2.7
Standards
Preparation
Connect
Multiplying and
Dividing Decimals
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Gr. 5 NS 2.1 Add, subtract, multiply, and divide with decimals;
add with negative integers; subtract positive integers from
negative integers, and verify the reasonableness of the results.
Before you multipled and divided fractions. Now you will
multiply and divide decimals to prepare for Grade 6 Standard NS 1.4.
Math and
FUNDRAISING
Ex. 73, p. 111
KEY VOCABULARY
• leading digit
• compatible
numbers
You can represent 1 whole with a
10 3 10 grid. The width of each row
or column is 0.1. Each small square
represents 0.01.
1.3
0.7
1
The area selected at the right
represents seven tenths of 1.3, or
0.7 3 1.3. There are 91 squares
selected, so 0.7 3 1.3 5 0.91.
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1
Transparency Available
Promotes interactive learning and
notetaking skills, pp. 44–47.
1
For Your Notebook
KEY CONCEPT
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Suggested Number of Days
Multiplying Decimals
Words
Numbers
EXAMPLE 1
.BUI
For an interactive
example of multiplying
decimals go to
classzone.com.
5.82
3
0.41
__
582
2328
__
2.3862
Transparency Available
Find the product or quotient.
1. 93 3 67 6231
2. 5000 3 300 1,500,000
3. 1664 4 52 32
4. 254,300 4 100 2543
5. How much does Sam earn for
mowing 5 lawns if he earns $18
for each lawn? $90
Multiply decimals as you would whole numbers. Then
place the decimal point in the product. The number of
decimal places in the product is equal to the sum of the
number of decimal places in the factors.
Basic
Average
Advanced
2 Days
2 Days
2 Days
Block: 1 Block
• See Teaching Guide/Lesson Plan
in Chapter 2 Resource Book,
pp. 67–68.
0.7 3 1.3 5 0.91
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.05*7"5&
Multiplying Decimals
2 decimal places
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1 2 decimal places
Big Idea 3, p. 66
How can you tell how many decimal places are in the product 0.35
3 0.9? Tell students they will
learn how to answer this question
by finding the sum of the number of
decimal places in the factors.
4 decimal places
CHECK REASONABLENESS To check that the product in Example 1 is
reasonable, round each factor to the place value of the leading digit, and
then multiply. The leading digit of a number is the first nonzero digit.
5.82
6
Round to the nearest whole number.
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0.41
0.4
Round to the nearest tenth.
Use decimal squares to model the
product in the lesson opener.
Because 6 3 0.4 5 2.4, the product in Example 1 is reasonable.
2.7 Multiplying and Dividing Decimals
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(S/4 Students should be familiar with the rules for multiplying and
dividing whole numbers in order to multiply and divide decimals.
• Multiply decimals as you would whole numbers.
• Count the total number of decimal points in the factors.
• Place this number of decimal places in the product.
• When dividing decimals, the divisor must be a whole number.
• If necessary, multiply the divisor by a power of ten to make it a whole number.
Multiply the dividend by the same power of ten.
• Line up the decimal point in the quotient with the one in the dividend and
divide as you would with whole numbers.
107
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The digits and the number of decimal
places in a decimal product are
determined by the products of the
numerators and denominators of
corresponding fractions.
For example,
3
3 3 21
21
3}
5}
0.3 3 0.21 5 }
10
63
5 } 5 0.063.
1000
100
10 3 100
EXAMPLE 2
5&"$)
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Find the product. Check that your
answer is reasonable.
8.19
3 0.65
5.3235
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•
a.
ANOTHER WAY
6.45
3
18
__
5160
64 5
__
116.10
You can also multiply
decimals by rewriting
them as fractions:
1273
6
1000
100
7638
} 5 0.07638
100,000
}3}5
An Animated Math activity
in which students choose the
appropriate operator tile to form
an expression equal to a decimal is
available online for Example 1. This
activity is also available on the
Power Presentations CD-ROM.
