Multi-Part Lesson
Multi-Part Lesson
1-1
1-1
Multiply Decimals
PART
A
B
C
D
PART
E
PART
Main Idea
Estimate the product
of decimals and judge
the reasonableness of
the results.
NGSSS
MA.6.A.5.3
Estimate the results
of computations with
fractions, decimals, and
percents and judge the
reasonableness of the
results.
glencoe.com
boxes highlight
Key Concept
rmulas, and
definitions, fo
le
t ideas. Multip
other importan
ls,
bo
m
sy
s,
—word
representations
models—help
examples, and
epts.
stand the conc
students under
27_033_C1L1_891639.indd 27
A
Estimate Products
SKATEBOARDING The record for the greatest
distance traveled on skateboard in 24 hours
was set by James Peters in 2007. He traveled
about 7.6 miles per hour.
Multiply Decimals
A
B
Estimate
Products
NGSSS
MA.6.A.5.3 Estimate the results of
computations with fractions, decimals, and percents
and judge the reasonableness of the results.
3. Is your estimate higher or lower than the
actual distance he traveled? Explain. The estimate is higher than
the actual distance he traveled because 7.6 was rounded up.
glencoe.com
To estimate products of decimals, round each number. Then
multiply.
1 FOCUS
Round Decimals
To round a decimal, first underline the digit to be rounded. Then look at
the digit to the right of the place being rounded.
• If the digit is 4 or less, the underlined digit remains the same.
• If the digit is 5 or greater, add 1 to the underlined digit.
• After rounding, change all digits after the underlined digit to zeros.
Activity Review how to round decimals to the
nearest whole number. Have students draw a
number line from 1 to 10. Then ask them to
locate and label 1.5, 2.5, 3.5, and so on
through 9.5.
Ask:
• Is 1.2 closer to 1 or to 2? How can you
tell? 1; The distance between 1.2 and 1 is
less than the distance between 1.2 and 2.
Estimate Products Using Rounding
Estimate 8.7 × 2.8.
• Is 4.75 closer to 4 or to 5? How can you
tell? 5; The distance between 4.75 and 5 is
less than the distance between 4.75 and 5.
Round to the nearest whole number to make it easier to
compute mentally.
Round 8.7 to 9.
Round 2.8 to 3.
• Use the number line to round the
following numbers to the nearest whole
number: 5.67; 3.41; 9.95. 6; 3; 10
The product is about 27.
Estimate each product.
a. 9.6 × 1.8 20
E
Students will estimate the product of decimals
and judge the reasonableness of the results.
2. Estimate how many miles James Peters
traveled in 24 hours. about 24 × 8 or 192 miles
9
×3
27
D
Objective
1. Round 7.6 to the nearest whole number. 8
8.7
× 2.8
C
b. 8.7 × 2.9 27
c. 68.4 × 21.3 1,400
2 TEACH
Scaffolding Questions
Lesson 1-1 Multiply Decimals
Tips for New Teachers
27
1/9/09 12:11:47 PM
Rounding If students have trouble remembering
the rules for rounding, teach them this rhyme:
5 and above, give it a shove.
4 and below, let it go.
Ask:
• Suppose James travels at an average of
5.4 miles per hour for 8.25 hours. How
would you round the numbers to
estimate how far he traveled? Round 5.4
to 5 and 8.25 to 8.
• About how far would James travel?
40 miles
• Would your estimate be higher or lower
than the actual distance? Explain. Sample
answer: Lower; both numbers are rounded
down, so the estimated distance is less than
the actual distance.
Lesson 1-1 Multiply Decimals
27
Formative Assessment
Use the Check Your Progress exercises after
each Example to determine students’
understanding of concepts.
fer
Study Tips of
l
fu
lp
he
students
t the
ou
ab
information
st
e udying.
topics they ar
Estimate 4.8 × 3.2. 5 × 3 =15
HELICOPTERS One of the first helicopters
flew at a speed of 44.7 kilometers per
hour. At this speed, about how far could
the helicopter travel in 2.5 hours? 135 km
RECIPES Anna has $20 to buy 8 pounds
of tomatillos for a party. The tomatillos
cost $2.89 per pound. Does she have
enough money to buy them? Explain your
reasoning. No; Sample answer: $2.89 is
close to $3. If you round $2.89 to $3, the
tomatillos will cost about $24.
Rounding Decimals When
rounding decimals, such
as 99.96 to the tenths,
the 9 must round up.
So, 99.96 rounded to the
nearest tenth is 100.0.
39.3
× 6.5
40
×7
280
Round 39.3 to 40.
Round 6.5 to 7.
The greyhound could travel about 280 miles in 6.5 hours.
d. MONEY Suppose one U.S. dollar is equal to 5.3 Egyptian
pounds. About how many Egyptian pounds would you
receive for $48.50? about 250 Egyptian pounds
e. ASTRONOMY The Earth is rotating around the Sun about
18.6 miles per second. About how many miles does it travel
in 4.8 seconds? about 100 mi
SCHOOL SUPPLIES Patrice has
$20 to buy 5 binders for her
classes. She found binders
that cost $4.29 each. Does she
have enough money to buy
these binders? Explain your
reasoning.
IWB INTERACTIVE WHITEBOARD READY
Foc us on Mathematical Content
Rounding decimals to the nearest whole
number before multiplying is one way to
estimate a product. Refer to the digit in the
tenths place. If the digit in the tenths place
is 5 or higher, the number is rounded to
the next whole number. If the digit is less
than 5, then the whole number remains
the same.
Estimate.
5 × $4 = $20
Estimate 4.29 as 4.
5 × $5 = $25
Estimate 4.29 as 5.
The actual cost of the binders is between $20 and $25. So,
Patrice does not have enough money to buy the binders.
f. Yes; $1 × 30 = $30 and
$2 × 30 = $60. So, they
will earn between $30
and $60.
28
f. PROFIT The art club makes a profit of $1.75 on every batch of
cookies they sell at a bake sale. The goal is to earn at least
$50 selling batches of cookies. They estimate they will need
to sell at least 30 batches. Is this estimate reasonable? Explain
your reasoning.
Chapter 1 Multiply and Divide Decimals
027_033_C1L1_891639.indd 28
28 Chapter 1 Multiply and Divide Decimals
DOGS A greyhound can travel 39.3 miles per hour. At
this speed, about how far could a greyhound travel in
6.5 hours?
1/21/09 8:59:27
indicates multi-step problem
Example 1
(p. 27)
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Estimate each product. 1–6. Sample answers given. 3. 60 × 30 = 1,800
1. 5.8 × 4 6 × 4 = 24
2. 27.3 × 9 27 × 10 = 270 3. 57.1 × 32
4. 3.5 × 1.8 4 × 2 = 8
Example 2
(p. 28)
Example 3
(p. 28)
5. 13.92 × 2.7
6. 94.89 × 3.11
14 × 3 = 42
90 × 3 = 270
7. MONEY A grocery store sells American cheese for $3.89 per pound.
About how much would 1.89 pounds of the cheese cost? about $8
8. MEMORY Greg has 52 megabytes of free
space left on his MP3 player. He wants
to download 7 songs that each use
Media Downloading...
7.9 megabytes of memory. He estimates
that he will need 56 megabytes of memory.
Explain why his estimate is reasonable. If 7.9
is rounded to 8, then the 7 songs will require about
56 megabytes of memory. Since 7.9 was rounded up, the actual amount
of memory he will use will be less than 56 megabytes.
AL
If
= Step-by-Step Solutions begin on page R1.
Extra Practice is on page EP2.
Example 1
(p. 27)
Estimate each product. 9–17. Sample answers given.
