal values.

Example 12: Calculate the perimeter of the given rectangle.

Use the formula for perimeter of a rectangle: P = 2L + 2W. Use L = 2.5 and W = 4.2.

Perimeter = 2 + 2

2 2.5 2 4.2

5.0 8.4

13.4 m (Don't forget the units in the final answer.)

L W

Practice 12: Calculate the perimeter of the given rectangle. Answer: P = 27.48 inches

Watch It: http://youtu.be/9CEkOg3LcSc

In previous sections, we learned about measures of central tendency: mean, median, and mode.

Let’s continue with these concepts where the data values are decimal numbers.

Example 13: Find the mean of 14.70, 15.3, 12.9, 13.1, 14.7, 13.9.

To calculate the mean, start by adding the six data values:

14.70 + 15.3 + 12.9 + 13.1 + 14.7 + 13.9 = 84.6

Now, divide that sum by 6 (the number of data values):

Mean = 84.6 6 14.1

Practice 13: Find the mean of 131.0 132.7 132.9 131 Answer: 131.9

Watch It: http://youtu.be/9DQAa7-9PDw

2.5 m

4.2 m

4.2 m

2.5 m

3.6 in

10.14 in

10.14 in

3.6 in

http://youtu.be/9CEkOg3LcSc

http://youtu.be/9DQAa7-9PDw


309

Example 14: Find the median of 14.70, 15.3, 12.9, 13.1, 14.7, 13.9.

Note: 14.70 = 14.7

Start by listing the data values in order from least to greatest:

12.9 13.1 13.9 14.70 14.7 15.3

Because there is an even number of data values (6), there are two middle values: 13.9 and 14.70.

Find the mean of these two values:

13.9 14.70 28.6

14.32 2

Practice 14: Find the median of 131.0 132.7 132.9 131 Answer: 131.85

Watch It: http://youtu.be/EMWN-Pll8ME

Example 15: Find the mode of 14.70, 15.3, 12.9, 13.1, 14.7, 13.9.

The mode is the data value that occurs most often. Order the data from smallest to largest:

12.9, 13.1, 13.9, 14.70, 14.7, 15.3,

Because 14.7 appears twice and every other data value appears only once, the mode is 14.7.

(Remember 14.70 = 14.7)

Practice 15: Find the mode of 131.0 132.7 132.9 131 Answer: 131

Watch It: http://youtu.be/ywPwLyWEvec

Watch All: http://youtu.be/UfqEJ6BVVJU

http://youtu.be/EMWN-Pll8ME

http://youtu.be/ywPwLyWEvec

http://youtu.be/UfqEJ6BVVJU


310

4.4 Multiplication and Division of Decimals Exercises

1. Without actually finding the product, determine how many places will show to the right of

the decimal point in the product:

0.05 1.4



15.612 18.41



15 3.79

4. Multiply: 0.6 5.8

5. Multiply: 73 0.004

6. Multiply: - 3.02 0.4

7. Multiply: 12.1 2.7

8. Multiply: (-12) (-3.5)

9. Calculate the perimeter and area of the given rectangle.

10. Calculate the perimeter and area of the given rectangle.

2.5 m

4.2 m

4.2 m

2.5 m

3 in

1.25 in

1.25 in

3 in


311

11. Identify the dividend and the divisor in the division problem. Then, without actually

finding the quotient, show how you would set up the long division problem.

5.6 7

12. Identify the dividend and the divisor in the division problem. Then, without actually

finding the quotient, show how you would set up the long division problem.

95.76 3.8

13. Without actually finding the quotient, show where the decimal point will be located in the

quotient:

8 329.6


quotient:

4.3 5.375


quotient:

0.002 6

16. Divide: 45 0.945

17. Divide: 25.25 0.05

18. Divide: 0.7 0.824 Round to the nearest hundredth.

19. Divide: 0.42 0.1268 Round to one decimal place.

20. Divide: 0.4 12

21. Divide: 16 0.08


312

22. Convert the fraction 32

5 to a decimal.


9 to a decimal. Round to the nearest thousandth.


6 to a decimal. Round to two decimal places.

25. Evaluate: 2(2.5 1.6)

26. Evaluate: 39.6 3 1.2

27. Evaluate: (12 1.5) 2.1

28. Evaluate: 20.6 0.1

29. Evaluate: 21.7

According to Weather.com, the average rainfall (in inches) for six months in Baltimore is:

4.07 3.29 4.03 3.33 3.30 3.37

30. Using the data above, find the mean rainfall.

31. Using the data above, find the median rainfall.

32. Using the data above, find the mode(s).

The following data represent the wait time (in minutes) in line for a hamburger at McWendy’s

Drive Thru Burger Joint.

1.01 0.90 0.84 0.9 1.23 2.50 1.88

33. Using the data above, find the mean wait time. Round the answer to three decimal places.

34. Using the data above, find the median wait time.

35. Using the data above, find the mode(s).


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4.4 Multiplication and Division of Decimals Exercises Answers

1. 3

2. 5

3. 2

4. 3.48

5. 0.292

6. - 1.208

7. 32.67

8. 42

9. Perimeter: 13.4 meters Area: 10.5 square meters

10. Perimeter: 8.5 inches Area: 3.75 square inches

11. Dividend: 5.6 Divisor: 7

7 5.6

12. Dividend: 95.76 Divisor: 3.8

3.8 95.76

13.

.

8 329.6

14.

.

4.3 5.375

15.

.

0.002 6.000

16. 0.021

17. 505

18. 1.18

19. 0.3

20. 30

21. - 200

22. 6.4

23. 0.556

24. 1.17

25. 0.81

26. 15.84

27. 22.05

28. 0.61

29. - 2.89

30. 3.565 in

31. 3.35 in

32. no mode

33. 1.323 min

34. 1.01 min

35. 0.9 mi

4.4 Multiplication and Division of Decimalsfaculty.ccbcmd.edu/~lwalte19/Math081C4S4Text.pdfCCBC Math...

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