GUIDED PRACTICE
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Multiple Representations
In Example 3, students should realize that 15.95 and 15.950 are different representations of the same
number.
for Examples 1 and 2
2. 0.98 3 0.21 0.2058
3. 6.89 3 0.07 0.4823
5. 12 3 0.05 0.6
6. 2.351 3 1.6 3.7616
Dividing a Decimal by a Whole Number
TEAM PHOTOS Your baseball team is ordering photo trading cards of each
player on your team. A set of 25 cards costs $15.95. Find the price of each
card. Round to the nearest cent.
SOLUTION
To find the cost per card, you need to divide.
chetrcher
Cat Ca
STEP 1 Divide $15.95 by 25.
0.638
}}}
25q15.950
15 0
95
75
200
200
0
Why can you drop the ending zero
in Part (a)? 0.10 5 0.1
Why is a zero placed in the
dividend? You must divide to the
thousandths place to round to the
nearest cent.
c Answer 1.273 3 0.06 5 0.07638
4. 4.63 3 9 41.67
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•
Write a zero before the 7 as a
placeholder so that the number
has five decimal places.
1. 1.4 3 7.2 10.08
EXAMPLE 3
Find the product. Check that your
answer is reasonable.
2.519
b.
a. 2.26
3 85
3 0.03
192.1
0.07557
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2 decimal places
DIVIDING DECIMALS To divide decimals by whole numbers, you can use
long division. Line up the decimal points in the quotient and the dividend.
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The cost of 18 tickets to attend a
concert is $544.50. What is the
cost of each ticket? $30.25
3 decimal places
1.273
3
0.06
1
2 decimal places
__
0.07638
5 decimal places
Find the product. Then check that your answer is reasonable.
classzone.com
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b.
c Answer 6.45 3 18 5 116.1
Math
•
2 decimal places
1 0 decimal places
After you place the decimal
point, you can drop any zeros
at the end of an answer.
1.273 3 0.06 5
In checking the answer, why
should you not round both
factors to the nearest whole
number? 0.41 would round to 0,
giving an estimate of 0.
Multiplying Decimals
About the Standards
Note that Grade 6
Standard MR 2.6
expects you to round
as specified. With
money, round to the
nearest hundredth to
find the nearest cent.
108
Line up decimal point in
quotient with decimal point
in dividend.
Divide as you would with
whole numbers.
Kevin
Baker
STEP 2 Round to the nearest cent.
$.638
$.64
c Answer The price of each card is about $.64.
Chapter 2 Fraction and Decimal Operations
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Example 2 In this example, students apply
Standard (3/4 to multiply with decimals. They can also verify the reasonableness
of the results.
• Use estimation to check reasonableness.
• In part(a), estimate using 6 3 20 5 120.
• In part(b), estimate using 1 3 0.05 5 0.05.
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"EWBODFE Challenge advanced students to use decimal
squares to create a model depicting the product 0.73 3 0.3.
About the Standards
Note that Grade 6
Standard MR 2.1 asks
you to verify the
reasonableness of
results.
To check that the quotient in Example 3 is reasonable, you can use leading
digits and compatible numbers. Compatible numbers are numbers that
make a calculation easier.
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Find the quotient.
a. 12.282 4 2.3 5.34
b. 0.476 4 6.8 0.07
Round divisor to place value of leading digit.
}
25q15.95
}
30q15.00
Round dividend to a compatible number.
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Because 15 4 30 5 0.5, the quotient in Example 3 is reasonable.
•
DIVIDING BY A DECIMAL Notice the pattern in the equations below.
64352
60 4 30 5 2
600 4 300 5 2
6000 4 3000 5 2
The quotient remains the same when the divisor and the dividend are
multiplied by the same power of 10. This is because the quotients can
5FBDIJOH4USBUFHZ
10
be written as equivalent fractions multiplied by }
, or 1. This fact can
10
help you to divide decimals.
Encourage students to insert a
zero as the leading digit in products
that are less than 1.
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For Your Notebook
KEY CONCEPT
When doing long division, suggest
that students place the decimal
point in the correct location immediately after moving the decimal
points in the divisor and dividend.
This will help them avoid placing
the decimal incorrectly in the
quotient.