(p. 28)
20. CRAFTS Lisha is making headbands using ribbon. She would like to
make 12 headbands. Each one requires 15.5 inches of ribbon. She
estimates that she will need to buy 160 inches of ribbon. Is her
estimate reasonable? Explain your reasoning.
20. Her estimate is
not reasonable.
Since 12 rounds
21. GIFT CARDS Miguel received a $50 gift card to a bookstore. He would
down to 10 and
like to buy 3 books that cost $15.75 each including tax. He estimates
15.5 rounds to 16
that he cannot buy all three books because each book costs about $20,
by a lesser amount,
and all three books would cost $60. Is his estimate reasonable? Explain
her estimate of 10
your reasoning. His estimate is not reasonable. He rounded $15.75 to $20. If he
× 16 = 160 will be
rounded $15.75 to $16, the estimate would be $48 for the three books.
too low.
B Use estimation to determine whether each answer is reasonable. If
the answer is reasonable, write yes. If not, write no and provide a
reasonable estimate.
22. 22.8 × 4.7 = 107.16 yes
23. 2.1 × 4.9 × 7.2 = 105.84 no; 70
24. 7.8 × 1.1 × 4.2 = 50 no; 32
25. 43.8 × 2.8 × 3.1 = 371.8 yes
Lesson 1-1 Multiply Decimals
Differentiated Homework Options
7_033_C1L1_891639.indd 29
Level
AL
Approaching Level
Assignment
9–21, 36–38, 39–44
OL
On Level
9–25 odd, 26–29, 31, 35,
36, 38–44
BL
Beyond Level
22–44
students have trouble
estimating the product of decimals,
Then
use one of these reteach
options:
9. 9.7 × 3.3 10 × 3 = 30 10. 3.4 × 5.6 3 × 6 = 18 11 17.5 × 8.4
12.
26.3 26 × 10 = 260 13.
33.6
14.
99.1
11. 20 × 8 = 160
× 9.7
× 82.1
× 11.2
13. 30 × 80 = 2,400
14. 100 × 11 = 1,100 15. 44.8 × 5.1
16. 28.21 × 8.02
17. 71.92 × 2.01
40 × 5 = 200
30 × 8 = 240
70 × 2 = 140
Example 2 18. FRUIT On average, the U.S. produces 36.5 million tons of fruit each
(p. 28)
year. About how much fruit does it produce in 2.25 years?
about 80 million tons
19. SCIENCE A single year on Saturn is equal to 29.4 years on Earth. About
how many Earth-years are equal to 3.2 years on Saturn? about 90
Example 3
Alternate Teaching
Strategy
1 Quick Review Math Handbook,
p. 132
2 Have them use a number line to
practice rounding decimals to the
nearest whole number.
Teaching
The Alternate
ides
Strategy prov
r remediation
suggestions fo
ho did not
for students w
ept.
grasp the conc
3 PRACTICE
Formative Assessment
Use Exercises 1–8 to check for understanding.
Then use the table below to customize
assignments for your students.
29
10/1/10 3:19:41 PM
Odd/Even Assignments
Exercises 9–21 are structured so that students
practice the same concepts whether they are
assigned odd or even problems.
Two-Day Option
9–21 odd, 39–42
9–21, 39–42
10–20 even, 36, 38, 39,
43, 44
22–36, 38, 43, 44
Common Error In Exercises 1–6, 9–11,
and 15–17, students may have difficulty
multiplying in horizontal form. Remind
students that they may rewrite the
problems in vertical form.
Lesson 1-1 Multiply Decimals
29
26. GRAPHIC NOVEL Refer to the graphic novel frame below for Exercises a–b.
AL
OL
BL
I’ve already saved
$68 for the $200
video game system.
Interpersonal Present these questions
to a small group.
• Why is being able to estimate
answers in mathematics important?
Sample answers: Sometimes you
do not need to find an exact answer;
estimates can help you check an
answer.
• Describe a situation in which you
estimated an answer. How and why
was estimation helpful? Sample
answer: Before I solved a problem, I
estimated the answer. It helped me
decide whether my actual solution
was reasonable.
• When in real life is estimating more
helpful than finding the exact
answer? Sample answer: to
determine how much I have spent
when I am shopping
• Name some real-world situations
where estimating an answer is not
helpful. Sample answer: In sports,
such as a race, an exact time is
needed to determine the winner.
Visit glencoe.com to rewatch
the animated version of “Money
Challenge.”
a. How much more does Raj need until he has enough to buy the
video game system? Raj needs to save $132 more.
b. If he works for 25 hours, will he have enough to buy the video
game system? Yes; if Raj works 25 hours, he will make $137.50.
27. More; her wage
was rounded up, so
the actual total is
less than the
estimate.
29. 35 × 8 = 280;
40 × 8 = 320;
Rounding to the
ones gives an
estimate closer to
the actual product.
30. 94 × 4 = 376;
90 × 4 = 360;
Rounding to the
ones gives an
estimate closer to
the actual product.
31. 59 × 6 = 354;
60 × 6 = 360;
Rounding to the
ones gives an
estimate closer to
the actual product.
32. Calories: 400;
carbohydrates:
100 g; Vitamin C:
400 mg; calcium:
80 mg
30
Day
shop is $5.85. The table shows the number of hours
she worked. She estimates her earnings to be
$120. Without calculating her actual earnings,
determine if her estimate is more or less than her
actual earnings. Explain your reasoning.
28. FUEL A car releases 19.6 pounds of carbon dioxide
for every 1 gallon of gasoline burned. Estimate
the number of pounds of carbon dioxide released
if 14.5 gallons is burned. about 300 pounds
Hours
Worked
Monday
3.5
Tuesday
4.25
Wednesday
3.75
Thursday
2.5
Friday
4.75
REASONING The accuracy of an estimate depends on the place value the
numbers are rounded to. For each exercise, round the first factor to the
tens and then the ones before estimating. Which way gives an estimate
that is closer to the actual product?
29. 35.1 × 8
30. 94.1 × 4
32. NUTRITION The table shows some nutritional
facts about orange juice. Estimate each value
for 1 quart of orange juice. (Hint: 4 cups is
equal to 1 quart.)
33. TREES A King Palm can grow about 2.1 feet
a year. Estimate the height of the King Palm,
in yards, after 15 years. about 10 yards
31. 58.8 × 6
Orange Juice (1 cup)
Calories
Vitamin C
112
96.9 mg
Carbohydrates
26.8 g
Calcium
22.4 mg
REASONING Estimate each product to determine if each calculator answer
is correct. Explain your reasoning.
34. 46.85
9.75; 456.7875
35. 90.8
3.1; 217.18
yes; 46.85 × 9.75 ≈ 45 × 10 ≈ 450
no; 90.8 × 3.1 ≈ 90 × 3 ≈ 270
Chapter 1 Multiply and Divide Decimals
027_033_C1L1_891639.indd 30
30 Chapter 1 Multiply and Divide Decimals
27 MONEY Hannah’s hourly wage at the ice cream
1/21/09 8:59:34
C
36. Sample answer:
1.9 × 5.3 × 3.81
36. OPEN ENDED Name three decimals with a product that is about 40.
37. CHALLENGE A scooter can travel between 22 and 28 miles on each
gallon of gasoline. If one gallon of gasoline costs between $3.75 and
$3.95 per gallon, about how much will it cost to travel 75 miles?
about $12
38.
Suppose your friend multiplied 1.2 and 2.6 and got
31.2 as the product. Is your friend’s answer reasonable? Justify your
response. No; using rounding, the answer should be close to 1 × 3 or 3.
NGSSS Practice
B. between $5 and $6
D. more than $7
Fruit Punch
$0.75
Milk
$0.80
Pudding
F. $4
H. $8
G. $6
I. $10
If Yes
C. $60
$0.85
Which of the following is a reasonable
estimate for the cost of two slices of
pizza, a salad, and fruit punch? G
D. $70
42.
