CCBC Math 081
Third Edition
Addition and Subtraction of Decimals
Section 4.3
13 pages
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.
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.
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
Watch It:
http://youtu.be/dF7CwnXbstE
Answer: 12.03
283
CCBC Math 081
Third Edition
Example 2:
Addition and Subtraction of Decimals
Section 4.3
13 pages
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.
12.00
Insert two zeros as placeholders.
 3.96
15.96
Answer:
12 + 3.96 = 15.96
Practice 2:
Add 9.367 + 24
Watch It:
http://youtu.be/99dccW4dG2k
Example 3:
Add 5.81 + 7.623
Answer: 33.367
Line up the decimal points and add the digits down.
1
5.810
Insert a 0 as a placeholder.
 7.623
13.433
Answer:
5.81 + 7.623 = 13.433
Practice 3:
Add 11.23 + 5.4
Watch It:
http://youtu.be/KV92VNX9BYg
Answer: 16.63
284
CCBC Math 081
Third Edition
Example 4:
Addition and Subtraction of Decimals
Section 4.3
13 pages
Calculate the perimeter of the given trapezoid.
2.8 in
3.8 in
3.4 in
7.5 in
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.
3.1 cm
2 cm
2.2 cm
4 cm
Watch It:
http://youtu.be/0YuPCNyLfm0
285
Answer: P = 11.3 cm
CCBC Math 081
Third Edition
Example 5:
Addition and Subtraction of Decimals
Section 4.3
13 pages
Calculate the perimeter of the given triangle.
1.7 cm
3.2 cm
0.7 cm
4.7 cm
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.
2 in
Answer: 11.37 in
4.1 in
1.3 in
5.27 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.
286
CCBC Math 081
Third Edition
Addition and Subtraction of Decimals
Section 4.3
13 pages
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.
Example 6:
Subtract 19.752 – 3.24
Line up the decimal points:
19.752
 3.240
Insert a 0 as a placeholder.
16.512
Answer:
19.752 – 3.24 = 16.512
Practice 6:
Subtract 22.513 – 4.9
Watch It:
http://youtu.be/9BhQmOl19mQ
Answer: 17.613
287
CCBC Math 081
Third Edition
Example 7:
Addition and Subtraction of Decimals
Section 4.3
13 pages
Subtract 8.13 – 5.051
Line up the decimal points:
8.130
 5.051
Insert a 0 as a placeholder.
We need to regroup (“borrow”) in order to finish the subtraction.
0 12
8. 1 3 10
 5. 0 5 1
3. 0 7 9
Answer:
8.13 – 5.051 = 3.079
Practice 7:
Subtract 9.2 – 7.83
Watch It:
http://youtu.be/RZhUwozs8qI
Example 8:
Subtract 5 – 2.536
Answer: 1.37
Write the whole number 5 as 5.000. Line up the decimal points and subtract:
4
9
9
5 . 10 10 10
 2. 5 3 6
2. 4 6 4
Answer:
5 – 2.536 = 2.464
Practice 8:
Subtract 6 – 3.01
Watch It:
http://youtu.be/NOLdKt47JRg
Answer: 2.99
288
CCBC Math 081
Third Edition
Example 9:
Addition and Subtraction of Decimals
Section 4.3
13 pages
(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
Petroleum
Natural Gas
Coal
Nuclear
Renewable Energy (hydroelectric, geothermal, etc.)
a.
1999
37.71
22.10
21.70
7.73
3.75
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
289
CCBC Math 081
Third Edition
Practice 9:
Weight
Not
Over
(pounds)
1
2
3
4
5
6
Addition and Subtraction of Decimals
Section 4.3
13 pages
The table below shows the postal rates for priority mail in 2009.