Dividing by a Decimal
Words
When you divide by a decimal, multiply both the divisor
and the dividend by a power of ten that will make the
divisor a whole number.
Numbers
12.5q8.75
0.7
}
125q87.5
}
If a decimal divisor has n decimal
places, what power of ten must
you multiply the divisor by to
make it a whole number? n
4UVEZ4USBUFHZ
EXAMPLE 4
a.
Dividing Decimals
}
3.17 q3.804
AVOID ERRORS
Don’t forget to write
zeros as placeholders
and line up the decimal
point in the quotient
with the decimal point in
the dividend.
b.
}
1.9q0.114
GUIDED PRACTICE
1.2
}
317q380.4
317
63 4
63 4
0
Multiply the divisor and dividend by 100
by moving both decimal points two places
to the right.
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Line up decimal points in dividend
and quotient.
0.06
}
19q1.14
1 14
0
Multiply the divisor and dividend by 10 by
moving both decimal points one place to
the right.
for Examples 3 and 4
Find the quotient. Round to the nearest hundredth if necessary.
7. 110.85 4 3 36.95
8. 2.234 4 1.3 1.72
9. 9.5 4 0.3 31.67
10. 0.208 4 5.2
0.04
2.7 Multiplying and Dividing Decimals
6OJWFSTBM"DDFTT
As students include examples in
their notebooks, encourage them
to include a note for each example
that they moved decimal points by
multiplying the divisor and dividend
by a power of ten.
109
Students have learned to multiply
and divide decimals. To bring closure, have students answer these
questions:
1. Essential Question: How can you
tell how many decimal places are
in the product 0.35 3 0.9? Find
the sum of the number of
decimal places in the factors.
There are 3 decimal places in
the product.
2. By what power of 10 do you multiply the divisor and dividend to
divide 1.68 by 0.7? Find the quotient of 1.68 4 0.7. 10; 2.4
7JTVBM Encourage students to draw arrows as shown in
Example 4 when they are dividing decimals.
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For a quick check of student understanding of key concepts, go over
the following exercises:
Basic: 8, 12, 26, 28, 76
Average: 16, 18, 34, 76, 82
Advanced: 20, 22, 38, 82, 84
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•
•
Student Edition, p. 693
Chapter 2 Resource Book:
Practice Levels A, B, C, pp. 70–72
A
An easily readable reduced
practice page (with answers)
for this lesson can be found
on pp. 66E–66F.
MULTIPLE CHOICE PRACTICE
Exs. 23, 42, 76, 78, 89–91
5 HINTS AND HOMEWORK HELP
for Exs. 7, 25, 79 at classzone.com
VOCABULARY Round to the place value of the leading digit.
1. 3.5 4
2. 9.15 9
3. 22.38 6
4. 18.06 20
5. VOCABULARY Using compatible numbers, what dividend and divisor
would you use to estimate the quotient 54.2 4 6.7? 56 and 7
6. WRITING Explain how you can use fractions to multiply decimals. Give
as fractions, and multiply. Sample answer:
an example. Write the decimals
7
7
11 }
77
17
5.5 3 0.7 5 5 }1 3 }
5}
3 5}
5 3}
5 3.85.
SEE EXAMPLES
1 AND 2
on pp. 107–108
for Exs. 7–23
10
2 10
2
20
20
FINDING PRODUCTS Find the product. Check that it is reasonable.
7. 0.4 3 0.03 0.012
11. 3.4 3 6.5 22.1
8. 0.06 3 0.6 0.036
9. 0.8 3 3 2.4
12. 9.3 3 8.1 75.33
10. 0.05 3 8 0.4
13. 3.9 3 0.91 3.549
15. 0.14 3 0.09 0.0126 16. 6.08 3 0.2 1.216
14. 0.7 3 0.01 0.007
17. 0.045 3 1.20 0.054 18. 25 3 0.052 1.3
19. 0.086 3 0.007
20. 33.501 3 3
21. 19.73 3 5.01
22. 40.21 3 1.03
0.000602
100.503
98.8473
41.4163
23. MULTIPLE CHOICE What is the value of the expression 54.3 3 4.2? B
A 32.58
B 228.06
C 325.8
D 2280.6
SEE EXAMPLES
3 AND 4
FINDING QUOTIENTS Find the quotient. Round your answer to the nearest
hundredth if necessary.