If No
SHORT RESPONSE Javier bought
4 pencil toppers at the school store
for $3.69 each. He estimated how
much he needs to pay and gave the
cashier $16. Is Javier’s estimation
reasonable? Explain your reasoning.
yes; 4 × $3.69 ≈ 4 × $4 = $16
AL
Reteach Worksheet
CRM
(p. 12)
OL
Skills Practice Worksheet
CRM
(p. 13)
BL
Enrich Worksheet
CRM
(p. 16)
NGSSS Practice
DIVING The table gives the scores for the Men’s Synchronized
10-Meter Diving at the 2008 Olympics. (Lesson 0-2)
43. How many more points did China earn than Germany? 17.76
44. What is the difference in the points China and the United
States earned? 27.54
27_033_C1L1_891639.indd 31
Are students continuing to
struggle with estimating
the product of decimals and judging the
reasonableness of the results?
B. $40
Friday
$1.15
Andrew
$5.85/hr
A. $30
40. Medina’s school lunch menu is shown.
Fish and Fries $2.25
Mario
$8.25/hr
Suppose Mario and Andrew each
worked 20 hours. About how much
more money did Mario earn? B
C. between $6 and $7
$1.75
Have students write how
to estimate 8.7 × 2.2.
41. Mario and Andrew’s hourly charge for
mowing lawns is shown.
A. less than $4
Salad
4 ASSESS
MA.6.A.5.3
39. Green peppers are on sale for $2.89
per pound. Mrs. Moseley bought
1.75 pounds of peppers. About how
much did she pay for the peppers? B
Pizza
s require
H.O.T. Problem
e Higher
students to us
g skills to
Order Thinkin
s.
solve problem
Country
China
Germany
Russian Federation
Australia
United States
Points
468.18
450.42
445.26
444.84
440.64
Lesson 1-1 Multiply Decimals
31
Follow-Up
1/9/09 12:12:07 PM
Remind students to keep any notes regarding
estimating products under the appropriate tab in
their Foldables.
Diagnose Student Errors
Survey student responses for each item.
Class trends may indicate common errors
and misconceptions.
39. A. rounded both numbers down
instead of rounding up
B. correct
C. estimated beyond upper limit of
range
D. guess
40. F. estimated pizza only
G. correct
H. estimated cost of all items
I. estimated cost of all items plus
an extra slice of pizza
41. A. subtracted rounded numbers
incorrectly
B. correct
C. rounded $5.85 to $5 instead of $6
D. subtracted rounded numbers
incorrectly
Lesson 1-1 Multiply Decimals
31
Multi-Part Lesson
1-1
PART
Multiply Decimals
A
B
C
D
Multi-Part Lesson
1-1
E
PART
Percents Decimals
Multiply
A
A
BB
C
D
E
PART
B
Multiply Decimals
by Whole Numbers
Objective
Main Idea
Multiply Decimals by
Whole Numbers
Use models to multiply
a decimal by a whole
number.
The table shows the relationship between decimals and base-ten
blocks. You can use base-ten blocks to multiply decimals.
Ones (1.0)
Tenths (0.1)
Hundredths (0.01)
One 10-by-10 flat
represents 1 or 1.0.
One 1-by-10 rod
represents 0.1.
One 1-by-1 cube
represents 0.01.
NGSSS
Students will use models to multiply a decimal
by a whole number.
NGSSS
MA.6.A.1.1 Explain and justify procedures for
multiplying and dividing fractions and decimals.
MA.6.A.1.2 Multiply and divide fractions and decimals
efficiently.
MA.6.A.1.1
Explain and justify
procedures for multiplying
and dividing fractions and
decimals.
MA.6.A.1.2 Multiply and
divide fractions and
decimals efficiently.
glencoe.com
Resources
WALKING Louisa walked her dog 0.2 mile on Monday, Wednesday,
and Friday. Find the total distance Louisa walked all week.
Manipulatives
• base-ten blocks
What do you need to find? the total distance Louisa walked
Easy-to-Use Manipulatives
Hands-On Activity Tools and Resources
• Base-Ten Models, p. 1
Just as 3 × 2 means 3 groups
of 2, 3 × 0.2 means 3 groups
of 2 tenths. Model three groups
of two tenths using base-ten blocks.
glencoe.com
3 groups
Combine the tenths. There are
six tenths.
1 FOCUS
Write these numbers on the board:
3.41 4.12 1.04
So, 3 × 0.2 = 0.6. Louisa walked a total of 0.6 mile.
Ask:
• Which number has a 4 in the ones
place? 4.12
and Apply
• Which number has no tenths? 1.04
Use base-ten blocks to find each product.
• Which number has a 1 in the hundredths
place? 3.41
2 TEACH
Activity 1 Have students work in pairs to
model and check each step.
32
1. 3 × 0.3 0.9
2. 2 × 0.4 0.8
3. 4 × 0.02 0.08 4. 5 × 0.01 0.05
5. 3 × 0.5 1.5
6. 4 × 0.6 2.4
7. 2 × 0.08 0.16 8. 8 × 0.04 0.32
Chapter 1 Multiply and Divide Decimals
027_033_C1L1_891639.indd 32
Interactive WhiteBoard Demonstrate
modeling decimals on an Interactive
WhiteBoard. Have a student volunteer
come to the IWB and use the highlighter
tool to identify ones, tenths, and
hundredths.
32 Chapter 1 Multiply and Divide Decimals
1–8. Check students’ work for models.
1/9/09 12:12:13
Activity 2 Point out that 10 tenths can be
combined to make one whole.
Model 2 × 1.6 to find the product.
Model two groups of one and six tenths.
3 ASSESS
Use Exercises 9–16 to assess whether students
know how to use models to multiply a decimal
by a whole number.
2 groups
From Concrete to Abstract Use Exercise 18
to bridge the gap between using models and
using an algorithm to multiply a whole number
and a decimal.
Combine the ones. Then combine the tenths.
Extending the Concept Have students use
base-ten blocks to compare the product of
3 × 12 with the product of 3 × 1.2. 3 × 12 =
36; The product of 3 × 1.2 has the same digits
as 3 × 12, but with one decimal place. 3 ×
1.2 = 3.6
one whole
Combine the 10 tenths into 1 whole.
Additional Answers
17. The factors have the same digits, but
one factor in 2 × 1.6 is a decimal.
The products, 32 and 3.2, have the
same digits, but one is a decimal.
So, 2 × 1.6 = 3.2.
and Apply
9–16. Check students’ work for models.
Use base-ten blocks to find each product.
9. 2 × 1.3 2.6
10. 3 × 1.1 3.3
11. 4 × 1.02 4.08
12. 6 × 2.01 12.06
13. 5 × 2.5 12.5
14. 2 × 3.8 7.6
15. 5 × 1.09 5.45
16. 4 × 3.07 12.28
the Results
18. Sample answer: Multiply 5 by 0.4 and
add to the product of 5 × 1. So, 5 × 1.4
is 7.0 or 7. Check students’ work for
models.
17–20. See margin.
19. Sample answer: The product is greater
than the whole number. For example,
5 × 1.8 = 9 and 5 × 0.8 = 4.
17. Compare and contrast 2 × 16 and 2 × 1.6. How are the products the
same? different?
18. MAKE A CONJECTURE Explain how to find 5 × 1.4 without using
base-ten blocks. Justify your procedure. Then check your answer
using base-ten blocks.
19. MAKE A CONJECTURE Suppose you multiply a whole number by a decimal
greater than one. Is the product less than, greater than, or equal to the
atures help
Write Math fe
whole number? Explain your answer.
the
20.