Postal Rate for Priority Mail 2009
Zones
Local,
1&2
$
4.95
$
4.95
$
5.50
$
6.10
$
6.85
$
7.55
3
$
$
$
$
$
$
4
4.95
5.20
6.25
7.10
8.15
9.25
$
$
$
$
$
$
4.75
5.75
7.10
8.15
9.45
10.75
5
$
$
$
$
$
$
4.95
7.10
9.05
10.80
12.70
14.65
6
$
$
$
$
$
$
4.95
7.60
9.90
11.95
13.75
15.50
7
$
$
$
$
$
$
4.95
8.10
10.60
12.95
15.20
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)
Watch It:
Answer: –200.04
http://youtu.be/Botzjk-Upqs
290
CCBC Math 081
Third Edition
Addition and Subtraction of Decimals
Section 4.3
13 pages
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:
3.10
Insert a 0 as a placeholder
 1.23
4.33
Answer:
3.1 – (-1.23) = 4.33
Practice 11: Subtract –5.7 – 1.62
Watch It:
Answer: –7.32
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
Watch It:
Answer: 3.55
http://youtu.be/aqdaHiPgt98
Watch All: http://youtu.be/Cdr-oH6j35g
291
CCBC Math 081
Third Edition
Addition and Subtraction of Decimals
Section 4.3
13 pages
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:
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.
0.07 + 1.3
5.7 mm
4.2 mm
3.4 mm
6.7 mm
9.
Calculate the perimeter of the given trapezoid.
5.3 in
3.5 in
2.8 in
8.7 in
10.
Calculate the perimeter of the given triangle.
2.8 cm
5 cm
1.3 cm
6.9 cm
292
CCBC Math 081
Third Edition
11.
Addition and Subtraction of Decimals
Section 4.3
13 pages
Calculate the perimeter of the given triangle.
12.8 km
15.13 km
12 km
13.85 km
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?
Weight
Not
Over
(pounds)
1
2
3
4
5
6
Postal Rate for Priority Mail 2009
Zones
Local,
1&2
$
4.95
$
4.95
$
5.50
$
6.10
$
6.85
$
7.55
3
$
$
$
$
$
$
4
4.95
5.20
6.25
7.10
8.15
9.25
$
$
$
$
$
$
4.75
5.75
7.10
8.15
9.45
10.75
293
5
$
$
$
$
$
$
4.95
7.10
9.05
10.80
12.70
14.65
6
$
$
$
$
$
$
4.95
7.60
9.90
11.95
13.75
15.50
7
$
$
$
$
$
$
4.95
8.10
10.60
12.95
15.20
17.50
CCBC Math 081
Third Edition
Addition and Subtraction of Decimals
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)
294
Section 4.3
13 pages
CCBC Math 081
Third Edition
Addition and Subtraction of Decimals
4.3 Addition and Subtraction of Decimals Exercises Answers
1.
4.50
13.
 12.97
15.620
 3.475
2.
350.00
 13.75
14.
 11.99
3.
12.232
15.
3.517
4.
1.37
16.
12.43
5.
21.167
17.
8.846
6.
0.179
18.
15.33
7.
76.37
19.
$17.50 - $9.25 = $8.25
8.
20 mm
20.
2.67
9.
20.3 in
21.
8.7934
10.
14.7 cm
22.
- 158.4
11.
41.78 km
23.
- 0.04
9.19
24.
- 1.74
25.
- 5.8
12.
 3.20
295
20.00
Section 4.3
13 pages
CCBC Math 081
Third Edition
Section 4.1 - 4.3
CHAPTER 4
Mid-Chapter Review
In the number 5768.293, what digit is in the:
1. hundredths place
2. tens place
Subtract.
24. 12.417  8.82
25. 53  7.69
In the number 1357.902:
3. name the place value of the 9
4. name the place value of the 1
Perform the indicated operation.
26.  1.73   0.9 
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.
345
16.
100
1
17.
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
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.
8.23 m
6.70 m
7.38 m
12.31 m
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)
Coffee (1 lb)
Eggs (1 dz)
Milk (1 gal)
$0.52
$2.82
$0.87
$0.78
$0.70
$2.94
$1.01
$1.32
$0.99
$3.21
$0.91
$2.79
$1.39
$4.15
$1.37
$3.32
CCBC Math 081
Third Edition
Mid-Chapter Review 4
Section 4.1 - 4.3
Mid-Chapter 4 Review Answers
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
1
25
25
16.
3.45
17.
0.2
18.
16.900
 7.348
 53.10
20.
21.826
21.
1.005
22.
297
0.25
19.
834.600
 29.742
1.59
23.
 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