2.3
Standards
Connect
Adding and Subtracting
Mixed Numbers
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8BSN6Q&YFSDJTFT
NS 2.1 Solve problems involving addition, subtraction, multiplication,
and division of positive fractions and explain why a particular operation
was used for a given situation.
Transparency Available
Find the sum or difference.
Before you added and subtracted fractions. Now you will add and subtract
mixed numbers to solve problems.
Math and
3
Example 1, p. 81
KEY VOCABULARY
• least common
denominator,
8
/PUFUBLJOH(VJEF
3
p. 35
1
Derek Lowe pitched 11 }
innings. What is the total number of innings
3
they pitched?
Transparency Available
Promotes interactive learning and
notetaking skills, pp. 33–34.
To find the total number of innings, you need to add two mixed numbers.
To add mixed numbers, first add the fraction parts as in Lesson 2.2. Then
add the whole number parts. These steps are summarized below.
1BDJOH
Suggested Number of Days
For Your Notebook
KEY CONCEPT
Adding and Subtracting Mixed Numbers
2. Rename the fractions, if necessary. Then add or subtract the fractions.
•
3. Add or subtract the whole numbers.
4. Simplify if possible.
1
3
1
3
Adding with a Common Denominator
3
Rewrite the mixed
numbers as improper
fractions and then add.
1
7}
Add the whole
numbers.
34
3
22
3
56
5}
3
7 } 1 11 } 5 } 1 }
3
1
1 11 }
3
3
Add the
fractions.
2 Days
See Teaching Guide/Lesson Plan
in Chapter 2 Resource Book,
pp. 23–24.
Ask students to explain the
meaning of the term innings
and why innings are divided into
thirds. Then ask students for other
examples of when they would need
to add or subtract mixed numbers.
CHECK Estimate the sum by rounding each mixed number to the nearest
whole number.
1
1
7}
1 11 }
ø 7 1 11 5 18. The answer is reasonable.
3
2.3 Adding and Subtracting Mixed Numbers
/4 Students will solve addition and subtraction problems involving mixed
numbers. Tell students:
• A mixed number is the sum of a whole number and a fraction.
• Find the LCD of the fractions, if necessary.
• To add mixed numbers, find two sums: the sum of the whole numbers and the
sum of the fractions. Then combine the sums and simplify.
• To subtract mixed numbers, find two differences: the difference of the
fractions (renaming if necessary) and the difference of the whole numbers.
Then combine the differences and simplify.
2 Days
.PUJWBUJOHUIF-FTTPO
2
c Answer Tim Wakefield and Derek Lowe pitched a total of 18 }
innings.
3
)PXUP5FBDIUIF$BMJGPSOJB4UBOEBSET
2 Days
Big Idea 1, p. 66
When do you rename a mixed
number? Tell students they will
learn how to answer this question
by subtracting mixed numbers.
3
3
Advanced
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3
2
18 }
2
5 18 }
Average
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1
1
To solve the real-world problem above, find the sum of 7 }
and 11 }
.
ANOTHER WAY
Basic
Block: 0.5 Block with Lesson 2.2
0.5 Block with Lesson 2.4
1. Find the LCD of the fractions, if necessary.
EXAMPLE 1
5 15
8
1
preceding the 2004 World Series, Tim Wakefield pitched 7 }
innings and
improper fraction,
15
9
fraction of his pizza was left? }5
first time in 86 years. In the American League Championship Series
p. 29
9
3. Gabe ate }3 of his pizza. What
WORLD SERIES In 2004, the Boston Red Sox won the World Series for the
• mixed number,
2
11
2. }
2 }3 }
1. }2 1 }4 1}1
SPORTS
81
Activity Generator
CD-ROM
For editable activities that
model mixed number addition
and subtraction using area
models and rulers, see the
Activity Generator CD-ROM.
.BUIFNBUJDBM#BDLHSPVOE
A mixed number is the sum of a
whole number and a fraction.
