**PART**

**A**

**A**

**B**

**C**

**D**

**E**

**Multiply Decimals**

**Multi-Part Lesson**

**1-1**

**PART**

**Estimate **

**Products**

**Objective**

Students will 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**

**FOCUS**

**1**

**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.

**• **

**• ** **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.

**• **

**• ** **Use the number line to round the **
**following numbers to the nearest whole **
**number: 5.67; 3.41; 9.95. **6; 3; 10

**TEACH**

**2**

**Scaffolding Questions**

**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.

**Tips**

**Tips**

** for New Teachers**

**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.

**Lesson 1-1 **Multiply Decimals **27**
**glencoe.com**

**Multiply Decimals**

**A**

**Multi-Part Lesson**

**1-1**

**PART**

**B**

**C**

**D**

**E**

**Lesson 1-1 **Multiply Decimals **27**

**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.

**1.** Round 7.6 to the nearest whole number. **8 **
**2.** Estimate how many miles James Peters

traveled in 24 hours. **about 24 × 8 or 192 miles**
**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.**

To estimate products of decimals, round each number. Then multiply.

**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.

**Estimate Products Using Rounding**

** Estimate 8.7 × 2.8. **

Round to the nearest whole number to make it easier to compute mentally. 8.7 × 2.8 9 × 3 27 Round 8.7 to 9. Round 2.8 to 3.

The product is about 27.

**Estimate each product.**

**a.** 9.6 × 1.8 **20 b. **8.7 × 2.9** 27 ** **c.** 68.4 × 21.3 **1,400**
**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.**

027_033_C1L1_891639.indd 27 1/9/09 12:11:47 PM

**Key Concept** boxes highlight
definitions, formulas, and
other important ideas. Multiple

representations—words, symbols, examples, and models—help

students understand the concepts.

027_031_C1L1A_891640.indd 27

** Formative Assessment**

Use the Check Your Progress exercises after each Example to determine students’ understanding of concepts.

**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 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.

**INTERACTIVE WHITEBOARDREADY**

**IWB**

**28 Chapter 1 **Multiply and Divide Decimals

**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?**
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.**

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.** **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.

**f. Yes; $1 × 30 = $30 and **
**$2 × 30 = $60. So, they **
**will earn between $30 **
**and $60.**

**Rounding Decimals **
**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.**

027_033_C1L1_891639.indd 28 1/21/09 8:59:27 AM

**Study Tips** offer
students helpful

information about the topics they are studying.

027_031_C1L1A_891640.indd 28

**PRACTICE**

**3**

** Formative Assessment**

Use Exercises 1–8 to check for understanding. Then use the table below to customize assignments for your students.

**Odd/Even Assignments**

Exercises 9–21 are structured so that students practice the same concepts whether they are assigned odd or even problems.

**Differentiated Homework Options**

**Level** **Assignment** **Two-Day Option**

**AL** Approaching Level 9–21, 36–38, 39–44 9–21 odd, 39–42 10–20 even, 36, 38, 39,

43, 44

**OL** On Level 9–25 odd, 26–29, 31, 35,

36, 38–44

9–21, 39–42 22–36, 38, 43, 44

**BL** Beyond Level 22–44

**Lesson 1-1 **Multiply Decimals **29**
**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.

**Check Your Understanding**

exercises are intended to be completed in

class. **Example** references show
students where to look back for review.

In homework exercises in
**Practice **
**and Problem Solving,** the

**Example**
references function in the same way.

**Lesson 1-1 **Multiply Decimals **29**

**Estimate each product. 1–6. Sample answers given. 3. 60 × 30 = 1,800 **

**Example 1**
**(p. 27)**
** 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 ** **5.** 13.92 × 2.7 **6.** 94.89 × 3.11
** ** ** 14 × 3 = 42 ** ** 90 × 3 = 270**
**Example 2**
**(p. 28)**

** 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**

**Example 3**

**(p. 28) 8. MEMORY **Greg has 52 megabytes of free

Media Downloading...

space left on his MP3 player. He wants
to download 7 songs that each use
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.**

=**Step-by-Step Solutions **begin on page R1.

