CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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4.3 Addition and Subtraction of Decimals

Now that we have a good understanding of decimal numbers and their relationship to fractions,

we will cover the basic arithmetic operations on decimal numbers. In this section, we will

consider the operations of addition and subtraction. While we could do all of these calculations

on a calculator, it is important to understand how to do them by hand as well.

Addition of Decimals

To add decimal numbers, use a vertical display to line up the decimal points of each addend. If

necessary, insert additional zeros as placeholders after the last digit to the right of the decimal

point. Then add the numbers as you would when adding whole numbers. The decimal point of

the sum (answer) is written directly below the decimal points of the addends.

Example 1: Add 2.945 + 8.329

Line up the decimal points and add the digits down, regrouping (“carrying”) as needed.

1 1 2.945

8.329

11.274

Answer: 2.945 + 8.329 = 11.274

Practice 1: Add 3.61 + 8.42 Answer: 12.03

Watch It: http://youtu.be/dF7CwnXbstE

ADDITION OF DECIMALS

1. Set up the problem in a vertical display with the decimal points lined up.

2. If necessary, insert additional zeros as placeholders after the last digit to the right of the

decimal point.

3. Add the numbers as you would whole numbers.

4. Place the decimal point of the sum (answer) directly below the decimal points of the addends.

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

284

Example 2: Add 12 + 3.96

Where is the decimal point for the whole number 12? Think of 12 as “12 dollars” or $12.00, and

then you’ll see the decimal point.

Any whole number can be written as a decimal with the decimal point at the right end of

the number (to the right of the ones digit) and with zeros to the right of the decimal point.

Line up the decimal points and add the digits down.

12.

3.96

15.96

00 Insert two zeros as placeholders.

Answer: 12 + 3.96 = 15.96

Practice 2: Add 9.367 + 24 Answer: 33.367

Watch It: http://youtu.be/99dccW4dG2k

Example 3: Add 5.81 + 7.623

Line up the decimal points and add the digits down.

1 5.81

7.623

13.433

0 Insert a 0 as a placeholder.

Answer: 5.81 + 7.623 = 13.433

Practice 3: Add 11.23 + 5.4 Answer: 16.63

Watch It: http://youtu.be/KV92VNX9BYg

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

285

Example 4: Calculate the perimeter of the given trapezoid.

Remember that perimeter is the distance around an object’s boundary. So add the lengths of the

four sides of the trapezoid:

2 2.8

3.8

7.5

3.4

17.5

Perimeter: P = 2.8 + 3.8 +7.5 + 3.4 = 17.5 in.

Practice 4: Calculate the perimeter of the given trapezoid. Answer: P = 11.3 cm

Watch It: http://youtu.be/0YuPCNyLfm0

2.8 in

3.8 in

7.5 in

3.4 in

3.1 cm

2.2 cm

4 cm

2 cm

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

286

Example 5: Calculate the perimeter of the given triangle.

Add the lengths of the three sides of the triangle:

1 3.2

4.7

1.7

9.6

Perimeter: P = 3.2 + 4.7 + 1.7 = 9.6 cm

Practice 5: Calculate the perimeter of the given triangle. Answer: 11.37 in

Watch It: http://youtu.be/KDfmOyZPjx0

Subtraction of Decimals

To subtract decimal numbers, use a vertical display to line up the decimal points. If necessary,

insert additional zeros as placeholders after the last digit to the right of the decimal point. Then

subtract the numbers as you would when subtracting whole numbers. The decimal point of the

difference (answer) is written directly below the decimal points of the subtrahend.

1.7 cm 3.2 cm

4.7 cm

0.7 cm

2 in 4.1 in

5.27 in

1.3 in

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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Example 6: Subtract 19.752 – 3.24

Line up the decimal points:

19.752

3.24

16.512

0 Insert a 0 as a placeholder.

Answer: 19.752 – 3.24 = 16.512

Practice 6: Subtract 22.513 – 4.9 Answer: 17.613

Watch It: http://youtu.be/9BhQmOl19mQ

SUBTRACTION OF DECIMALS

1. Set up the problem in a vertical display with the decimal points lined up.

2. If necessary, insert additional zeros as placeholders after the last digit to the right of the

decimal point.