Therefore, 7}1 1 11}1
3
5 7 1 }1 1 11 1 }1
3
3
3
5 (7 1 11) 1 (}1 1 }1)
3
5 18 1 }2 or 18}2.
3
3
3
Subtracting with a Common Denominator
EXAMPLE 2
7
6
1
6}
2 4}
5 2}
5&"$)
9
9
Subtract fractions and then subtract whole numbers.
9
2
5 2}
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Simplify.
3
3
2
1
Add 32}
1 13}
. 45}
11
11
11
8
1
7
Subtract 7}
2 1}
. 6}
15
15
15
5
3
10
9
4}
1 3}
5 4}
1 3}
3
7
Add 6}3 1 4}
. 11}
5
10
10
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&YBNQMF
How are the sums in Example 1
and Example 3 different? The
sum in Example 3 must be
renamed.
4
6
ESTIMATE ANSWERS
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•
Adding with Different Denominators
EXAMPLE 3
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12
19
5 7}
You can estimate the
answer by rounding
each mixed number
to the nearest whole
number. Because
5 1 4 5 9, the answer
is reasonable.
Add fractions and then add whole numbers.
12
7
5 7 1 1}
Write improper fraction as a mixed number.
7
5 8}
Add whole numbers.
12
12
1
17
a. Subtract 12}
2 3}3. 8}
8
1
1
6}
55111}
24
6
6
b. Subtract 10 2 3}1. 6}3
4 4
6 1
1}
551}
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7
7
, or 5 }
551}
6
6
•
3
4
RENAMING When subtracting mixed numbers, sometimes the fractional
part of the second mixed number is greater. If so, you have to rename the
first mixed number to subtract the fractional parts. For example:
&YUSB&YBNQMF
12
5
6
Rewrite fractions using LCD of } and }, 12.
12
6
6
In part (b), why is 7 renamed as
6}8? You must create a fraction
1
1
1
2
a. 6 }
2 3}
5 6}
2 3}
subtract }5 from, and 7 5 6 1 1
8
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8
Math
classzone.com
15
.
2. The sum of two fractions is 5}
8
How would you rename this
8
1
6
7
5 5}
2 3 }2
Rename 6 } as 5 }.
5 2 }5
Subtract fractions and then subtract whole numbers.
1
6
6
6
8
8
5
8
5
8
7
6
8
8
b. 7 2 5 } 5 6 } 2 5 }
Rename 7 as 6 }.
Subtract fractions and then subtract whole numbers.
8
1
3
Rewrite fractions using LCD of } and }.
6
5 1 }3
GUIDED PRACTICE
for Examples 1, 2, 3, and 4
Find the sum or difference. Simplify if possible.
$MPTJOHUIF-FTTPO
Students have learned to add and
subtract mixed numbers. To bring
closure, have students answer
these questions:
1. Essential Question: When do you
rename a mixed number?
When you are subtracting mixed
numbers where you need to
subtract a larger fraction from a
smaller one.
6
6
For an interactive
example of adding
and subtracting
mixed numbers go to
classzone.com.
An Animated Math activity in
which students use blocks to add
or subtract mixed numbers is
available online for Example 4. This
activity is also available on the
Power Presentations CD-ROM.
fraction? 6}7
3
6
5 6 1 }8 5 6}8.
8
Renaming to Subtract Mixed Numbers
EXAMPLE 4
8
with a denominator of 8 to
1
1. 3 }
1 2 } 5 }3
8
82
5
8
2. 1 } 1 4 } 6 }1
3
4
4
3
8
8
1 4
3. 8 } 2 4 }
4}
5
7
7
7
1
9
4. 8 2 5 }
2}
10
Chapter 2 Fraction and Decimal Operations
"QQMZJOH4UBOEBSET
Example 4 In this example, students apply
Standard /4 by subtracting mixed
numbers.
• Recognize when to rename a mixed number
when subtracting mixed numbers.
• Find the LCD if necessary to rename the
mixed number.
• Perform the subtraction.