on pp. 108–109
for Exs. 24–39
24. 0.245 4 6 0.04
25. 3.65 4 8 0.46
26. 3.45 4 15 0.23
27. 9 4 7.2 1.25
28. 7 4 1.4 5
29. 12 4 6.4 1.88
30. 68 4 3.1 21.94
31. 9.97 4 2.9 3.44
32. 75.4 4 5.2 14.5
33. 0.3445 4 6.5 0.05
34. 172.2 4 82 2.1
35. 1500.96 4 16
93.81
39. 8.7822 4 3.57
2.46
36. 2199.24 4 41 53.64 37. 37.857 4 7.5 5.05
38. 18.01 4 3.28 5.49
ERROR ANALYSIS Describe and correct the error made in finding the
product or quotient.
40. The decimal
40.
41.
point must move
0.346
6. 21 3 0.04 5 24.84
}
}
four places;
2.7q9.342
27q9.342
6.21 3 0.04 5
0.2484.
41. The decimal 42. MULTIPLE CHOICE Which quotient is not equal to the others? A
point must
A 225 4 180
B 22.5 4 1.8
C 225 4 18
D 2.25 4 0.18
move the same
number of
places in the
ESTIMATING PRODUCTS Round to the place value of the leading digit to
divisor and
estimate the product.
the dividend;
43. 3.45 3 90.2 270
44. 0.32 3 2.8 0.9
45. 4.57 3 199.4 1000 46. 18.23 3 4.7
9.342 4 2.7 5
100
93.42 4 27 5
47.
6.92
3
0.08
48.
561
3
0.7
49. 15.75 3 0.013 0.2 50. 0.35 3 42.82 16
0.56
420
3.46.
110
1SBDUJDF8PSLTIFFU
5
HOMEWORK
KEY
SKILLS • PROBLEM SOLVING • REASONING
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Answer Transparencies
available for all exercises
Basic:
Day 1: pp. 110–113
Exs. 1–14, 23, 40
Day 2: EP p. 693 Exs. 46–53
pp. 110–113
Exs. 24–31, 72–80, 89–91
Average:
Day 1: MCP p. 65 Exs. 10–12
pp. 110–113
Exs. 1–6, 14–18, 23, 43–46, 60–63
Day 2: MCP p. 65 Exs. 13–15
pp. 110–113
Exs. 32–35, 41, 42, 51–54, 59,
64–70, 76, 78–85
Advanced:
Day 1: MRSPS p. 26 Exs. 4, 5
pp. 110–113
Exs. 1–5, 19–23, 47–50, 60–63
Day 2: MRSPS p. 26 Exs. 6–8
pp. 110–113
Exs. 36–39, 42, 55–59, 65–71, 76,
78, 80–88*
Block:
MCP p. 65 Exs. 10–15
pp. 110–113
Exs. 1–6, 14–18, 23, 32–35, 41–46,
51–54, 59–70, 76, 78–85
EXERCISES
2.7
Chapter 2 Fraction and Decimal Operations
6OJWFSTBM"DDFTT
*ODMVTJPO For Exercises 7–22, some students may need help
when counting decimal places. Make sure that all students
understand that they should count from the right when placing
the decimal point in a product. Because students read numbers
from the left, they may find this confusing. Remind them that the
rightmost digit determines the place value of the decimal.
ESTIMATING QUOTIENTS Use compatible numbers to estimate the
quotient.
51. 104.26 4 4.98 20
B
52. 1206.47 4 29.2 40 53. 1.90 4 2.007 1
54. 32.158 4 4.374
8
55. 143.865 4 3.99 36 56. 15.4 4 2.861 5
57. 36.794 4 9.018 4 58. 358.1 4 49.86
7
59. MODELING Copy the number line below. Use your copy to show how to
represent 0.8 4 0.2. Use the fact that division is repeated subtraction. See margin.
