Name
3.1
ALGEBRA
?
Number and
Operations—5.3.E
MATHEMATICAL PROCESSES
5.1.F
Multiplication Patterns with
Decimals
Essential Question
How can patterns help you place the decimal point in a product?
Unlock
Unlock the
the Problem
Problem
Cindy is combining equal-sized rectangles from different fabric
patterns to make a postage-stamp quilt. Each rectangle has an area
of 0.75 of a square inch. If she uses 1,000 rectangles to make the quilt,
what will be the area of the quilt?
Use the pattern to find the product.
1 × 0.75 = 0.75
10 × 0.75 = 7.5
100 × 0.75 = 75.
1,000 × 0.75 = 750.
The quilt will have an area of __ square inches.
1. As you multiply by 10, 100, and 1,000, how does
the position of the decimal point change in the product? ______
Place value patterns can be used to find the product of a number and the
decimals 0.1 and 0.01.
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Example
• What fraction of the actual size
of the building is the model?
Jorge is making a scale model of the Willis Tower in Chicago for a
1
theater set. The height of the tower is 1,353 feet. If the model is ___
100
of the actual size of the building, how tall is the model?
• Write the fraction as a decimal.
1 × 1,353 = 1,353
0.1 × 1,353 = 135.3
0.01 × 1,353 =
←
1
____
of 1,353
100
Jorge’s model of the Willis Tower is __ feet tall.
2. As you multiply by 0.1 and 0.01, how does the position of the decimal
point change in the product?
Module 3
105
Share
Share and
and Show
Show
Complete the pattern.
1. 1 × $17.04 = $17.04
10 × $17.04 = $170.40
Think: The decimal point moves one place to the _ for each equation.
Think: Money is expressed in hundredths. 170.4 = 170.40.
100 × $17.04 = $1,704
1,000 × $17.04 = __
2. 1 × 3.19 = _
3. 45.6 × 1 = _
4. 1 × 6,391 = _
10 × 3.19 = _
45.6 × 10 = _
0.1 × 6,391 = _
100 × 3.19 = _
45.6 × 100 = _
0.01 × 6,391 = _
1,000 × 3.19 = _
45.6 × 1,000 = _
Math Talk
Mathematical Processes
Explain how you know
that when you multiply the
product of 10 × 34.1 by 0.1,
the result will be 34.1.
Problem
Problem Solving
Solving
Algebra Find the value of n.
5. n × $3.25 = $325.00
n=_
6. 0.1 × n = 89.5
7. 1,000 × n = 630
n=_
n=_
8. Multi-Step A glacier in Alaska moved more than 29.9 meters a day.
9.
106
Analyze Three friends are selling items at an arts and
crafts fair. Josey makes $45.75 selling jewelry. Mark makes 100 times as
much as Josey makes by selling his custom furniture. Chance makes a
tenth of the money Mark makes by selling paintings. How much money
does each friend make?
© Houghton Mifflin Harcourt Publishing Company
About how much farther would it move in 1,000 days than it would
move in 100 days?
Name
Problem
Problem Solving
Solving
What’s the Error?
10. Kirsten is making lanyards for a convention.
She needs to make 1,000 lanyards and knows
that 1 lanyard uses 1.75 feet of cord. How
much cord will Kirsten need?
Kirsten’s work is shown below.
1 × 1.75 = 1.75
10 × 1.75 = 10.75
100 × 1.75 = 100.75
1,000 × 1.75 = 1,000.75
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Find and describe Kirsten’s error.
Solve the problem using the
correct pattern.
So, Kirsten needs __ feet of cord to make 1,000 lanyards.
11. Communicate how Kirsten could have solved the problem without
writing out the pattern needed.
Module 3 • Lesson 1
107
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
12. Connect When a number is multiplied by 1,000, the result is 320.
When the number is multiplied by 100, the result is 32. What it
the result when the number is multiplied by 10?
A
3.2
C
16
B
3,200
D
160
13. Use Math Language When a number is multiplied by 1,000, the
result is 8,510. When the number is multiplied by 10, the result is 85.1.
Which sentence follows the same pattern?
A
When multiplied by 100, the result is 8.51.
B
When multiplied by 100, the result is 851.
C
When multiplied by 1, the result is 85.1.
D
When multiplied by 1, the result is 851.
14. Multi-Step When a number is multiplied by 1,000 and then by 0.1,
the result is 6,810. What is the original number?
A
0.681
B
681
C
6.81
D
68.1
TEXAS Test Prep
15. A box of crackers costs $0.26 per ounce. If the box contains 10 ounces,
108
A
$0.026
B
$2.60
C
$0.260
D
$26.00
© Houghton Mifflin Harcourt Publishing Company
what is the cost of the box of crackers?
Number and Operations—5.3.E
MATHEMATICAL PROCESSES 5.1.F
H o mewo rk
and Practice
3.1
Name
Multiplication Patterns with Decimals
Find the value of n.
1. n × 43.50 = 435
n=
4. n × $5.06 = $506.00
n=
2. 394 × n = 3.94
n=
5. 0.074 × n = 74
n=
3. n × 721 = 72.1
n=
6. 8,034 × n = 80.34
n=
Problem
Problem Solving
Solving
7. Jaden sells a painting for 10 times the original
© Houghton Mifflin Harcourt Publishing Company
price. He sells the painting for $45.50. What was
the original price of the painting?
8. Marla thinks her dog might not be feeling
well. He ate 0.1 times as much dog food on
Wednesday as he ate on Tuesday. If her dog
ate 6 cups of dog food on Tuesday, how much
did he eat on Wednesday?
Module 3 • Lesson 1 109
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
project. They cut 1,000 pieces of ribbon. Each
ribbon is 1.45 feet long. Which equation
correctly shows the number of feet of ribbon
cut for the project?
A
1,000 × 1.45 = 14.50
B
1,000 × 1.45 = 145
C
1,000 × 1.45 = 1,450
D
1,000 × 1.45 = 14,500
11. Which equation correctly shows the next
product in the pattern?
1 × 0.67 = 0.67
10 × 0.67 = 6.7
100 × 0.67 = 67
marbles at the warehouse store contains
100 ounces of marbles. What is the cost of
the box of marbles?
A
$5
B
$50
C
$500
D
$5,000
12. Bianca plants a tree at the park that is
0.3 meter tall. An oak tree nearby is 100 times
taller. How tall is the oak tree?
A
0.03 meter
B
3 meters
A
1,000 × 0.67 = 0.067
C
30 meters
B
1,000 × 0.67 = 67,000
D
300 meters
C
1,000 × 0.67 = 6,700
D
1,000 × 0.67 = 670
13. Multi-Step Leo practices his violin 12.5 hours
each week. He also practices singing for 3.5
hours each week. If he practices the same
amount of time each week, how many hours
does Leo practice in 10 weeks?
110
10. Marbles cost $0.50 per ounce. A box of
A
125 hours
B
160 hours
C
16 hours
D
1,600 hours
14. Multi-Step Greg ran 3 times as far as Jed. RJ
ran 0.1 times as far as Greg. If Jed ran 25 yards,
how far did Greg and RJ run?
A
Greg: 75 yards; RJ: 7.5 yards
B
Greg: 7.5 yards; RJ: 75 yards
C
Greg: 750 yards; RJ: 75 yards
D
Greg: 7.5 yards; RJ: 0.75 yards
© Houghton Mifflin Harcourt Publishing Company
9. The camp counselors cut ribbons for an art