6OJWFSTBM"DDFTT
*ODMVTJPO Students who have difficulty with adding and subtracting mixed numbers may be more successful if they align the
problems vertically. For example:
6}1 5
5}7
6
6
1
2 3} 5 2 3}2
3
6
2}5
6
10
EXERCISES
2.3
HOMEWORK
KEY
5
MULTIPLE CHOICE PRACTICE
Exs. 25, 26, 45, 53–55
13"$5*$&
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5 HINTS AND HOMEWORK HELP
for Exs. 13, 19, 45 at classzone.com
SKILLS • PROBLEM SOLVING • REASONING
A
8
SEE EXAMPLES
1 AND 2
on pp. 81–82
for Exs. 3–12
11. The first
mixed number
needs to be
renamed;
2 }7 2 1 }5 5 1 }1.
6
6
"TTJHONFOU(VJEF
1. VOCABULARY When subtracting, when is it necessary to rename a
mixed number? When the fractional part of the second mixed number is
greater than the fractional part of the first mixed number.
3
2. WRITING Describe how to rename the mixed number 7 } so that the
8
8 3
11
whole part is 6. Change the fraction to 6 1 } 1 } 5 6 }.
8
8
USING COMMON DENOMINATORS Find the sum or difference. Simplify if
possible. Then estimate to check the answer.
1
17 }4
3. 12 } 1 5 }
2
4
4. 22 }
1 17 }
39 }6
5. 8 } 1 4 } 13
2
1 1
7. 3 }
2 2}
1}
3
3 3
3
1 2
8. 7 } 2 3 }
4}
5
5 5
4
2 2
9. 8 }
2 5}
3}
9
9 9
3
5
5
5
7
7
12
7
7
6. 8 } 1 2 } 11 }1
5
12
3
4
3
4
2
5
1 2
10. 13 } 2 9 }
4}
6
6 3
ERROR ANALYSIS Describe and correct the error made in finding the
difference.
11.
12.
5
2
4
3 }1 2 1 }
5 2}
5 2}
6
3
6
6
6
6
3
10
4
4}
2 2}
5 4}
2 2}
5 2}
7
3
7
7
7
7
SEE EXAMPLES
3 AND 4
FINDING SUMS AND DIFFERENCES Find the sum or difference. Simplify if
possible. Then estimate to check the answer.
on p. 82
for Exs. 13–25
1
13. 4 }
1 3} 7}
2
1
11 }
14. 3 }
1 8}
2
11 }
15. 4 } 1 6 }
1
1
16. 5 }
1 2} 8}
17
2
1
17 }
17. 6 }
1 11 }
5
6
30
31
7
1
13 }
18. 8 }
1 5}
6
20
60
5 1
1
6}
19. 8 }
2 1}
8
8 2
3
7
1
3}
20. 12 } 2 9 }
4
6 12
1 3
21. 5 } 2 2 }
3}
4
2 7
22. 8 }
2 5}
2}
7
23. 7 2 3 } 3 }
4 5
24. 9 2 7 }
1}
12. The whole
number part
of the first
mixed number
needs to be
decreased by 1;
10
3}
2 2 }6 5 1 }4 .
7
7
7
4
5
8
3
8
4
5
8
8
9
5
6
6
3
3
4
3
10
9
5
12
3
10
5
6
4
9
12
9
5
6
1
25. MULTIPLE CHOICE What is the value of 8 }
2 3 }? B
4
A 4
B
3
5
B 4}
2
C 5}
12
3
D 6
2
26. MULTIPLE CHOICE Which expression has the sum 3 }
? B
7
1
A 1}
1 2}
8
16
3
17
7
C 1} 1 1 }
18
9
5
1
B 2}
1 1}
4
12
)PNFXPSL$IFDL
13
9
D 1}
1 1}
15
10
2
1
xy ALGEBRA Evaluate the expression when x 5 7 }
and y 5 5 }
.