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
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60. 7.654 p p 20.20656 61. 1.12 p q 1.008
Exercises 24–39 Some students
may multiply the divisor by a power
of 10, but not the dividend. Remind
students that they must multiply
the divisor and the dividend by the
same power of 10.
65. p 4 0.275 9.6
62. p p 5.08 p p
63. q p 1.12 p p
35.405568
2.66112
66. p 4 0.03 4 2.5 35.2 67. q 4 0.1 4 q 10
68. OPEN-ENDED Describe the pattern
Position n
1
2
3
used to relate the value of a term
Value
of
term
1.5
3
4.5
to its position n in the list. Create
and describe your own pattern. Multiply n by 1.5; check students’ work.
70. Divide
the previous
number by 2;
0.0625, 0.03125,
0.015625.
71. Multiply
the previous
number by 1.5;
10.125, 15.1875,
22.78125.
Exercises 7–22 Students should
realize that when using estimation
to check for reasonableness, if they
round one factor to 0, the estimate
of the product will be 0. Thus, it is
advisable to avoid rounding a
factor to 0.
xy ALGEBRA Evaluate the expression when p 5 2.64 and q 5 0.9.
64. 3.6 4 q 4
69. Multiply
the previous
number by 5;
75, 375, 1875.
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4
n
6
?
"DBEFNJD7PDBCVMBSZ
Exercises 51–58 “Use compatible
numbers to estimate the quotient”
means students should use numbers that will make it easy to estimate the quotient. You may wish to
ask students to explain their
answers to see if they used different compatible numbers and why.
DESCRIBING PATTERNS Describe the pattern. Write the next three numbers.
69. 0.12, 0.6, 3, 15, . . .
70. 1, 0.5, 0.25, 0.125, . . .
71. 2, 3, 4.5, 6.75, . . .
CONNECT SKILLS TO PROBLEM SOLVING Exercises 72–75 will help you
prepare for problem solving.
Write the expression you would use to solve the problem.
72. Grapes are on sale for $1.25 per pound. You buy 1.8 pounds. How much
do you pay for the grapes? 1.25 3 1.8
59.
73. Your class holds a car wash to raise money for a field trip. You charge
$4.75 per car and earn $779. How many cars does your class wash? 779 4 4.75
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
74. You have a wooden board that is 30 inches long. You cut it into pieces
that are 3.75 inches long. How many pieces of wood do you have? 30 4 3.75
75. Wanda buys 3 CDs. With tax, each CD costs $14.69. How much does
she spend? 3 3 14.69
SEE EXAMPLE 3
on p. 108
for Exs. 76–77
76. MULTIPLE CHOICE You knit a scarf using 4 balls of yarn. The yarn costs
a total of $24.88. How much does each ball of yarn cost? B
A $.16
California
77. 45 pages;
36 min; 1.25 3
60 5 75 pages
in 1 hour. 120 2
75 5 45 pages
left, 45 4 1.25 5
36 more
minutes.
B $6.22
C $20.88
D $99.52
for problem solving help at classzone.com
77. READING RATE Tyler can read about 1.25 pages per minute. Can he finish
reading a 65-page book in one hour? About how long would it take him to
finish? How many pages would he have left after reading a 120-page book
for one hour? How much more time would he need? Explain.
California
for problem solving help at classzone.com
2.7 Multiplying and Dividing Decimals
111
"QQMZJOH4UBOEBSET
Exercise 68 In this exercise, students apply
Standard .3 to develop a generalization
of the results to find the value of the nth term.
• In positions 1, 2, 3, and 4, the value of each
term is one and a half times the position
number.
• Generalize to the value of the nth position.
• The value of the nth term is one and a half
times n, or 1.5n.
78. MULTIPLE CHOICE A wheelchair racer takes
about 5.95 minutes to travel 1 mile. Which
expression shows how long it would take the
racer to finish a 26.2-mile marathon? D
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Exercise 78 Students should reason that the number of minutes it
will take to complete the marathon
is greater than 5.95. The division in
choices A and B will give numbers
that are less than 5.95. The subtraction in choice C would not
make sense because you would be
subtracting minutes from miles.