27_033_C1L1_891639.indd 33
Write a rule that you can use to multiply a whole
number by a decimal without using base-ten blocks.
to use
students learn
athematics.
language of m
Lesson 1-1 Multiply Decimals
20. Sample answer: Multiply the whole
number by the decimal as with whole
numbers and place the decimal point
the same places to the left as the
decimal number.
33
1/9/09 12:12:24 PM
Lesson 1-1 Multiply Decimals
33
Multi-Part Lesson
1-1
PART
PART
C
Multiply Decimals
A
B
C
D
Multi-Part Lesson
1-1
E
Multiply
Decimals by
Whole Numbers
Objective
Multiply Decimals
PART
A
Main Idea
Estimate and find the
product of decimals
and whole numbers.
NGSSS
Students will estimate and find the product of
decimals and whole numbers.
NGSSS
MA.6.A.1.1 Explain and justify procedures for
multiplying and dividing fractions and decimals.
MA.6.A.1.2 Multiply and divide fractions and decimals
efficiently.
Also addresses MA.6.A.1.3, MA.6.A.5.3.
MA.6.A.1.1
Explain and justify
procedures for multiplying
and dividing fractions and
decimals.
MA.6.A.1.2 Multiply and
divide fractions and
decimals efficiently.
Also addresses MA.6.A.1.3,
MA.6.A.5.3.
glencoe.com
3. Multiply 6 by 492. Place
the decimal point two
places from the right.
1 FOCUS
• Have students find the length of 3, 5, and
10 of their object.
• What is the error in the third answer?
The decimal place was not shown.
34 Chapter 1 Multiply and Divide Decimals
Multiply Decimals by
Whole Numbers
PLANTS Bamboo can grow about
4.92 feet in height per day. The
table shows different ways to find
the total height a bamboo plant can
grow in two days. 2. See margin.
Growth of Bamboo Over Two Days
1. Use the addition problem and the
estimate to find 2 × 4.92. 9.84
Add.
4.92 ft + 4.92 ft = 9.84 ft
Estimate.
4.92 is about 5.
2 × 5 = 10
Multiply.
2 × 4.92 ft = 2. Write an addition problem, an estimate, and a multiplication
problem to find the total growth over 3 days, 4 days, and 5 days.
Using repeated addition can help you place the decimal point in
the product of a whole number and a decimal. The whole number
represents the number of times the decimal is used as an addend.
So, place the decimal point in the product the same number of
places from the right as the decimal factor.
Estimate
4×1=4
0.83
× 4
3.32
two decimal places
0.83
0.83
0.83
0.83
4 groups of 0.83
Place the decimal point two places from the right.
Check for Reasonableness
3.32 ≈ 4
✓
Find 3 × 14.2.
Estimate
3 × 14 = 42
14.2
× 3
42.6
one decimal place
14.2
a. 5 × 0.25 1.25
34
14.2
14.2
3 groups of 14.2
Place the decimal point one place from the right.
Check for Reasonableness
Write the following on the board:
1. 429 × 11 = 793
2. 569 × 6 = 3,414
3. 13.3 × 5 = 665
• How would you round to determine if
the third answer is reasonable? Sample
answer: Round 13.3 to 13 and then multiply
by 5: 13 × 5 = 65. The answer is not
reasonable.
E
Find 4 × 0.83.
been
lessons have
Some parts of
rt
pa
these as a
animated. Use
for
or as a review
of the lesson
e.
at a later tim
your students
e.
lable onlin
They are avai
Scaffolding Questions
• Is the second answer reasonable? How
do you know? Sample answer: Yes; round
569 to 600 and multiply: 600 × 6 = 3,600.
D
Multiply Decimals
2 TEACH
• How can you use rounding to tell
whether the first answer is reasonable?
Sample answer: Round 429 to 400 and 11
to 10. Then multiply 400 × 10 = 4,000.
The answer is not reasonable.
C
3. MAKE A CONJECTURE Explain how to find 6 × 4.92.
glencoe.com
Activity Provide each pair of students with
a small object, such as a marker. Have them
measure the length of their object to the
nearest tenth using a metric ruler.
• Have students estimate the length of two
of their object.
B
42.6 ≈ 42
✓
b. 8 × 4.47 35.76
c. 9 × 2.63 23.67
Chapter 1 Multiply and Divide Decimals
Additional Answer
034_043_C1L1_891639.indd 34
2. 4.92 + 4.92 + 4.92 = 14.76; 3 × 5 = 15;
3 × 4.92 = 14.76; 4.92 + 4.92 + 4.92 +
4.92 = 19.68; 4 × 5 = 20; 4 × 4.92 =
19.68; 4.92 + 4.92 + 4.92 + 4.92 + 4.92
= 24.6; 5 × 5 = 25; 5 × 4.92 = 24.6
1/9/09 12:12:49
If there are not enough decimal places in the product, you need to
annex zeros to the left.
Foc us on Mathematical Content
Multiplying a decimal by a whole number is
similar to multiplying two whole numbers.
The only difference is determining where to
place the decimal point in the product.
Annex Zeros in the Product
Everyday Use
Annex to add something
Math Use
Annex to annex a zero
means to place a zero at
the beginning or end of a
decimal
Find 2 × 0.018.
1
0.018
× 2
0.036
three decimal places
Formative Assessment
Use the Check Your Progress exercises after
each Example to determine students’
understanding of concepts.
Annex a zero on the left of 36 to
make three decimal places.
Check by Adding 0.018 + 0.018 = 0.036 ✓
d. 3 × 0.02 0.06
e. 0.12 × 8 0.96
Find 2 × 0.45. 0.90
f. 11 × 0.045 0.495
Find 4 × 18.9. 75.6
Find 3 × 0.016. 0.048
TRAIL MIX A batch of trail
mix calls for 1.2 pounds of
dry cereal. Nigela is making
5 batches of trail mix. She
already has 2.2 pounds of
cereal. How many more pounds
of dry cereal does she need?
Subtracting Decimals
When subtracting
decimals, remember to
line up the decimal points.
e
trate all of th
Examples illus
on
ht in the less
concepts taug
e exercises in
and mirror th
Your
sets. Check
the exercise
ents
st
e
cises giv ud
Progress exer
r
ila
y to try a sim
an opportunit
eir own.
problem on th
34_043_C1L1_891639.indd 35
Step 1
1.2
×5
6.0
Multiply.
one decimal place
one decimal place
MUFFINS A berry muffin recipe calls for
0.75 cups of blueberries. Paul is making
5 batches. He already has 2.5 cups of
blueberries. How many more cups does
he need? 1.25 cups
Step 2
IWB INTERACTIVE WHITEBOARD READY
Subtract.
6.0
- 2.2
3.8
Subtracting Decimals Remind
So, Nigela will need 3.8 more pounds of dry cereal.
students to annex zeros if needed to line
up decimal places.
g. BIRDS A bee hummingbird has a mass of 1.8 grams. How
many grams are 6 hummingbirds and a 4-gram nest? 14.8 g
h. MONEY Rafael has saved $45 for a new computer screen. He
is saving $8.75 a week for 5 weeks for the remaining amount.
What is the total cost of the computer screen? $88.75
Lesson 1-1 Multiply Decimals
35
AL
Alternate Teaching
Strategy
If
students have trouble finding
the product of decimals and whole
numbers,
Then
use the following reteach
option:
1/9/09 12:12:58 PM
Remind them to estimate the product
first. Have them write their estimates
in the margin of their papers before
calculating the actual products. Then
they can compare their solutions with
their estimates.
Lesson 1-1 Multiply Decimals
35
indicates multi-step problem
3 PRACTICE
Examples 1–3
Formative Assessment
(pp. 34–35)
Use Exercises 1–9 to check for understanding.
Then use the table below to customize
assignments for your students.
Example 4
(p. 35)
Odd/Even Assignments
Exercises 10–25 are structured so that students
practice the same concepts whether they are
assigned odd or even problems.