5
38
34. 13 }
63
3
4 91
}
27. x 1 1 }
5 5
23
1
28. 11 }
2 x 3}
30
6
2 12
}
29. y 2 3 }
3 3
7
8
31. 9 } 1 x 17 }
9
45
3 19
32. y 2 3 } 1 }
7 21
7
3
9
1
1
33. x 2 3 }
2 2}
34. 7 }
1 y 1 1}
1}
4
10 20
18
14
11
7
30. y 1 2 } 7 }
12
2.3 Adding and Subtracting Mixed Numbers
6OJWFSTBM"DDFTT
#FMPX-FWFM Ideally, students will compute the LCD before
adding or subtracting fractions in Exercises 13–24. However, if
computing the LCD is difficult, students can use the product of
the denominators as the common denominator. After combining the original fractions, students can write the fraction in its
simplest form.
Answer Transparencies
available for all exercises
Basic:
Day 1: pp. 83–85
Exs. 1–11, 13–18, 53–55
Day 2: EP p. 693 Exs. 12–19
pp. 83–85
Exs. 19–22, 25–29, 41–45
Average:
Day 1: MRSPS p. 53 Exs. 1, 2
pp. 83–85
Exs. 1, 2, 5–10, 12, 14–18, 35–37
Day 2: MRSPS p. 53 Exs. 3–5
pp. 83–85
Exs. 20–23, 25, 26, 28–32, 38–40,
44–49
Advanced:
Day 1: MCP p. 65 Exs. 8, 9
pp. 83–85
Exs. 1, 5–10, 14–18, 35–37
Day 2: MCP p. 65 Exs. 10–12
pp. 83–85
Exs. 22–26, 31–34, 38–40, 44–52 *
Block:
MRSPS p. 53 Exs. 1, 2
pp. 83–85
Exs. 1, 2, 5–10, 12, 14–18, 35–37
(with 2.2)
MRSPS p. 53 Exs. 3–5
pp. 83–85
Exs. 20–23, 25, 26, 28–32, 38–40,
44–49 (with 2.4)
12
83
For a quick check of student understanding of key concepts, go over
the following exercises:
Basic: 4, 14, 20, 42, 44
Average: 6, 16, 22, 46, 48
Advanced: 8, 18, 24, 47, 50
&YUSB1SBDUJDF
•
•
Student Edition, p. 693
Chapter 2 Resource Book:
Practice Levels A, B, C, pp. 26–28
1SBDUJDF8PSLTIFFU
An easily readable reduced
practice page (with answers)
for this lesson can be found
on pp. 66E–66F.
5FBDIJOH4USBUFHZ
Exercises 35–40 In these exercises, some students may feel
pressured to use mental math or
estimation rather than pencil and
paper. Encourage students to try
all three methods on two or three
exercises. This will help each student determine which method
works best for him or her. It will
also serve as a check on students’
work.
.BUIFNBUJDBM3FBTPOJOH
Exercise 47 Students should
sketch the picture frame and label
the outside dimensions in attempting to solve this problem. From the
sketch, they should be able to
reason that by subtracting }3 inch
4
twice from the outside dimensions,
a 5 inch by 7 inch picture will not
fit.
CHOOSE A METHOD Copy and complete the statement using <, >, or 5.
Tell whether you used mental math, estimation, or pencil and paper.
35–40. Sample answers are given.
1
1
1
1
1
1
1
1
1
46. Yes; }4 ft.
35. 3 }
1 4}
? 7}
36. 8 }
2 2}
? 6}
37. 10 }
1 16 }
? 27 }
5
4
4
4
2
8
2
10
2
2
Sample answer:
5; mental math
<; mental math
<; mental math
7
3
5
2
2
4
11
11
1
One car is 14 }4
38. 12 }
2 2}
? 10 }
39. 9 }
2 3}
? 5}
40. 7 } 1 4 } ? 12 }
5
7
4
3
9
3
14
14
12
6
feet long and the
<; estimation
5; pencil and paper
5; pencil and paper
other car is
1
CONNECT SKILLS TO PROBLEM SOLVING Exercises 41–43 will help you
feet
14 }4 1 1 }
5
10
prepare for problem solving.
long. Together
they are
Which operation would you use to solve the problem? Explain why.
7
30 }
feet long.