85. Sample answer : No, when
dividing, the quotient times
the divisor must equal the
dividend, so if the quotient is a
whole number and the divisor
b is a whole number, whole
number times whole number is
always equal to a whole number, yes, 5 4 2.5 5 2; yes, 2.2
4 1.1 5 2; yes, 0.5 4 0.1 5 5.
B 26.2 4 5.95
C 26.2 2 5.95
D 5.95 3 26.2
79. COMETS Encke’s comet takes about 3.3 years to
orbit the sun. Halley’s comet takes about 23.06
times as long. About how long does Halley’s comet
Athletes use racing chairs.
take to orbit the Sun? Round to the nearest tenth.
76.1 yr
80. SHORT RESPONSE Copy the division problem below. Explain how
to use estimation to place the decimal point in the quotient.
"DBEFNJD7PDBCVMBSZ
Exercise 82 To complete this
exercise, students must understand the meaning of rates. To find
the cost per ounce of cereal means
to find the cost of 1 ounce of
cereal.
A 5.95 4 26.2
32 Sample answer: 10 p 3 is 30, so the decimal
}
9.76q31.232 should be placed between the 3 and the 2.
81. Start at 1.5
and then move
back 0.2 spaces
until you reach
0. The quotient
is the number of
times you have
to take away
0.2 from 1.5 to
reach 0; Trade
one dollar for 10
dimes. Separate
the dimes into
groups of 2.
The quotient is
the number of
groups.
83. Yes; no;
$27.75; 30.45 4
8.7 5 $3.50 per
gallon, 32.19 4
8.7 5 $3.70 per
gallon, 3.19 p
8.7 5 $27.75.
81. WRITING Explain how to use a number line model to find 1.5 4 0.2.
Then explain how to use dollars and dimes to model $1.50 4 0.2.
82. MULTI-STEP PROBLEM It costs $4.75 for a 25 ounce box of cereal and
$3.45 for a 15 ounce box.
a. What is the cost per ounce of each box of cereal? $.19, $.23
b. How many times the cost per ounce of the smaller box is the cost per
ounce of the larger box? Explain. about 1.21 times; $.23 4 $.19 ø 1.21
83. GASOLINE At one time, the price of gasoline ranged from $3.19 to $3.59
per gallon. A car needs 8.7 more gallons of gasoline to have a full tank.
Is it possible that the cost to fill the tank is $30.45? What is the least
possible cost to fill the tank? Explain how you solved the problem.
84. MEASUREMENT The objects below have been magnified. Their actual
width w is much smaller. Measure each object in millimeters.
Pollen
Algae
Blood cell
w 0.0013 width shown
w 0.0037 width shown
w 0.0006 width shown
84a. 0.0364 mm;
0.0888 mm;
0.0114 mm
a. Use your measurements to find the actual width w of each object.
C
112
b. List the actual objects in order from least to greatest width.
blood cell, pollen, algae
85. xy REASONING The quotient of a and b is a whole number. Can a be a
decimal number if b is a whole number? Can b be a decimal number if
a is a whole number? Can both a and b be decimal numbers? Can the
quotient be greater than a? Justify your answers and give examples. See margin.
5 MULTIPLE
CHOICEOperations
PRACTICE
Chapter 2 Fraction
and Decimal
5 HINTS AND HOMEWORK HELP at classzone.com
86. decimals
less than 5.29;
decimals
greater than
5.29; 5.29; 5.29
divided by 2.3 is
2.3, so decimals
smaller than
5.29 will be less
than 2.3 when
divided, and
decimals
greater than
5.29 will be
greater than 2.3
when divided.
86. REASONING Which decimal number(s) can you divide by 2.3 to make
the quotient less than 2.3? greater than 2.3? equal to 2.3? Explain your
reasoning.