Multiply. 4. $4.98
1. 2.7 × 6 16.2
2. 1.4 × 4 5.6
5. 5 × 0.09 0.45
6. 4 × 0.012 0.048 7. 0.065 × 18 1.17 8. 0.015 × 23
0.345
9
3. 0.52 × 3 1.56
VACATIONS The table shows the number
of gallons of gasoline the Beckleys
purchased on their road trip. What was
the total cost for gas for the trip? Justify
your procedure. $215.27; (12 × $4.89) +
(17 × $4.72) + (15 × $5.09)
4. $0.83 × 6
14.7
69.389
Fuel
Number of Cost per
Gallons Gallon ($)
12
17
15
4.89
4.72
5.09
= Step-by-Step Solutions begin on page R1.
Extra Practice begins on page EP2.
Common Error Students may have
trouble placing the decimal point when
there are leading or trailing zeros. In
Exercise 21, remind students that the
trailing zero in the product may be
deleted.
Examples 1–3
(pp. 34–35)
Multiply.
10. 1.2 × 7 8.4
11. 1.7 × 5 8.5
12. 0.7 × 9 6.3
14. 2 × 1.3 2.6
15. 2.4 × 8 19.2
16. 0.8 × 9 7.2
13. 0.9 × 4 3.6
17. 3 × 0.5 1.5
18. 3 × 0.02 0.06 19. 7 × 0.012 0.084 20. 0.0036 × 19
0.0684
21. 0.0198 × 75
1.485
22. MEASUREMENT Asher recently bought the
poster shown at the right. What is its area?
(Hint: Use A = bh.) 12.8 ft2
23. MEASUREMENT The height of Mount Everest, in
meters, can be found by multiplying 8.85 by 1,000.
Find the height of Mount Everest. Explain your
answer. 8,850 m; 8.85 rounds to 9 and 9 × 1,000 = 9,000
Finding Area In Exercise 22, remind
students to find the area of the poster
by multiplying its base by its height.
Example 4
(p. 35)
AL
24. SCHOOL SUPPLIES Sharon buys 14 folders for $0.75 each. How much
change will she receive if she pays with $15? $4.50
25 TEMPERATURE The hottest temperature recorded in the world, in degrees
Fahrenheit, can be found by multiplying 13.46 by 10. Find this
temperature. Justify your procedure. 134.6° F; 1,346 × 10 = 13,460.
Since 13.46 has 2 decimal places, 13.46 × 10 = 134.60
B 26. MEASUREMENT The thickness of
Thickness
Coin
each type of coin is shown in
(mm)
penny
1.55
the table. How much thicker
nickel
1.95
is a stack of a dollar’s worth
dime
1.35
of nickels than a dollar’s
quarter
1.75
worth of quarters? Explain
your answer. 32 mm; 20 × 1.95 = 39;
4 × 1.75 = 7; 39 - 7 = 32
Visual/Spatial Have students use grid
paper to align their columns and keep
track of the decimal point. Their work
might resemble the following.
2 1 .6
1
6 4 8
2 1 6 2
2 8 1 .0
3.2 ft
OL
ELL
X
4 ft
2
3
6
36
6
Chapter 1 Multiply and Divide Decimals
Differentiated Homework Options
034_043_C1L1_891639.indd 36
ework
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36 Chapter 1 Multiply and Divide Decimals
Level
Assignment
1/28/09 3:54:14
Two-Day Option
AL
Approaching Level
10–24, 27, 29–37
11–23 odd, 31, 32
10–24 even, 27, 29, 30,
33–37
OL
On Level
11–23 odd, 25–27, 29–37
10–24, 31, 32
25–27, 29, 30, 33–37
BL
Beyond Level
25–37
4 ASSESS
27–29. See Ch. 1 C 27. OPEN ENDED Write a real-world problem involving multiplication by
a decimal factor. Then solve the problem.
Answer Appendix.
28. CHALLENGE Discuss two different ways to find the value of the
expression 5.4 × 1.17 × 100 that do not require you to first multiply
5.4 × 1.17.
Ask students to explain the method they
used to solve Exercise 15.
29. REASONING Use the product of 123 × 47 to find the product of
123 × 0.47. Explain the difference in the two products.
30.
NGSSS Practice
31.
Your friend thinks that 1.5 × 8 = 1.20 because you
do not count the zero when placing the decimal point. Is your friend
correct? Justify your reasoning. No; zero represents the number of
hundredths and should be counted.
MA.6.A.1.3
GRIDDED RESPONSE The school
store is selling the following items.
Item
32. The table shows the admission prices
to an amusement park.
Price
Pennant
$2.49
Bumper Sticker
$1.79
Magnet
$0.89
If Miguel buys two pennants, two
bumper stickers, and four magnets,
how much in dollars will he spend for
all the items? 12.12
Estimate.
(Lesson 1-1A)
Admission
Prices
One-Day
Pass
Two-Day
Pass
Adult
Child (ages 3–9)
$39.59
$30.59
$43.99
$33.99
If Yes
What is the total price of one-day
passes for two adults and three
children? B
A. $140.36
C. $179.95
B. $170.95
D. $189.95
34. 3.86 × 5.19 20
12
37. GEOMETRY Find the perimeter of a triangle with
side lengths 2.12 centimeters, 2.03 centimeters, and
1.98 centimeters. (Lesson 0-2) 6.13 cm
Day
Monday
Wednesday
Friday
Reteach Worksheet
(p. 18)
Differentiated Instruction
Option 1 (p. 27c)
If No
OL
Skills Practice Worksheet
CRM
(p. 19)
BL
Enrich Worksheet
CRM
(p. 22)
ovides
Quick Check pr
estions for
reteaching sugg
le.
ntinue to strugg
students who co
Hours
Practiced
2_
1
3
1
1_
3
3
1_
4
NGSSS Practice
Lesson 1-1 Multiply Decimals
, or
New teachers
to teaching
teachers new
may
mathematics,
eciate the
pr
ap
especially
Teachers.
Tips for New
AL
CRM
AL
35. 108.39 × 72.9 7,000
36. SPORTS Kaitlyn recorded the number of hours that she
practiced soccer drills. What was the total time she
5
h
practiced? (Lesson 0-5) 5_
34_043_C1L1_891639.indd 37
Remind students to summarize what they
learned in this lesson under the Multiply
Decimals by Whole Numbers tab of their
Foldables. Encourage them to include several
original examples.
Are students continuing to
struggle with multiplying
decimals by whole numbers?
33–35. Sample answers given.
33. 47.2 × 1.8 100
Follow-Up
Tips for New Teachers
37
1/21/09 9:00:47 AM
Multiplying Decimals When students multiply
by decimals such as 15 × 0.052, they may write
the product as 00.780. Explain that only one zero
is needed to the left of the decimal point, and
that they should omit all zeros after the last
nonzero digit to the right of the decimal point.
Diagnose Student Errors
Survey student responses for each item.
Class trends may indicate common errors
and misconceptions.
32. A. found the cost of one-day passes
for 2 adults and 2 children
B. correct
C. found the cost of 3 adult and
2 children’s one-day passes
D. found for two-day passes instead
of one-day passes
Lesson 1-1 Multiply Decimals
37
Multi-Part Lesson
1-1
PART
Multiply Decimals
A
B
C
D
Multi-Part Lesson
1-1
E
Multipy Decimals
PART
A
B
C
D
E
PART
Multiply Decimals by Decimals
D
Multiply Decimals
by Decimals
Main Idea
NGSSS
Objective
Students will use decimal models to multiply
decimals.
NGSSS
MA.6.A.1.1 Explain and justify procedures
for multiplying and dividing fractions and decimals.