3. Subtract the numbers as you would whole numbers.

4. Place the decimal point of the difference (answer) directly below the decimal points of the

subtrahend.

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

288

Example 7: Subtract 8.13 – 5.051

Line up the decimal points:

8.13

5.051

0 Insert a 0 as a placeholder.

We need to regroup (“borrow”) in order to finish the subtraction.

0 12

8. 1 3 1 0

5. 0 5 1

3. 0 7 9

Answer: 8.13 – 5.051 = 3.079

Practice 7: Subtract 9.2 – 7.83 Answer: 1.37

Watch It: http://youtu.be/RZhUwozs8qI

Example 8: Subtract 5 – 2.536

Write the whole number 5 as 5.000. Line up the decimal points and subtract:

4 9 9

5 1. 0 10 10

2 . 5 3 6

2 . 4 6 4

Answer: 5 – 2.536 = 2.464

Practice 8: Subtract 6 – 3.01 Answer: 2.99

Watch It: http://youtu.be/NOLdKt47JRg

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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Example 9: (Source: Interactive online study via Cengage Learning)

The following data represent the consumption of energy (in quadrillion BTUs) in 1999.

Note: one quadrillion = 1,000,000,000,000,000

Source 1999

Petroleum 37.71

Natural Gas 22.10

Coal 21.70

Nuclear 7.73

Renewable Energy (hydroelectric, geothermal, etc.) 3.75

a. In 1999, how much more energy (in quadrillion BTUs) was consumed from petroleum than

coal?

Reading from the table, 37.71 quadrillion BTUs were consumed from petroleum and 21.70

quadrillion BTUS were consumed from coal. Find the difference in energy consumption by

subtracting:

37.71

21.70

16.01

quadrillion BTUs

b. In 1999, how much total energy (in quadrillion BTUs) was consumed from Nuclear and

Renewable Energy?

Reading from the table, 7.73 quadrillion BTUs were consumed from Nuclear Energy and 3.75

quadrillion BTUs were consumed from Renewable Energy. Find the total in energy

consumption by adding:

1 7.73

3.75

11.48

quadrillion BTUs

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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Practice 9: The table below shows the postal rates for priority mail in 2009.

Postal Rate for Priority Mail 2009

Weight Zones

Not

Over Local,

(pounds) 1 & 2 3 4 5 6 7

1 $ 4.95 $ 4.95 $ 4.75 $ 4.95 $ 4.95 $ 4.95

2 $ 4.95 $ 5.20 $ 5.75 $ 7.10 $ 7.60 $ 8.10

3 $ 5.50 $ 6.25 $ 7.10 $ 9.05 $ 9.90 $ 10.60

4 $ 6.10 $ 7.10 $ 8.15 $ 10.80 $ 11.95 $ 12.95

5 $ 6.85 $ 8.15 $ 9.45 $ 12.70 $ 13.75 $ 15.20

6 $ 7.55 $ 9.25 $ 10.75 $ 14.65 $ 15.50 $ 17.50

a. How much more does it cost to send a 2.7 pound package to Zone 6 than to Zone 5?

b. A customer sends one 1.5 pound package to Zone 3 and another 1.5 pound package to

Zone 7. How much will it cost to mail both packages?

Answers: a. $ 0.85 b. $ 13.30

Watch It: http://youtu.be/unqOMjdP7yo

Now we will practice addition and subtraction involving signed decimal numbers. The rules for

adding and subtracting signed numbers are the same whether we are working with integers,

fractions, or decimals.

Example 10: Add - 0.65 + (- 4.12)

We will use the Triple-S method since we are adding two numbers that have the same sign.

Compute the sum of the absolute values of each of the two numbers.

Add 0.65 and 4.12 by lining up the decimal points:

0.65

4.12

4.77

The final answer takes the same sign as the sign of the two original numbers. Since -0.65 and

-4.12 are both negative numbers, the sum is a negative number.