10
3
1
pounds of ground beef and 7 }
pounds of
Since both cars 41. For a barbeque, you buy 2 }
4
4
together are
chicken. What is the total weight of the meat? Addition; you want to find the total weight
shorter than
of the meat.
1
1
42. Anna was 19 }
inches long at birth. At her 3 month checkup, she was
31 } feet, they
2
will fit in the
driveway. There
7
is 31 }1 2 30 }
5
4
5
2
10
2
1
23 }
inches long. How much did she grow during that time? Subtraction; you want to
4
find the difference in length.
5
3
43. You have 5 } cups of cornmeal. You need 1 } cups for a recipe. After you
8
SEE EXAMPLES
3 AND 4
8
make the recipe, how much cornmeal do you have left? Subtraction; you want to find
the how much cornmeal is left.
} foot left over.
1
44. RUNNING At track practice, you walk }
mile,
4
1
1
run 5 }
miles, and then walk 1 }
miles. What is
your total distance? 7 mi
California
for problem solving help
at classzone.com
5FBDIJOH4USBUFHZ
Exercise 48 Ask students to share
their situations with a partner and
solve each other’s problems.
4
2
on p. 82
for Exs. 44–47
45. MULTIPLE CHOICE A boat begins a trip with
7
22 }
gallons of fuel in its tank. When the boat
8
reaches its destination, the tank contains
"DBEFNJD7PDBCVMBSZ
1
14 }
gallons of fuel. On the return trip, the boat
Exercise 50 Remind students that
a proper fraction is less than 1
because the numerator is less than
the denominator.
original destination. How many total gallons of fuel does the boat use? C
Four laps around the track is 1 mile.
4
5
uses 2 }
gallons more fuel than it used to get to its
12
5
A 3}
gal
24
1
B 11 }
gal
2
C 19 }
gal
24
1
D 48 }
gal
3
6
47. No; the width
California
for problem solving help at classzone.com
enclosed by the
frame is
4
1
46. SHORT RESPONSE A car is 14 }
feet long. Another car is 1 }
feet longer.
5
10
6 }1 2 }3 2 }3 5
1
2 4 4
Can the two cars fit end to end in a driveway that is 31 } feet long? If so,
2
5 inches, and the
how much space is left? If not, how much more space is needed? Explain
length enclosed
how you solved the problem.
by the frame is
8 }1 2 }3 2 }3 5
4 4 4
6 }3 inches which,
4
47. CRAFTS You construct a rectangular picture frame out of strips of wood
3
that are }
inch wide. The dimensions of the outside of the frame are
4
1
1
6}
inches wide by 8 }
inches long. Can you fit a picture that is 5 inches
is less than
7 inches.
84
2
5 MULTIPLE
CHOICEOperations
PRACTICE
Chapter 2 Fraction
and Decimal
"QQMZJOH4UBOEBSET
Exercise 45 Students identify relationships
and sequence and prioritize information, as
called for in Standard .3
• The amount of gas used on the return trip is
based on the amount used on the first part of
the trip.
• Recognize the relationship between the
amount of fuel in the tank at the beginning
and end of the trip.
4
wide and 7 inches long in your frame? Justify your answer.
5 HINTS AND HOMEWORK HELP at classzone.com
48. Sample answer: A baker needs 2}1 cups of sugar to bake
4
a cake and 1}1 cups of sugar to make cookies. How much
2
sugar does he need in total? 2}1 1 1}1 5 3}3 cups of
4
2
4
sugar; A carpenter has a 5}7 feet of wood, he uses 3}1 feet
8
4
to build a bench. How much wood does he have left?
5}7 2 3}1 5 2}5 ft.
8
4
8
49. Sample
answer: Think
of 7 as 6 }5 .
48. OPEN-ENDED Give an example of a real-world situation where you need
to add two mixed numbers. Give an example of a real-world situation
where you need to subtract two mixed numbers. Write and evaluate an
expression to solve each problem. See margin.
5
Subtract 3 }2 to
5
get 3 }3.