**Extra Practice **is on page EP2.

**Estimate each product. 9–17. Sample answers given. **

**Example 1**
**(p. 27) _{ 9.}**
9.7 × 3.3

**10 × 3 = 3010.**3.4 × 5.6

**3 × 6 = 18**

**1111**17.5 × 8.4

**11. 20 × 8 = 160**

**13. 30 × 80 = 2,400**

**14. 100 × 11 = 1,100**

**12.**26.3

**26 × 10 = 26013.**33.6

**14.**99.1 × 9.7 ×82.1 × 11.2

**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**

**(p. 28)**

** 18. FRUIT **On average, the U.S. produces 36.5 million tons of fruit each
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**

**(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.

** 21. GIFT CARDS **Miguel received a $50 gift card to a bookstore. He would

like to buy 3 books that cost $15.75 each including tax. He estimates
that he cannot buy all three books because each book costs about $20,
and all three books would cost $60. Is his estimate reasonable? Explain
your reasoning. **His estimate is not reasonable. He rounded $15.75 to $20. If he **
**rounded $15.75 to $16, the estimate would be $48 for the three books.**

**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**
**20. Her estimate is **
**not reasonable. **
**Since 12 rounds **
**down to 10 and **
**15.5 rounds to 16 **
**by a lesser amount, **
**her estimate of 10 **
**× 16 = 160 will be **
**too low.**

**indicates multi-step problem**

027_033_C1L1_891639.indd 29 10/1/10 3:19:41 PM

**AL**

** Alternate Teaching **

**Strategy**

**If**

_{students have trouble }

estimating the product of decimals,

**Then**

use one of these reteach
options:

**1 **

**1 ***Quick Review Math Handbook,*

p. 132

**2 **

**2 **Have them use a number line to
practice rounding decimals to the
nearest whole number.

The **Alternate Teaching**
**Strategy** provides

suggestions for remediation for students who did not

grasp the concept.

027_031_C1L1A_891640.indd 29

**30 Chapter 1 **Multiply and Divide Decimals

**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.

**AL** **OL**

**BL**

Visit **glencoe.com** to rewatch
the animated version of “Money
Challenge.”

**30 ** **Chapter 1 **Multiply and Divide Decimals

** 26. GRAPHIC NOVEL **Refer to the graphic novel frame below for Exercises a–b.

**I’ve already saved **
**$68 for the $200 **
**video game system.**

** 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.**

**27**

**27** **MONEY** Hannah’s hourly wage at the ice cream

**Day** **Hours**
**Worked**
Monday 3.5
Tuesday 4.25
Wednesday 3.75
Thursday 2.5
Friday 4.75

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**

**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 **31.** 58.8 × 6

** 32. NUTRITION **The table shows some nutritional **Orange Juice (1 cup)**

Calories 112 Vitamin C 96.9 mg Carbohydrates 26.8 g Calcium 22.4 mg

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**

**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**
**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**
027_033_C1L1_891639.indd 30 1/21/09 8:59:34 AM
027_031_C1L1A_891640.indd 30
027_031_C1L1A_891640.indd 30 3/2/09 11:03:52 AM3/2/09 11:03:52 AM

**ASSESS**

**4**

Have students write how to estimate 8.7 × 2.2.

**Are students continuing to **
**struggle with estimating **
**the product of decimals and judging the **
**reasonableness of the results?**

**If Yes ** **AL** _{ Reteach Worksheet }

**CRM** (p. 12)

**If No ** **OL** _{ Skills Practice Worksheet }

**CRM** _{(p. 13)}

**BL** _{ Enrich Worksheet }

**CRM** (p. 16)

** Follow-Up**

Remind students to keep any notes regarding estimating products under the appropriate tab in their Foldables.

**Lesson 1-1 **Multiply Decimals **31**

**Practice**

**NGSSS**

**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**

**DIVING** **The table gives the scores for the Men’s Synchronized ** **Country** **Points**

China 468.18

Germany 450.42

Russian Federation 445.26 Australia 444.84 United States 440.64

**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**

**Practice** _{MA.6.A.5.3}

**NGSSS**

** 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**

** A.** less than $4

** B.** between $5 and $6

** C.** between $6 and $7

** D.** more than $7

** 40.** Medina’s school lunch menu is shown.

**Pizza $1.75 Fruit Punch $0.75**
**Fish and Fries $2.25 Milk ** **$0.80**
**Salad $1.15 Pudding $0.85**

**Friday**

Which of the following is a reasonable
estimate for the cost of two slices of
pizza, a salad, and fruit punch? **G**