MA.6.A.1.2 Multiply and divide fractions and
decimals efficiently.
You can also model decimals on a 10-by-10 grid.
Use decimal models to
multiply decimals.
Find 0.7 × 0.6. Use decimal models.
MA.6.A.1.1
Explain and justify
procedures for multiplying
and dividing fractions and
decimals.
MA.6.A.1.2 Multiply and
divide fractions and
decimals efficiently.
Draw a 10-by-10
decimal model. Recall
that each small square
represents 0.01.
Shade a rectangle that is
7 tenths units wide and
6 tenths units long.
glencoe.com
0.7
0.6
Resources
Count the number of
shaded squares.
Materials
• 10-by-10 grids
There are forty-two hundredths in the shaded region.
So, 0.7 × 0.6 = 0.42.
Easy-to-Use Manipulatives
Hands-On Activity Tools and Resources
• Decimal Models, p. 2
and Apply
glencoe.com
1–3. See Ch. 1 Answer Appendix for models.
Use decimal models to show each product.
1. 0.3 × 0.3 0.09
1 FOCUS
Have each student explain how to use models
to multiply a decimal by a whole number.
Then review by demonstrating how to use
base-ten blocks to model 2 × 1.23.
4. 1 in each factor and
2 in the product; 1 in
each factor and 2 in the
product; 1 in each factor
and 2 in the product
4. Tell how many decimal places are in each factor and in each
product of Exercises 1–3 above.
5. Is 0.2 × 0.3 equal to 0.6 or 0.06? Justify your reasoning with a
model. 0.06; See margin for model.
6. MAKE A CONJECTURE Use the pattern you discovered in Exercise 4
to find 0.6 × 0.2. Check your conjecture with a model or a
calculator. See margin.
7. Find two decimals with a product of 0.24. Sample answer: 0.6 × 0.4
38
Chapter 1 Multiply and Divide Decimals
Additional Answers
034_043_C1L1_891639.indd 38
5.
Virtual Manipulatives Use a 10-by-10
grid on the Interactive WhiteBoard and
the Virtual Base-Ten Blocks to model the
steps students should follow to multiply
decimals in the lab. Be sure they
understand that each small square in the
grid is a hundredth, and each row or
column is a tenth.
38 Chapter 1 Multiply and Divide Decimals
3. 0.9 × 0.5 0.45
the Results
2 TEACH
Activity 1 Have students read the
multiplication in words: “Seven tenths times six
tenths.” Be sure students understand that each
small square represents 0.01, which is one
hundredth of the 10-by-10 decimal model.
2. 0.4 × 0.9 0.36
0.3
0.2
6. Sample answer: There is 1 decimal place
in each factor, so the product will have
2 decimal places, and you can multiply
normally, but add the decimals from right
to left; 0.12
answers
made to show
Every effort is
n
io
Student Edit
on the reduced
Teacher
margin of the
e
th
in
or
e
g
pa
do not
, answers that
er
ev
ow
H
n.
io
Edit
can be
these places
fit in either of
pages at
er Appendix
found in Answ
ch chapter.
the end of ea
1/9/09 12:13:15
3 ASSESS
Model 0.8 × 0.16. Use an area model.
Activity 2 Make sure students understand
why they need a 10-by-100 grid that shows
thousandths. Reinforce to students that the
model is not to scale.
Since you are multiplying tenths by hundredths, think about a
10-by-100 grid. There are 1,000 squares in all, but you will not
draw them.
100 units
Ask:
• How many decimal places are in the
factors? 3
10 units
• How many decimal places will be in the
product? 3
Draw and shade 8 tenths of the height to model 0.8 and shade
16 hundredths across to model 0.16.
• What is the place value of a decimal with
three places? thousandths
100 units
Use Exercises 1 and 8 to determine whether
students understand how to use models to
multiply decimals.
10 units
0.8
0.16
From Concrete to Abstract Use Exercise 13
to bridge the gap between using models to
find the product of decimals and using rules to
determine where to place the decimal point in
the product.
Find the number of squares shaded. Each square represents one
thousandth of the full rectangle.
There are 128 out of 1,000 squares, or 128 thousandths, shaded.
So, 0.8 × 0.16 = 0.128.
Extending the Concept Have students
discuss how to estimate the product of 0.84 ×
0.9. Sample answer: 0.84 is approximately 1
and 0.9 is approximately 1. 1 × 1 = 1
and Apply
Use decimal models to show each product. 8–10. See students’ work for models.
8. 0.3 × 0.14 0.042
9. 0.8 × 0.03 0.024
10. 0.5 × 0.04 0.020
Additional Answers
13. Sample answer: The total number of
decimals in the factors is the same as
the number of places the decimal is
placed from right to left in the product.
the Results
11. MAKE A CONJECTURE Find the product of 0.04 and 0.08 without using
a model. 0.04 × 0.08 = 0.0032
12. Explain why 0.4 × 0.5 = 0.2. Since 4 rows of 5 will be shaded this represents 0.20 or 0.2.
13. MAKE A CONJECTURE How does the number of decimal places
in the product relate to the number of decimal places in the factors?
14. Analyze each product. 13–14. See margin.
34_043_C1L1_891639.indd 39
a. Explain why the first product is less than 0.6.
b. Explain why the second product is equal to 0.6.
c. Explain why the third product is greater than 0.6.
First
Factor
0.9
1.0
1.5
Second
Factor
×
×
×
0.6
0.6
0.6
Product
=
=
=
0.54
0.60
0.90
Lesson 1-1 Multiply Decimals
39
1/21/09 9:00:59 AM
14a. Sample answer: The first product is less
than the multiplicand because the
multiplier is less than one. You don’t
want all of what you started with, only
a part of a whole, so the product is less
than the multiplicand.
14b. Sample answer: The second product is
equal to the multiplicand because of the
Identity Property. Any number times
one is equal to that number itself.
14c. Sample answer: The third product is
greater than the multiplicand because
the multiplier is more than one. So,
the product is more than what you
started with.
Lesson 1-1 Multiply Decimals
39
Multi-Part Lesson
1-1
PART
Multiply Decimals
A
B
C
D
E
1-1
EE
Multiply
Decimals
by Decimals
PART
Multi-Part Lesson
Multipy Decimals
PART
Main Idea
Multiply decimals by
decimals.
NGSSS
Objective
Students will multiply decimals by decimals.
NGSSS
MA.6.A.1.1 Explain and justify procedures for
multiplying and dividing fractions and decimals.
MA.6.A.1.2 Multiply and divide fractions and decimals
efficiently.
Also addresses MA.6.A.1.3, MA.6.A.5.3.
MA.6.A.1.1
Explain and justify
procedures for multiplying
and dividing fractions and
decimals.
MA.6.A.1.2 Multiply and
divide fractions and
decimals efficiently.
Also addresses MA.6.A.1.3,
MA.6.A.5.3.
glencoe.com
glencoe.com
1 FOCUS
Activity Write the following on the board.
Ask students to evaluate each expression and
describe the pattern in the products.
100 × 7
10 × 7
1×7
0.1 × 7
0.01 × 7
700; 70; 7; 0.7; 0.07; Sample answer: Each
product is one tenth of the previous product.
A
B
C
E
D
Multiply Decimals by Decimals
PLANETS The table shows the
weight of a 1-pound object on
each planet.
1. A 0.5-pound object weighs
one half as much as a
1-pound object. What
would this object weigh
on Jupiter? 1.15 lb
Planet
Weight
(pounds)
Mercury
Venus
Mars
Earth
Jupiter
Saturn
Uranus
Neptune
0.3
0.9
0.3
1
2.3
1
0.8
1.1
2. What would an object that
weighs 5 pounds on Earth
weigh on Jupiter? 11.5 lb
3. MAKE A CONJECTURE How can you use the results of Exercises 1
and 2 to find 0.5 × 2.3? Find 5 × 23 and place the decimal point two
places from the right.
