Page 1 of 5
Adding and Subtracting Decimals
BEFORE
Now
WHY?
You added and subtracted
whole numbers.
You’ll add and subtract
decimals.
So you can compare the areas
of cornfield mazes, as in Ex. 24.
You can use base-ten pieces to model decimal addition
and subtraction.
Word Watch
0.76
front-end estimation, p. 59
0.58
1 Model the sum of 0.76
and 0.58 using base-ten
pieces.
2 Combine and group the pieces.
3 Trade 10 tenths for 1 one and
10 hundredths for 1 tenth.
The sum of 0.76 and 0.58 is
1.34.
1.34
Use base-ten pieces to find the sum or difference.
1. 2.2 1.85
2. 2.77 1.47
3. 1.26 1.08
Use a vertical format to add or subtract decimals. Begin by lining up the
decimal points. Then add or subtract as you would with whole numbers.
Be sure to write the decimal point in the answer.
EXAMPLE
1
Adding and Subtracting Decimals
a. 6.047 13.46
6.047
13.460
19.507
58
Chapter 2
Decimal Operations
b. 9 5.28
Write zero as
a placeholder.
9.00
5.28
3.72
Write zeros as
placeholders.
Page 2 of 5
Your turn now
tch Out!
Wa
Don’t forget to
add and subtract from left
to right when evaluating
expressions horizontally.
Find the sum or difference.
1. 13.8 9.3
2. 8.41 2.6
3. 1.937 2.28
4. 1.6 0.8
5. 6 3.74
6. 4.59 3.17
EXAMPLE
2
Evaluating a Variable Expression
Evaluate 6.7 r t when r 2.14 and t 5.2.
6.7 r t 6.7 2.14 5.2
Your turn now
Substitute 2.14 for r and 5.2 for t.
8.84 5.2
Add.
3.64
Subtract.
Evaluate the expression when a 4.2 and b 6.27.
7. a b
8. b a
9. 10.03 a b
Estimation When you do not need to find an exact sum, you can
estimate. One type of estimation is front-end estimation. To use
front-end estimation to estimate a sum, add the front-end digits,
estimate the sum of the remaining digits, and then add the results.
EXAMPLE
3
Estimating a Sum
Video Games For your birthday you
receive a $25 gift certificate. You want to
buy 3 used video games whose prices are
shown. Can you buy all 3 games using
the gift certificate?
Solution
1 Add the front-end
digits: the dollars.
$8.79
$7.29
$7.89
$22
2 Estimate the sum
of the remaining
digits: the cents.
$8.79
$7.29
$7.89
$1
$1
$2
3 Add the results.
$22
$2
$24
ANSWER The estimated sum is less than $25, so you can buy all three
games using the gift certificate.
Lesson 2.2
Adding and Subtracting Decimals
59
Page 3 of 5
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 706
Getting Ready to Practice
1. Vocabulary Explain how to use front-end estimation to add decimals.
Find the sum or difference.
2. 6.04 12.51
3. 5.8 2.4
4. 16.5 3.675
5. 47.85 5.741
6. Guided Problem Solving Is $20 enough
money to buy the art supplies listed?
1 Add the front-end digits: 8 3 6.
Watercolor paints $8.69
Paint brushes $3.78
Canvas $6.32
2 Estimate the sum of the remaining
digits: 0.69 0.78 0.32.
3 Add the results. Is the sum greater than
or less than $20?
with
Example
1
2
3
Homework
Exercises
13–21, 37–42
25–28, 43–45
29–34
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Practice and Problem Solving
Write the decimal in expanded form. For example, 3.24 in expanded
form is 3 0.2 0.04.
7. 6.912
8. 523.974
9. 43.07
Decide Would you add or subtract to find the answer? Explain.
10. How much does it cost to buy a pair of jeans and a shirt?
11. How much warmer is today’s high temperature than yesterday’s high?
12. How much more does a cheeseburger cost than a hamburger?
Find the sum or difference. Use estimation to check your answer.
13. 15.8 7.6
14. 124.6 47.01
15. 53.24 14.023
16. 0.79 14.55
17. 90.2 7.5
18. 24.98 3.3
19. 4.29 3.456
20. 168.42 5.608
21. 900 15.7
22. Stilts Jared is 2.75 meters tall while on stilts and 1.6 meters tall without
stilts. How far off the ground do the stilts raise Jared?