** F.** $4 **H.** $8

** G.** $6 **I.** $10

** 41. ** Mario and Andrew’s hourly charge for
mowing lawns is shown.

**Mario** **Andrew**
$8.25/hr $5.85/hr

Suppose Mario and Andrew each
worked 20 hours. About how much
more money did Mario earn? **B**

** A.** $30

** B.** $40

** C.** $60

** D.** $70

** 42.** **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**

**C** ** 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.**
**36. Sample answer: **

**1.9 × 5.3 × 3.81**

027_033_C1L1_891639.indd 31 1/9/09 12:12:07 PM

**H.O.T.** Problems require
students to use **Higher **

**Order Thinking skills to **
solve problems.

027_031_C1L1A_891640.indd 31

**Multiply Decimals **

**by Whole Numbers **

**Objective**

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.**

**Resources**

**Manipulatives**

**•**

**•**base-ten blocks

**Easy-to-Use Manipulatives**

*Hands-On Activity Tools and Resources*

**• **

**• ** Base-Ten Models, p. 1

**glencoe.com**

**FOCUS**

**1**

Write these numbers on the board: 3.41 4.12 1.04

**Ask: **

**• **

**• ** **Which number has a 4 in the ones **
**place? **4.12

**• **

**• ** **Which number has no tenths? **1.04

**• **

**• ** **Which number has a 1 in the hundredths **
**place? **3.41

**TEACH**

**2**

**Activity 1 **Have students work in pairs to
model and check each step.

**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

**PART**

**B**

**A**

_{B}**C**

**D**

**E**

**Multiply Decimals**

**Multi-Part Lesson**

**1-1**

**PART**

**Percents**

**A**

**Multi-Part Lesson**

**1-1**

**PART**

**B**

**C**

**D**

**E**

**glencoe.com**

**Multiply Decimals **

**A**

**Multi-Part Lesson**

**1-1**

**PART**

**B**

**C**

**D**

**E**

**32 ** **Chapter 1 **Multiply and Divide Decimals

**Main Idea**

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.**

**Multiply Decimals by **

**Whole Numbers**

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.

** WALKING **Louisa walked her dog 0.2 mile on Monday, Wednesday,
and Friday. Find the total distance Louisa walked all week.

**What do you need to find? **the total distance Louisa walked
Just as 3 **×** 2 means 3 groups

3 groups

of 2, 3 **×** 0.2 means 3 groups
of 2 tenths. Model three groups
of two tenths using base-ten blocks.

Combine the tenths. There are six tenths.

So, 3 × 0.2 = 0.6. Louisa walked a total of 0.6 mile.

** and Apply **

**1–8. Check students’ work for models.**

**Use base-ten blocks to find each product.**

** 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**

027_033_C1L1_891639.indd 32 1/9/09 12:12:13 PM

032_033_C1L1B_891640.indd 32

**Activity 2 **Point out that 10 tenths can be
combined to make one whole.

**ASSESS**

**3**

Use Exercises 9–16 to assess whether students know how to use models to multiply a decimal by a whole number.

**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.

**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

**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.

** 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.

** 19. **Sample answer: The product is greater
than the whole number. For example,
5 × 1.8 = 9 and 5 × 0.8 = 4.

** 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.

**Lesson 1-1 **Multiply Decimals **33**

**Lesson 1-1 **Multiply Decimals **33**
Model 2 ** _{×}** 1.6 to find the product.

Model two groups of one and six tenths.

2 groups

Combine the ones. Then combine the tenths.

one whole

Combine the 10 tenths into 1 whole.

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 **

**17–20. See margin.**

** 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
whole number? Explain your answer.

** 20.** Write a rule that you can use to multiply a whole
number by a decimal without using base-ten blocks.

027_033_C1L1_891639.indd 33 1/9/09 12:12:24 PM

**Write Math** features help
students learn to use the

language of mathematics.

032_033_C1L1B_891640.indd 33

**Additional Answer**
** 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

**34 Chapter 1 **Multiply and Divide Decimals

**Objective**

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.*

**glencoe.com**

**FOCUS**

**1**

**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.

**• **

**• ** Have students find the length of 3, 5, and
10 of their object.

**TEACH**

**2**

**Scaffolding Questions**

Write the following on the board: 1. 429 × 11 = 793

2. 569 × 6 = 3,414 3. 13.3 × 5 = 665

**• **

**• ** **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.

**• **

**• ** **Is the second answer reasonable? How **
**do you know? **Sample answer: Yes; round
569 to 600 and multiply: 600 × 6 = 3,600.