"/%
"44&44
3&5&"$)
2
49. WRITING Explain how you can use mental math to find 7 2 3 }
.
5
5
C
50. REASONING Can you subtract two mixed numbers and get an answer less
than 1? Can you subtract a proper fraction from a mixed number and get
an answer less than 1? Explain your reasoning and provide two examples. See margin.
51. 9 }5 1 8 }3 1
4
6
1
7 }1 5 26 }
2
12
51. CHALLENGE Using each digit from 1 to 9 exactly once and only
proper fractional parts, write an expression with the greatest
1
y
z
b
n
value that has the form a }
1 m}
1 x }. What is its value?
c
p
y
3
52. xy CHALLENGE The perimeter of the figure shown is 9 }.
15
5
z
x
5
4
, y 5 2 }1 , z 5 1 }3
Find the values of x, y, and z. x 5 }
1
13
5
1
35
CALIFORNIA STANDARDS SPIRAL REVIEW
%BJMZ)PNFXPSL2VJ[
Find the sum or difference.
1. 15}2 1 4}5 19}7
9
9
9
13
7
2. 24} 2 13} 11}1
18
18
3
6
19
4
3. 29} 1 12} 42}
5
11
55
5
13
4. 68} 2 40} 2729
}
12
16
48
5. Kara buys 30}3 yards of blue
4
ribbon and 41}1 yards of gold
2
ribbon to decorate the gym for a
party. How many yards of ribbon
53. What is the value of 1216 4 8? (p. 664) C
Gr. 4 NS 3.2
A 0.00152
B 0.152
C 152
did she buy in all? 72}1 yd
4
D 1527
54. What is 814,746 rounded to the nearest hundred? (p. 665) C
Gr. 4 NS 1.3
A 800,000
B 814,000
C 814,700
17
28
Online Quiz
classzone.com
D 814,750
An alternate quiz for Lessons 2.1–2.3
is available online in multiple choice
format.
29
42
55. The height of a plant is } inch. After one week, it is } inch tall. How
NS 2.1
much did the plant grow in one week? (p. 75) A
3
B }
in.
1
A }
in.
3
C 1}
in.
7
12
25
D 1}
in.
14
%JBHOPTJT3FNFEJBUJPO
84
Practice A, B, C in Chapter 2
Resource Book, pp. 26–28
• Study Guide in Chapter 2
Resource Book, pp. 29–30
• Practice Workbook, pp. 21–22
• California@HomeTutor
•
QUIZ for Lessons 2.1—2.3
Find the sum or difference. Simplify if possible. (pp. 69, 75, 81)
7 5 1
1. } 1 } 1 }
1
2. } 1 }
}
3. } 2 } }
11
2 3
4. }
2}
}
5
4 13
5. } 1 }
}
18 9 18
2 3 5
6. }
1 } 1}
3 4 12
1
2 7
7. }
2}
}
2 11 22
3 7
8. 1 2 } }
10 10
8
17. 1 }7 mi; you
8
want to find the
distance that
remains so you
need to subtract
what you have
already walked
from the total.
8
7
7
5
9. 11 } 1 24 } 36 }
8
12
24
7
5 1
13. 3 } 2 2 } 1 }
8
8
4
10 5
7
10
2
4
45"/%"3%4
41*3"-
3&7*&8
11
3
9
11. 21 } 1 5 } 27 }
4
14
28
3
1 7 11
}
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16
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9
17. FUNDRAISING A charity fundraising walk is 5 miles long. You stop for
1
a break after walking 3 }
miles. How many more miles do you need to
8
walk after the break? Explain your choice of operation. (p. 81)
2.3 AddingONLINE
and Subtracting
Numbers
QUIZMixed
at classzone.com
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Additional challenge is available in
the Chapter 2 Resource Book,
p. 34.
2VJ[
An easily readable reduced
copy of the quiz on Lessons
2.1–2.3 (with answers) from
the Assessment Book can be
found on pp. 66G–66H.