When multiplying a decimal by a decimal, multiply as with whole
numbers. To place the decimal point, find the sum of the number of
decimal places in each factor. The product has the same number
of decimal places.
Multiply Decimals
Find 4.2 × 6.7.
4.2
× 6.7
294
+ 252
28.14
Estimate 4.2 × 6.7
one decimal place
one decimal place
two decimal places
The product is 28.14.
Find 3.6 × 0.05.
3.6
× 0.05
0.180
2 TEACH
Scaffolding Questions
4 × 7 or 28
Compared to the estimate, the product is reasonable.
Estimate 3.6 × 0.05
4 × 0 or 0
one decimal place
two decimal places
three decimal places
The product is 0.180 or 0.18. Once you place the decimal point,
you can drop the zero at the right.
Display the table of download prices.
Downloads
Price
MP3
$0.99
Unlimited play MP3
$1.49
Music video
$2.89
Ask:
• How could you estimate the cost of 3
MP3 downloads? Sample answer: Round
$0.99 to $1, and multiply 1 by 3. So 3
downloads cost about $3.
• How would you estimate the cost of 6
music video downloads? Sample answer:
Round $2.89 to $3 and multiply 3 by 6. So 6
video downloads cost about $18.
40 Chapter 1 Multiply and Divide Decimals
a. 5.7 × 2.8 15.96
40
b. 4.12 × 0.05 0.206 c. 0.014 × 3.7 0.0518
Chapter 1 Multiply and Divide Decimals
• How would you find the estimated cost of
034_043_C1L1_891639.indd 40
8 unlimited play MP3 downloads?
Sample answer: Round $1.49 to $1 and
multiply 1 by 8. So 8 unlimited play
downloads costs about $8.
• Is your estimate for 8 unlimited play
downloads greater or less than the actual
cost? Explain. Sample answer: less, since the
actual cost was rounded down
1/21/09 9:01:03
Internet Research Show students a
video on multiplying decimals. You can
find videos on education video-sharing
Web sites. Have students work in small
groups to take notes on what they
learned. Tell them they will make their
own video in a later lesson.
Annex a Zero
Formative Assessment
Find 1.4 × 0.067.
0.067
× 1.4
268
+ 67
0.0938
Use the Check Your Progress exercises after
each Example to determine students’
understanding of concepts.
three decimal places
one decimal place
Annex a zero to make four decimal places.
Find 8.3 × 2.9. 24.07
d. 0.04 × 0.32 0.0128 e. 0.26 × 0.205 0.0533 f. 1.33 × 0.06 0.0798
Find 5.3 × 0.12. 0.636
Find 2.4 × 0.013. 0.0312
CARS A certain car can travel 28.45 miles with one gallon of
gasoline. The gasoline tank can hold 11.5 gallons. How many
miles can this car travel on a full tank of gas? Justify your
answer.
Estimate 28.45 × 11.5
Real-World Link
A car that can travel
21 miles on one gallon
of gasoline will cost
about $925 per year
more, in gasoline costs
alone, than a car that
can travel 31 miles on
one gallon of gasoline.
28.45
× 11.5
14225
2845
+ 2845
327.175
30 × 12 or 360
two decimal places
one decimal place
MONEY Jennifer makes $8.79 an hour
walking dogs. She walks dogs for 6.75
hours per week. How much money does
she earn each week? $59.33 Justify your
answer. Since $59.3325 is about 9 × 7,
or 63, the answer is reasonable.
IWB INTERACTIVE WHITEBOARD READY
The product has three decimal places.
AL
The car could travel 327.175 miles. Since 327.175 ≈ 360, the
answer is reasonable.
g. 9.375 g; 25 × 375 = 9,375, and there are 3
total decimal places, so the decimal point is
placed 3 places from the right.
g. NUTRITION FACTS A nutrition label indicates that one serving
of apple crisp oatmeal has 2.5 grams of fat. How many grams
of fat are there in 3.75 servings? Justify your answer.
Alternate Teaching
Strategy
If
students have trouble
multiplying decimals by decimals,
Then
use one of these reteach
options:
1 Quick Review Math Handbook,
pp. 131–132
indicates multi-step problem
Examples 1–3
(pp. 40–41)
Example 4
(p. 41)
Multiply. 3. 29.87127
1. 0.6 × 0.5 0.3
2. 1.4 × 2.56 3.584
3. 27.43 × 1.089
4. 0.3 × 2.4 0.72
5 0.52 × 2.1 1.092
6. 0.45 × 0.053 0.02385
7. 2.7 × 1.35 3.645
8. 0.03 × 0.09 0.0027
9. 0.04 × 2.12 0.0848
10. MEASUREMENT A mile is equal to approximately 1.609 kilometers.
How many kilometers is 2.5 miles? Justify your answer. 4.0225 km;
1.609 ≈ 1.5 and 1.5 × 2.5 = 3.75; 3.75 ≈ 4.0225
Lesson 1-1 Multiply Decimals
3 PRACTICE
34_043_C1L1_891639.indd 41
Formative Assessment
Use Exercises 1–10 to check for understanding.
Then use the table on the next page to
customize assignments for your students.
41
Foc us on Mathematical Content
2 Use grid paper to line up the numbers
and keep track of decimal placement.
Some students may benefit from
removing the decimals. Their work
might resemble the following. Have
students highlight the squares in each
factor that are after the decimal. Then
have them count the highlighted
squares, and use that number to
place the decimal.
1/28/09 3:54:34 PM
In adding decimals, the decimal points must
be aligned. In multiplying decimals, the
decimal points are not aligned. The decimals
are multiplied as if they were whole numbers.
The position of the decimal point in the
product is based on the sum of the number
of decimal places in each factor.
X
1 1 8
5
5 9 0
0. 5 9 0
Lesson 1-1 Multiply Decimals
41
Odd/Even Assignments
= Step-by-Step Solutions begin on page R1.
Extra Practice begins on page EP2.
Exercises 11–24 are structured so that students
practice the same concepts whether they are
assigned odd or even problems.
Examples 1–3
(pp. 40–41)
Multiply.
11. 0.7 × 0.4 0.28
12. 1.5 × 2.7 4.05
13. 0.4 × 3.7 1.48
14. 3.1 × 0.8 2.48
15. 0.98 × 7.3 7.154
16. 2.4 × 3.48 8.352
17. 6.2 × 0.03 0.186
18. 5.04 × 3.2 16.128
19. 14.7 × 11.36 166.992
20. 27.4 × 33.68 922.832 21. 0.28 × 0.08 0.0224
Common Error Students may have
trouble remembering the order of
operations in Exercises 29–31. Remind
them to multiply before adding and
subtracting.
Example 4
(p. 41)
22. 0.45 × 0.05 0.0225
23. ANIMALS A giraffe can run up to 46.93 feet per second. How far could a
giraffe run in 1.8 seconds? Justify your answer. 84.474 ft; 46.93 × 1.8 ≈
45 × 2 = 90
24. MEASUREMENT Katelyn has a vegetable garden that measures
16.75 feet in length and 5.8 feet in width. Find the area of
the garden. Justify your answer. 97.15 ft2; 16.75 × 5.8 ≈ 17 × 6 = 102
Multiply.
B
! Exercise Alert!
FIND THE DATA In Exercise 36, students
25. 25.04 × 3.005 75.2452 26. 1.03 × 1.005 1.03515 27. 5.12 × 4.001 20.48512
28. WALKING Junnie walked for 2.5 hours at a speed of 3.2 miles per hour.
Maurice walked for 1.8 hours at a speed of 4.1 miles per hour.