"/%
"44&44
3&5&"$)
87. CHALLENGE Runner A runs at a pace of 6.54 miles per hour for 1.3 hours.
Runner B runs at a pace of 7.08 miles per hour for 1.1 hours. Who runs
farther? How much longer must the other runner continue to run to
match the distance of the first runner? Round to the nearest hundredth
of an hour. Explain how you solved the problem. Runner A; 0.10 h; 6.54 3 1.3 5 8.502
and 7.08 3 1.1 5 7.788, 8.502 2 7.788 5 0.714, then, 0.714 4 7.08 5 0.10.
88. CHALLENGE A store sells crafts. The first week it prices 5 baskets at $20
each. After each week, the price of each unsold basket drops to 0.9 times
the previous week’s price. All 5 baskets sell in the same week for a total
of at least $53. In what week(s) could they have been sold? week 7 or before
%BJMZ)PNFXPSL2VJ[
Find the product or quotient.
1. 0.3 3 0.875 0.2625
2. 2.505 4 1.5 1.67
3. Estimate the product of 19.67 3
3.6 by rounding each factor to
the place value of the leading
digit. 80
4. Jose bought 2.3 pounds of fish
for $19.49. Use compatible numbers to estimate the cost per
pound. $9.50
CALIFORNIA STANDARDS SPIRAL REVIEW
NS 2.1
5
7
89. What is the value of } 1 }? (p. 75) C
6
10
6
23
B }
C }
5
15
1
90. Which number is 6 } written as a decimal? (p. 40) A
8
3
A }
4
Gr. 5 NS 1.2
A 6.125
Gr. 4 NS 3.4
B 6.18
49
D }
Online Quiz
30
C 6.81
classzone.com
An alternate quiz for Lessons 2.4–
2.7 is available online in multiple
choice format.
D 61.8
91. During 4 days of basketball practice, you shoot a total of 140 free
throws. You shoot the same number of free throws each day. How many
free throws do you shoot per day? (p. 671) C
A 25
B 30
C 35
%JBHOPTJT3FNFEJBUJPO
Practice A, B, C in Chapter 2
Resource Book, pp. 70–72
• Study Guide in Chapter 2
Resource Book, pp. 73–74
• Practice Workbook, pp. 29–30
• California@HomeTutor
•
D 40
QUIZ for Lessons 2.4–2.7
Find the product or quotient. (p. 88, 94)
7
3 7
1. } 3 } }
1
2. 2 } 3 1 } 4 }
3. 17 3 } 7 }1
1
2 17
4. 1 }
3 4}
5}
7 128
16
}
5. }
4}
9
1
6. 5 } 4 }
81 }
1
7. 5 }
4 1 } 3 }1
3
8. 3 } 4 6 }5
15
21
5
8
5 25
5
9
5
11
8 147
12
11
15
15
34
2
2
3
4
3
7
9
4
27
8
10. 13.1 1 0.137
13.237
11. 24.194 2 5.08
19.114
12. 7.2 2 0.006
7.194
Find the product or quotient. Round quotients to the nearest hundredth if
necessary. Then check your answer. (p. 107)
13. 9.58 3 6.19 59.30
14. 4.01 3 12.8 51.33
Additional challenge is available in
the Chapter 2 Resource Book, p. 77.
2VJ[
Find the sum or difference. Then check your answer. (p. 102)
9. 6.67 1 14.2 20.87
$IBMMFOHF
An easily readable reduced
copy of the quiz on Lessons
2.4–2.7 (with answers) from
the Assessment Book can be
found on pp. 66G–66H.
15. 52 4 0.079 658.23
16. 3.374 4 0.35
9.64
3
1
17. BOOKS Ryan had 180 books. He gave away }
of his books and sold }
of
4
3
the rest. How many books did he sell? Explain your reasoning. (p. 88)
90 books; 180 2 }1 (180) 5 120, 120 3 }3 5 90
3
EXTRA PRACTICE for Lesson 2.7, p. 693
&953"
45"/%"3%4
41*3"-
3&7*&8
4
2.7 Multiplying
Dividing
Decimals
ONLINE and
QUIZ
at classzone.com
113
(S U 8IBUJTUIFWBMVFPG} 1 } D
/4
6 }
7 }
8 }
9 }
(S U 8IJDIOVNCFSJT} XSJUUFOBTBEFDJNBM D
/4
6 7 8 9 (S U 'PVSCJDZDMFNFDIBOJDTNBEFSFQBJSTJOEBZT5IFZNBEFUIFTBNF
OVNCFSPGSFQBJSTFBDIEBZ)PXNBOZSFQBJSTEJEUIFZNBLFQFSEBZ A
/4
6 7 8 9 off Skills and
MIXED REVIEW Problem
Solving
California
Multiple Choice Practice for Lessons 2.4—2.7
1. You have a piece of wood that is 51 inches
long. For a craft project, you need pieces
classzone.com
Students who need more review
and practice should see the
following lessons in the
California@HomeTutor.