**• **

**• ** **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.

**• **

**• ** **What is the error in the third answer? **

The decimal place was not shown.

**Multiply **

**Decimals by **

**Whole Numbers**

**PART**

**C**

**A**

**B**

_{C}**D**

**E**

**Multiply Decimals**

**Multi-Part Lesson**

**1-1**

**PART**

**glencoe.com**

**Multiply Decimals **

**A**

**Multi-Part Lesson**

**1-1**

**PART**

**B**

**C**

**D**

**E**

**34 ** **Chapter 1 **Multiply and Divide Decimals

**Main Idea**

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.*

**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.**
**1.** Use the addition problem and the

estimate to find 2 × 4.92. **9.84**

**2.** Write an addition problem, an estimate, and a multiplication
problem to find the total growth over 3 days, 4 days, and 5 days.
**3. MAKE A CONJECTURE **Explain how to find 6 × 4.92.

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.

**Multiply Decimals **

** Find 4 × 0.83. **

**0.83** **0.83** **0.83** **0.83**

4 groups of 0.83
**Estimate** 4**×** 1 **=** 4

0.83 two decimal places

× 4

3.32 Place the decimal point two places from the right.
**Check for Reasonableness** 3.32**≈ **4 ✓

** Find 3 × 14.2. **

**14.2** **14.2** **14.2**

3 groups of 14.2
**Estimate** 3**×** 14 **=** 42

14.2 one decimal place

× 3

42.6 Place the decimal point one place from the right.
**Check for Reasonableness** 42.6**≈** 42 ✓

**a.** 5 × 0.25 **1.25 b. **8 × 4.47** 35.76 ** **c.** 9 × 2.63 **23.67**
**Growth of Bamboo Over Two Days**
Add. 4.92 ft + 4.92 ft = 9.84 ft
Estimate. 4.92 is about 5._{2}

× 5 = 10 Multiply. 2 × 4.92 ft =

**3. Multiply 6 by 492. Place **
**the decimal point two **
**places from the right.**

034_043_C1L1_891639.indd 34 1/9/09 12:12:49 PM

Some parts of lessons have been animated. Use these as a part of the lesson or as a review

for your students at a later time.

They are available online.

034_037_C1L1C_891640.indd 34

**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.
** Formative Assessment**

Use the Check Your Progress exercises after each Example to determine students’ understanding of concepts.

**Subtracting Decimals **

Remind
students to annex zeros if needed to line
up decimal places.
**AL**

** Alternate Teaching **

**Strategy**

**If**

students have trouble finding
the product of decimals and whole numbers,

**Then**

use the following reteach
option:

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**

Find 2 × 0.45. 0.90 Find 4 × 18.9. 75.6 Find 3 × 0.016. 0.048

** 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

**INTERACTIVE WHITEBOARDREADY**

**IWB**

**Lesson 1-1 **Multiply Decimals **35**
If there are not enough decimal places in the product, you need to
annex zeros to the left.

**Annex Zeros in the Product**

** Find 2 × 0.018.**

** 1**

0.018 three decimal places

× 2 0.036

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 ** **f.** 11 × 0.045 **0.495**

** 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?**

**Step 1** Multiply. **Step 2** Subtract.

1.2 one decimal place 6.0

× 5 - 2.2

6.0 one decimal place 3.8

So, Nigela will need 3.8 more pounds of dry cereal.

**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**

**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

**Subtracting Decimals**

When subtracting decimals, remember to line up the decimal points.

034_043_C1L1_891639.indd 35 1/9/09 12:12:58 PM

**Examples** illustrate all of the
concepts taught in the lesson
and mirror the exercises in

the exercise sets. **Check Your **
**Progress** exercises give student

s an opportunity to try a similar

problem on their own.

034_037_C1L1C_891640.indd 35

The **Differentiated Homework **

**Options** provide suggestions for the

exercises that are appropriate for basic, core, or advanced students. Many of

the homework exercises are paired so

that students could do the od ds one

day and the evens the next day.

**PRACTICE**

**3**

** Formative Assessment**

Use Exercises 1–9 to check for understanding. Then use the table below to customize assignments for your students.