Answer: - 0.65 + (- 4.12) = -4.77

Practice 10: Add –99.99 + (–100.05) Answer: –200.04

Watch It: http://youtu.be/Botzjk-Upqs

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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Example 11: Subtract 3.1 – (-1.23)

First, recognize that we are subtracting a negative number. Using the rules for operations on

integers, 3.1 – (-1.23) is equivalent to 3.1 + 1.23. We have rewritten the subtraction problem as

an equivalent addition problem. Now add by lining up the decimal points:

3.1

1.23

4.33

0 Insert a 0 as a placeholder

Answer: 3.1 – (-1.23) = 4.33

Practice 11: Subtract –5.7 – 1.62 Answer: –7.32

Watch It: http://youtu.be/PQl8ah7exEU

Example 12: Add - 31.5 + 27.2.

We will use the Triple-D method since we are adding two numbers that have different signs.

Compute the difference between the absolute value of each of the two numbers. We subtract

31. 5 – 27.2 by lining up the decimal points:

31.5

27.2

4.3

The final answer takes the sign of the dominant number. Notice that -31.5 has a larger absolute

value than 27.2 so the final answer is a negative number.

Answer: - 31.5 + 27.2 = - 4.3

Practice 12: Add –3.15 + 6.7 Answer: 3.55

Watch It: http://youtu.be/aqdaHiPgt98

Watch All: http://youtu.be/Cdr-oH6j35g

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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4.3 Addition and Subtraction of Decimals Exercises

1. Without actually finding the sum, show how you would set up the addition problem when

calculating by hand:

4.5 + 12.97

2. Without actually finding the sum, show how you would set up the addition problem when

calculating by hand:

350 + 13.75

3. Add: 1.213 + 11.019

4. Add: 0.07 + 1.3

5. Add: 18 + 3.167

6. Add: 0.15 + 0.029

7. Add: 55.3 + 21.07

8. Calculate the perimeter of the given trapezoid.

9. Calculate the perimeter of the given trapezoid.

10. Calculate the perimeter of the given triangle.

5.7 mm

4.2 mm

6.7 mm

3.4 mm

5.3 in

3.5 in

8.7 in

2.8 in

2.8 cm 5 cm

6.9 cm

1.3 cm

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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11. Calculate the perimeter of the given triangle.

12. Without actually finding the difference, show how you would set up the subtraction

problem when calculating by hand:

9.19 – 3.2

13. Without actually finding the difference, show how you would set up the subtraction

problem when calculating by hand:

15.62 – 3.475

14. Without actually finding the difference, show how you would set up the subtraction

problem when calculating by hand:

20 – 11.99

15. Subtract: 4.827 – 1.31

16. Subtract: 15.1 – 2.67

17. Subtract: 12 – 3.154

18. Subtract: 20 – 4.67

19. The table below shows the postal rates for priority mail in 2009. How much more does it

cost to send a 5.25 pound package to Zone 7 than to Zone 3?

Postal Rate for Priority Mail 2009

Weight Zones

Not

Over Local,

(pounds) 1 & 2 3 4 5 6 7

1 $ 4.95 $ 4.95 $ 4.75 $ 4.95 $ 4.95 $ 4.95

2 $ 4.95 $ 5.20 $ 5.75 $ 7.10 $ 7.60 $ 8.10

3 $ 5.50 $ 6.25 $ 7.10 $ 9.05 $ 9.90 $ 10.60

4 $ 6.10 $ 7.10 $ 8.15 $ 10.80 $ 11.95 $ 12.95

5 $ 6.85 $ 8.15 $ 9.45 $ 12.70 $ 13.75 $ 15.20

6 $ 7.55 $ 9.25 $ 10.75 $ 14.65 $ 15.50 $ 17.50

12 km

15.13 km 12.8 km

13.85 km

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

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20. Add: 4.17 + (- 1.5)

21. Subtract: 5.6234 – (- 3.17)

22. Add: - 100.6 + (-57.8)

23. Add: - 0.1 + 0.06

24. Subtract: - 0.54 – 1.2

25. Subtract: - 9.8 – (- 4)

CCBC Math 081 Addition and Subtraction of Decimals Section 4.3 Third Edition 13 pages

295

4.3 Addition and Subtraction of Decimals Exercises Answers

1. 4.5

12.97

0

2. 350.