23. Find the Error Describe and
correct the error in finding the
sum of 3.8504 and 625.
60
Chapter 2
Decimal Operations
3.8504
625
3.9129
Page 4 of 5
24. Cornfield Mazes The first cornfield maze, grown in Annville,
j7pe-0202-000-h
Pennsylvania, in 1993, covered 3.3 acres. The largest cornfield maze,
grown in Lindon, Utah, in 1999, covered 12.6 acres. How many acres
larger was the Lindon maze than the Annville maze?
Algebra Evaluate the expression when y 26.3 and z 12.28.
25. 20.1 y
26. 34 z
27. y z
28. 30 y z
Estimate the sum or difference using front-end estimation.
29. 5.24 9.79
30. 3.44 8.38
31. 4.11 5.90 8.02
32. 5.78 9 2.2
33. 8.75 5.67
34. 6.6 4.45
35. Rainfall A city had 3.57 inches of rain in April, 7.30 inches of rain in
Cornfield maze in
Lindon, Utah
May, and 5.14 inches of rain in June. During this three-month period,
did the city have more than 15 inches of rain? Explain why an estimate
is sufficient in answering the question.
36. Critical Thinking When is the sum of two decimals a whole number?
When is the difference of two decimals a whole number? Explain.
Evaluate the expression.
37. 467.2 5.63 11
38. 27 3.204 10.8
39. 8.55 20.4 15
40. 0.032 0.29 1
41. 26.17 9.002 1.9 42. 3.876 2.2 4.10
Algebra Evaluate the expression when k 5.874 and m 123.1.
43. m k 6.401
44. 140 (k m)
45. m 6.78 k 28.3
46. Directions Internet driving directions from Washington D.C.’s National
Zoo to the White House Visitor Center are shown below. How much
shorter is the shortest route than the fastest route?
Fastest Route
Directions
Go SE on Connecticut
Ave. NW
Connecticut Ave. NW
becomes 17th St. NW
Turn left onto H St. NW
Turn right onto 14th St. NW
Turn right onto
Pennsylvania Ave. NW
Shortest Route
Distance
2.1 miles
0.2 mile
0.4 mile
0.3 mile
0.0 mile
Directions
Go SE on Connecticut
Ave. NW
Connecticut Ave. NW
becomes 17th St. NW
Turn left onto E St. NW
E St. NW becomes
Pennsylvania Ave. NW
Distance
2.1 miles
0.5 mile
0.3 mile
0.0 mile
Challenge Solve the equation using mental math.
47. w 1.5 5
48. 6 x 8.8
Lesson 2.2
49. y 2.4 0.6 50. 0.82 – z 0.7
Adding and Subtracting Decimals
61
Page 5 of 5
Mixed Review
Order the numbers from least to greatest. (Lesson 2.1)
51. 2.46, 4.26, 4.06, 2.64, 2.42
52. 13.8, 8.3, 13.08, 8.31, 8.83
Choose a Strategy Use a strategy from
the list to solve the following problem.
Explain your choice of strategy.
Problem Solving Strategies
Look for a Pattern
Draw a Diagram
■ Work Backward
■
■
53. On Monday, Jeff sold 3 raffle tickets. On
Tuesday, he sold 6 tickets. On Wednesday,
he sold 9 tickets. If the pattern continued
through Friday, how many tickets did Jeff
sell during the week?
Basic Skills Find the product.
54. 15 23
55. 21 5
56. 7 19
57. 11 29
Test-Taking Practice
58. Multiple Choice Which of the following numbers, when added to 8.43
INTERNET
using front-end estimation, results in an estimated sum of 15?
State Test Practice
CLASSZONE.COM
A. 6.59
B. 7.59
C. 8.04
D. 8.45
59. Multiple Choice What is the value of the expression
15.2 9.8 7.12 2.07?
F. 0.1581
G. 1.581
H. 15.81
I. 158.1
Decode the Riddle
Find the values of M, T, C, F, and Y that make the
sum and difference correct. Then replace the number
in each box with its letter to find the answer to the
riddle below.
3 .1 T5
M. TC2
11 .6 1 C
62
Chapter 2
0.3 F1 F
0.2 C0 F
0.0 91 Y
Decimal Operations
Why did the cookie go to the hospital?
I
4
6
E
L
4
7
R U
8
8
0