**Odd/Even Assignments**

Exercises 10–25 are structured so that students practice the same concepts whether they are assigned odd or even problems.

**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.

**Differentiated Homework Options**

**Level** **Assignment** **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

**36 Chapter 1 **Multiply and Divide Decimals

**Finding Area **

In Exercise 22, remind
students to find the area of the poster
by multiplying its base by its height.
**Visual/Spatial **

Have students use grid
paper to align their columns and keep
track of the decimal point. Their work
might resemble the following.
**AL** **OL**
**ELL**
**2 1 .**
**.**
**6 2**
**6 4 8 6**
**6**
**2 1 6 2**
**2 8 1 0**
**1 3**
**X**

**36 ** **Chapter 1 **Multiply and Divide Decimals
**Multiply. 4. $4.98**
**Examples 1–3**
**(pp. 34–35) _{ 1.}**
2.7 × 6

**16.2**

**2.**1.4 × 4

**5.6**

**3.**0.52 × 3

**1.56 4.**$0.83 × 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**

**Example 4**

**(p. 35)**

**9**

**9** **VACATIONS** The table shows the number **14.7** **69.389**

**Fuel**
**12 4.89**
**17 4.72**
**15 5.09**
**Number of**
**Gallons**
**Cost per**
**Gallon ($)**
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)**

= **Step-by-Step Solutions **begin on page R1.

**Extra Practice **begins on page EP2.

**Multiply. **
**Examples 1–3**
**(pp. 34–35)**
** 10.** 1.2 × 7 **8.4 ** **11.** 1.7 × 5 **8.5 ** **12.** 0.7 × 9 **6.3 13. **0.9 × 4 **3.6**
** 14. ** 2 × 1.3 **2.6 ** **15.** 2.4 × 8 **19.2 ** **16.** 0.8 × 9 **7.2 17. **3 × 0.5 **1.5**
** 18.** 3 × 0.02 **0.06 ** **19.** 7 × 0.012 **0.084 20.** 0.0036 × 19 ** 21. **0.0198 × 75
**0.0684** **1.485**

** 22. MEASUREMENT **Asher recently bought the

3.2 ft 4 ft

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**

**Example 4**

**(p. 35)**

** 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**

**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

**Coin** **Thickness**
**(mm)**
penny 1.55
nickel 1.95
dime 1.35
quarter 1.75
each type of coin is shown in

the table. How much thicker is a stack of a dollar’s worth of nickels than a dollar’s worth of quarters? Explain

your answer. **32 mm; 20 × 1.95 = 39; **
**4 × 1.75 = 7; 39 - 7 = 32**

**indicates multi-step problem**

034_043_C1L1_891639.indd 36 1/28/09 3:54:14 PM

034_037_C1L1C_891640.indd 36

**ASSESS**

**4**

Ask students to explain the method they used to solve Exercise 15.

** Follow-Up**

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?**

**If Yes ** _{ }**AL** _{ Reteach Worksheet }

**CRM** _{(p. 18)}

**AL** _{ Differentiated Instruction }
Option 1 (p. 27c)

**If No ** _{ }**OL** _{ Skills Practice Worksheet }

**CRM** _{(p. 19)}

**BL** _{ Enrich Worksheet }

**CRM** (p. 22)

**Practice**

**NGSSS**

**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

**Tips**

**Tips**

** for New Teachers**

**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.

**Lesson 1-1 **Multiply Decimals **37**
**Quick Check** provides

reteaching suggestions for students who continue to struggle.

**Lesson 1-1 **Multiply Decimals **37**
**C** ** 27. OPEN ENDED **Write a real-world problem involving multiplication by

a decimal factor. Then solve the problem.

** 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.

** 29.** **REASONING** Use the product of 123 × 47 to find the product of

123 × 0.47. Explain the difference in the two products.