50. Yes; yes. Sample answer: If the
mixed numbers have the same
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6 7 8 9 15
37
3
7
10. 6 } 1 9 } 15 }
16
12
48
EXTRA PRACTICE for Lesson 2.3, p. 693
&953"
3 5
13 13
8
13
whole number part, 1}7 2 1}5 5 }1;
8
4
8
if the whole number part of the
mixed number is one and the
proper fraction is greater than
the fraction part of the mixed
number; 1}2 2 }5 5 }4.
7
7
7
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off Skills and
MIXED REVIEW Problem
Solving
California
Multiple Choice Practice for Lessons 2.1—2.3
classzone.com
1. The table gives the lengths of 5 red pandas.
What is the difference in the length of the
longest panda and the shortest panda? NS 2.1
D
Students who need more review
and practice should see the
following lessons in the
California@HomeTutor.
Exercise 1: Lesson 2.3
Exercise 2: Lesson 2.3
Exercise 3: Lesson 2.3
Exercise 4: Lesson 2.2
Exercise 5: Lesson 2.2
Exercise 6: Lesson 2.3
Exercise 7: Lesson 2.2
Panda
A
B
C
D
E
Length
(feet)
2
1}
3
1
2}
8
3
1}
4
1
2}
2
1
2}
3
11
A }
ft
2
B }
ft
3
ft
C }
4
5
D }
ft
24
6
7
25
61
B }
75
C 1
1
D 2}
12
3
B 1}
4
31
C 1}
1
D 2}
3
5. The storage area of an apartment complex
is shared among three apartment units.
The storage space is shown below. Which
expression can you use to find the fraction
of storage space allocated to Unit 3? NS 2.1,
MR 1.1 C
3
16
A }
25
6
19
A }
27
36
2. What is the value of 1 } 2 w when
7
w5}
? NS 2.1 B
15
7
9
1 11
4. What is the value of } 1 }
1 }? NS 2.1 C
Unit 1
Unit 2
3
{{
10
{25
3. A “bookworm” eats its way through the three
books of the same size shown below. It starts
at the last page of Book I and continues until
it comes to the first page of Book III. It always
travels perpendicular to the pages and
1
covers. Each cover is }
inch thick, and the
8
1
pages of each book are 2 }
inches thick. How
4
far does the “bookworm” eat? NS 2.1 C
?
3
2
A }
1}
3
2
B }
2}
3
2
2}
C 12}
10 5
3
2
D 11}
1}
5
2
Unit 3
5
10
10
5
10
7
8
6. What is the value of x 1 4 } when
9
x 5 4}
? NS 2.1 B
20
1
A 1}
13
B 9}
4
C 10 }
13
D 11 }
14
40
7
40
3
4
1
7. You have } pound of roast beef and }
pound
2
of turkey. You want to make 4 sandwiches,
1
each with }
pound of meat. How can you
3
determine if you have enough meat? NS 2.1,
MR 1.3 A
3 1
1 1 1 1
A Compare }
1 } with }
1 } 1 } 1 }.
4
3
A 6}
in.
B 7 in.
1
in.
C 7}
1
D 7}
in.
4
4
86
2
3
3
3
3
3 1
1 1 1 1
2 } with }
1 } 1 } 1 }.
B Compare }
4 2
3 3 3 3
3 1
1
1 } with }
.
C Compare }
4
2
3
3 1
1
D Compare }
2 } with }
.
4 2
3
2
Chapter 2 Fraction and Decimal Operations
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Exercise 5 In this exercise, students apply Standard .3
to analyze problems by identifying relationships and identifying
missing information.
• The total storage area is the sum of the three units.
• Each unit has storage space represented by a fraction. Therefore
the total storage area of the three units is 1.
• Find the fraction of storage space of Unit 3 using 1 2 area of
Unit 1 2 area of Unit 2.
Exercise 7 In this exercise, students apply Standard .3 to
determine when and how to break a problem into simpler parts.
•
Find total amount of meat.
•
Find amount of meat needed to make 4 sandwiches using }1
pound of meat for each sandwich.
• Compare the two amounts.
3