13.75

00

3. 12.232

4. 1.37

5. 21.167

6. 0.179

7. 76.37

8. 20 mm

9. 20.3 in

10. 14.7 cm

11. 41.78 km

12. 9.19

3.2 0

13. 15.62

3.475

0

14. 20.

11.99

00

15. 3.517

16. 12.43

17. 8.846

18. 15.33

19. $17.50 - $9.25 = $8.25

20. 2.67

21. 8.7934

22. - 158.4

23. - 0.04

24. - 1.74

25. - 5.8

CCBC Math 081 Section 4.1 - 4.3 Third Edition

8.23 m

7.38 m 6.70 m

12.31 m

Mi d -Ch a p t e r R e v i ew

In the number 5768.293, what digit is in the: 1. hundredths place 2. tens place

In the number 1357.902: 3. name the place value of the 9 4. name the place value of the 1

Fill in the blank with <, >, or =.

5. 0.486 ___ 0.483 6. 0.05 ___ 0.053

Write the numbers in order (least to greatest).

7. 1.365, 1.374, 1.382, 1.309, 1.38

Estimate each number. 8. 469 9. 0.836 10. 3.5

Round 1745.6295 11. to the nearest tenth 12. to the nearest thousand 13. to the nearest thousandth

Write each as a fraction in simplest form.

14. 0.071 15. 1.56

Write each as a decimal.

16. 345

100

17. 1

5

Show how to set up the addition problem to calculate by hand. Do not add.

18. 16.9 + 7.348 19. 0.25 + 53.1

Add.

20. 13.456 + 8.37 21. 0.98 + 0.025

Show how to set up the subtraction problem

to calculate by hand. Do not subtract.

22. 834 6 29 742. .

23. 1 59 0 3. .

Subtract.

24. 12 417 8 82. .

25. 53 7 69.

Perform the indicated operation.

26. 1 73 0 9. .

27. 7 528 3 91. .

28. 2 9 4 57. .

29. 24 79 82 81. .

30. 0 138 0 65. .

31. 0 15 7 6. .

32. 4 32 89.

The average rainfall (in inches) for five

months was 4.23, 2.45, 1.46, 3.45, and 2.48.

33. Find the median rainfall.

Calculate the perimeter of the trapezoid.

34.

Use the table below to answer each question.

35. What would have been the cost for purchasing a loaf of bread, a gallon of milk, and a dozen eggs in 1990?

36. How much more was a pound of coffee in 2010 compared to 1980?

Item 1980 1990 2000 2010 Bread (1 lb) $0.52 $0.70 $0.99 $1.39

Coffee (1 lb) $2.82 $2.94 $3.21 $4.15

Eggs (1 dz) $0.87 $1.01 $0.91 $1.37

Milk (1 gal) $0.78 $1.32 $2.79 $3.32

CHAPTER 4

CCBC Math 081 Mid-Chapter Review 4 Section 4.1 - 4.3 Third Edition

297

M i d - C h a p t e r 4 R e v i e w A n s w e r s

1. 9

2. 6

3. Tenths

4. Thousands

5. >

6. <

7. 1.309, 1.365, 1.374, 1.38, 1.382

8. 500

9. 0.8

10. 4

11. 1745.6

12. 2000

13. 1745.630

14. 71

1000

15. 39 14

125 25

16. 3.45

17. 0.2

18. 16 900

7 348

.

.

19. 0 25

53 10

.

.

20. 21.826

21. 1.005

22. 834 600

29 742

.

.

23. 1 59

0 30

.

.

24. 3.597

25. 45.31

26. –2.63

27. 11.438

28. 1.67

29. –58.02

30. –0.512

31. –7.75

32. 28.89

33. 2.48 in

34. 34.62 m

35. $3.03

36. $1.33