Exercise 1: Lesson 2.5
Exercise 2: Lesson 2.7
Exercise 3: Lesson 2.7
Exercise 4: Lesson 2.7
Exercise 5: Lesson 2.6
Exercise 6: Lesson 2.7
Exercise 7: Lesson 2.4
Exercise 8: Lesson 2.5
5. The table shows the amount of money raised
by 3 homerooms at a school fair. How much
more was the total raised by homerooms 6A
and 6C than by homeroom 6B? Gr. 5 NS 2.1 B
1
that are each 4 }
inches long.
2
Homeroom
51 in.
1
How many pieces that are 4 }
inches long can
2
Money raised
6B
6C
$148.59
$122.77
you cut from the wood? NS 2.1 A
A $14.71
B $108.06
A 11
B 12
C $137.48
D $159.70
C 229
D 230
6. What is the value of 13.57 3 2.8? Gr. 5 NS 2.1 B
2. What is the value of the expression x p 16.83
when x 5 0.14? Gr. 5 NS 2.1 B
A 0.8415
B 2.3562
C 84.15
D 235.62
3. What is 0.23 4 6.18 rounded to the nearest
hundredth? Gr. 5 NS 2.1 D
A 0.004
B 0.03
C 0.037
D 0.04
A 13.570
B 37.996
C 135.70
D 379.96
7. The recipe shown makes enough garlic
mashed potatoes for 5 servings. You want
to make 150 servings for a garlic festival.
How many cups of water and cups of milk
do you need? NS 2.1, MR 3.1 B
G
M ar
P as lic
ot he
at d
oe
s
4. In the table below, which description relates
a position n to its value? NS 2.2, MR 1.2 C
Position n
Value
1
2}
2
5
3
7}
4
10
n
?
Garlic
Mashed Potatoes
1 box garlic mashed
potato mix
1 tbsp butter
2 1/3 c water
1/3 c milk
1
2
1
2
2
2
A 67 }
cups water and 9 }
cups milk
3
3
B 70 cups water and 10 cups milk
1
A Multiply n by 1 }
.
2
2
cups water and 16 }
cups milk
C 116 }
1
.
B Divide n by 1 }
2
D 350 cups water and 50 cups milk
3
2
3
3
16
1
8. What is the value of 2 } 4 2 }
? NS 2.2 C
1
.
C Multiply n by 2 }
2
12
20
B }
21
1
D 52 }
2
192
A }
875
1
C 1}
20
1
D Divide n by 2 }
.
2
114
6A
$133.88
Chapter 2 Fraction and Decimal Operations
"QQMZJOH.BUIFNBUJDBM3FBTPOJOHUP/4BOE/4
Exercise 4 In this exercise, students formulate and justify mathematical conjectures based on a general description, as called for
in Standard .3.
• Formulate a conjecture.
• Justify the conjecture using reasoning.
• The values are greater than the position numbers, so n is multiplied to obtain the value of position n.
• Each value is more than double its position number.
•
The only reasonable choice is C. The value of each number is 2}1
2
times its position.
Exercise 7 In this exercise, students evaluate the reasonableness of the solution in the context of the original situation, as
called for in Standard .3.
• You want to make 150 4 5, or 30 times the given recipe
amounts.
•
Calculate 30 3 2}1 cups water and 30 3 }1 cup milk.
•
Check the reasonableness of the answer using estimation:
3
3
30 3 2 5 60 cups water and 30 3 }1 5 15 cups milk is needed.
2