(Hint: distance equals speed times time.)
should use the Data File on pp. 2–5 to write
a real-world problem.
a. Who walked farther? Junnie
b. How much farther did that person walk? 0.62 mile farther
Focus Question Follow-Up
ALGEBRA Evaluate each expression if a = 1.3, b = 0.042, and c = 2.01.
Ask:
• What do you know about multiplying a
whole number by a decimal greater than
1? Sample answer: The product is greater
than the number.
Algebra To show
29.
multiplication with
variables, the variables 31.
and/or numbers are
placed next to each 33.
other.
ab means a × b
6.023a means
34.
6.023 × a.
• What do you know about multiplying a
whole number by a decimal between 0
and 1? Sample answer: The product is less
than the number.
OL
ELL
Intrapersonal Have students work
through at least one problem in this
lesson on their own. Ask them to
describe the steps they used to solve the
problem in a short paragraph. Encourage
students to include an explanation of
why their answers are reasonable when
compared to their original estimates.
Additional Answer
33. 30.39 in2; Since 3.1 × 6.9 = 21.39 and
3(6.1 - 3.1) = 9, then the area of the
figure is 21.39 + 9 or 30.39 in2.
42 Chapter 1 Multiply and Divide Decimals
30. 6.023a - c 5.8199
3.25c + b 6.5745
32. abc 0.109746
6.1 in.
MEASUREMENT Find the area of the figure at
the right. Justify your procedure. See margin.
3 in.
6.9 in.
ALGEBRA Which of the three numbers
9.2,
9.5,
or
9.7
is
the
correct
solution
of
37. Sample answer: If
2.65t = 25.705? Explain your answer.
a = 1.5 and b = 0.2,
9.7; 2.65 × 9.7 = 25.705
then ab = 0.3, which
3.1 in.
is less than 1; if 35 GROCERY SHOPPING Pears cost $0.98 per
pound and apples cost $1.05 per pound.
a = 1.5 and b = 0.8,
then ab = 1.2, which
Mr. Bonilla bought 3.75 pounds of pears and 2.1 pounds of apples.
is not less than 1.
How much did he pay for the pears and apples? Explain your answer.
38. Sample answer: $5.88; Each price is about $1. He bought about 6 pounds of fruit. 6 × 1 = 6 ≈ $5.88
If ab = 0.63, then a 36. FIND THE DATA Refer to the Data File on pages 2–5. Choose some
could be 0.9 and b
data and write a real-world problem in which you would multiply
could be 0.7, which
decimals. See students’ work.
are both less than 1;
if ab = 0.5, then a
For each statement below, find two decimals a and b that make the
could be 0.5, which is
statement true. Then find two decimals a and b that make the
less than 1, but b
would be 1.0, which statement false. Explain your reasoning.
37. If a > 1 and b < 1, then ab < 1.
38. If ab < 1, then a < 1 and b < 1.
is not less than 1.
• Do you think those same rules apply to
dividing by a decimal? Sample answer:
I think they will be the opposite.
AL
ab + c 2.0646
42
Chapter 1 Multiply and Divide Decimals
Differentiated Homework Options
034_043_C1L1_891639.indd 42
Level
Assignment
1/28/09 3:54:47
Two-Day Option
AL
Approaching Level
11–24, 39–42, 46–57
11–23 odd, 47, 48
12–24 even, 39–42, 46,
49–57
OL
On Level
11–27 odd, 28, 29, 31,
33–37, 39–42, 44–57
11–24, 47, 48
25–42, 46, 49–57
BL
Beyond Level
25–57
4 ASSESS
C
39. OPEN ENDED Write a multiplication problem in which the product is
between 0.05 and 0.75. Sample answer: 0.1 × 0.6
Ask students
to write a short paragraph explaining
how the previous lesson on multiplying
decimals by whole numbers helped
them in understanding how to multiply
decimals by decimals.
40. NUMBER SENSE Place the decimal point in the answer to make it
correct. Explain your reasoning. 3.9853 × 8.032856 = 32013341...
40. 32.013341...;
Sample answer:
3.9853 × 8.032856
rounds to 4 × 8 =
32, so the answer
must be about 32.
41. always; Sample
answer: 0.3 × 0.5
= 0.15; 0.75 × 0.6
= 0.45
42. greater than 0.4;
It is being multiplied
by a decimal greater
than 1.
41. REASONING Determine whether the following statement is always,
sometimes, or never true. Give examples to justify your answer.
The product of two decimals less than 1
is less than either of the factors.
42. NUMBER SENSE Is the product of 0.4 × 1.8 greater than or less than
0.4? Explain your reasoning.
Formative Assessment
CHALLENGE Evaluate each expression.
43. 0.3(3 - 0.5) 0.75
46.
NGSSS Practice
44. 0.16(7 - 2.8) 0.672
45. 1.06(2 + 0.58) 2.7348
Describe two methods for determining where to
place the decimal point in the product of two decimals.
See Ch. 1 Answer Appendix.
Are students continuing to
struggle with multiplying
decimals by decimals?
MA.6.A.1.1, MA.6.A.1.2
47. What is the area of the rectangle? D
48.
1.4 cm
5.62 cm
A. 14.04 cm2
C. 8.992 cm2
B. 10.248 cm2
D. 7.868 cm2
SHORT RESPONSE A soccer ball
and 12 golf balls weigh a total of
1 kilogram. Each golf ball weighs
about 0.046 kilogram. What is the
weight of the soccer ball? Explain
your reasoning.
If Yes
If No
48. 0.448 kilogram; The golf balls’ total mass is 12 × 0.046 or 0.552 kilogram.
Multiply.
50. 3.2 × 109 348.8
51. 24 × 5.6 134.4
53. The distance around Earth at the equator is
about 24,889.78 miles. The distance around
Earth through the North Pole and South Pole is
about 24,805.94 miles. (Lesson 1-1A) a–b. Sample answers given.
_4
5
Skills Practice Worksheet
(p. 25)
BL
Enrich Worksheet
CRM
(p. 29)
NGSSS Practice
24,889.78 mi
(Lesson 0-3)
2
7
55. _ + _
1
9
9
_
5
2 3
56. _
-_
8
8 8
_
10
7 3
57. _ - _
11
11 11
Lesson 1-1 Multiply Decimals
4_043_C1L1_891639.indd 43
OL
CRM
24,805.94 mi
b. Estimate how many more miles you would travel if you
circled the equator 10 times rather than 10 times around the poles. about 1,000 mi
5
3
54. _
+_
10
10
Reteach Worksheet
(p. 24)
52. 2.94 × 16 47.04
a. Estimate how many miles you would travel if you
circled the equator 3 times. about 75,000 mi
Add or subtract.
AL
CRM
BL Differentiated Instruction
Option 1 (p. 27c)
(Lesson 1-1C)
49. 45 × 0.27 12.15
Check for student understanding of concepts
in Multi-Part Lesson 1-1.
CRM Chapter Quiz 1, p. 64
43
Diagnose Student Errors
Survey student responses for each item.
Class trends may indicate common errors
and misconceptions.
47. A. found perimeter, not area
B. made mistake in computation
C. made mistake in computation
D. correct
10/1/10 3:21:42 PM
Ask students to compare and contrast multiplying whole numbers and decimals. Sample
answer: Multiplying whole numbers and decimals is similar because you can multiply decimals
as if they were whole numbers. Multiply each digit of one factor by the ones, tens, hundreds, and
so on of the other factor. Multiplying decimals is different from multiplying whole numbers
because you need to place the decimal point in the product. You can count the number of decimal
places in each factor and use this number for the number of decimal places in the product,
annexing zeros to the left if needed.
ctice
NGSSS Pra
lp students
exercises he
knowledge
solidify their
s in a format
using exercise
state test.
similar to the
Lesson 1-1 Multiply Decimals
43