** 30.** 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.**

**Estimate.** (Lesson 1-1A) **33–35. Sample answers given.**

**33.** 47.2 × 1.8 **100 ** **34.** 3.86 × 5.19 **20 ** **35.** 108.39 × 72.9 **7,000**

** 36. SPORTS **Kaitlyn recorded the number of hours that she _{Day}**Hours**
**Practiced**
Monday 2 _1_{3}
Wednesday 1 _1

3

Friday 1 _3_{4}

practiced soccer drills. What was the total time she

practiced? (Lesson 0-5) **5 _ 5**

**12 h**

** 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**

**Practice** _{MA.6.A.1.3}

**NGSSS**

** 31.** **GRIDDED RESPONSE** The school
store is selling the following items.

**Item** **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**

** 32.** The table shows the admission prices

to an amusement park.
**Admission**
**Prices**
**One-Day**
**Pass**
**Two-Day**
**Pass**
**Adult** $39.59 $43.99
**Child (ages 3–9)** $30.59 $33.99

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
**27–29. See Ch. 1 **
**Answer Appendix.**
034_043_C1L1_891639.indd 37 1/21/09 9:00:47 AM
New teachers, or
teachers new to teaching

mathematics, may especially appreciate the

**Tips for New Teachers.**

034_037_C1L1C_891640.indd 37

**Multiply Decimals **

**by Decimals**

**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.**

**Resources**

**Materials**

**•**

**•**10-by-10 grids

**Easy-to-Use Manipulatives**

*Hands-On Activity Tools and Resources*

**• **

**• ** Decimal Models, p. 2

**glencoe.com**

**FOCUS**

**1**

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.

**TEACH**

**2**

**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.

**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.

**Additional Answers**
**5. **

0.2 0.3

**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

**38 Chapter 1 **Multiply and Divide Decimals

**PART**

**D**

**A**

**B**

**C**

_{D}**E**

**Multiply Decimals**

**Multi-Part Lesson**

**1-1**

**PART**

**glencoe.com**

**Multipy Decimals**

**A**

**Multi-Part Lesson**

**1-1**

**PART**

**B**

**C**

**D**

**E**

**38 ** **Chapter 1 **Multiply and Divide Decimals

**Multiply Decimals by Decimals**

You can also model decimals on a 10-by-10 grid.

**Find 0.7 _{×} 0.6. Use decimal models.**
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.

0.6 0.7

Count the number of shaded squares.

There are *forty-two hundredths *in the shaded region.
So, 0.7 × 0.6 = 0.42.

** and Apply **

**1–3. See Ch. 1 Answer Appendix for models.**

**Use decimal models to show each product.**

**1.** 0.3 × 0.3 **0.09 2. **0.4 × 0.9 **0.36 3. **0.9 × 0.5 **0.45**

** the Results**

**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**
**Main Idea**

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.**

**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**

034_043_C1L1_891639.indd 38 1/9/09 12:13:15 PM

Every effort is made to show
**answers**
on the reduced Student Edit

ion page or in the margin of the Teacher

Edition. However, answers that do not fit in either of these places can be

found in **Answer Appendix**

pages at the end of each chapter.

038_039_C1L1D_891640.indd 38

**ASSESS**

**3**

**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.

**Ask:**

**• **

**• ** **How many decimal places are in the **
**factors?** 3

**• **

**• ** **How many decimal places will be in the **
**product?** 3

**• **

**• ** **What is the place value of a decimal with **
**three places?** thousandths

Use Exercises 1 and 8 to determine whether students understand how to use models to multiply decimals.

**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.

**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

**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.

** 14a. **Sample answer: The fi rst 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**

**Lesson 1-1 **Multiply Decimals **39**
**Model 0.8 × 0.16. Use an area model.**

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

10 units

Draw and shade 8 tenths of the height to model 0.8 and shade 16 hundredths across to model 0.16.

100 units

10 units 0.8

0.16

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.

** 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**

** 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. ** **First** **Second** _{Product}

**Factor** **Factor**

0.9 × 0.6 = 0.54 1.0 × 0.6 = 0.60 1.5 × 0.6 = 0.90

** 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.

034_043_C1L1_891639.indd 39 1/21/09 9:00:59 AM

038_039_C1L1D_891640.indd 39

**• **

**• ** **How would you find the estimated cost of **
**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

**40 Chapter 1 **Multiply and Divide Decimals

**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.*

**glencoe.com**

**FOCUS**

**1**

**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.

**TEACH**

**2**

**Scaffolding Questions**

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.

**Multiply **

**Decimals **

**by Decimals**

**PART**

**E**

**A**

**C**

**D**

**E**

**PART**

**A**

**B**

**C**

**D**

_{E}**Multiply Decimals**

**Multi-Part Lesson**

**1-1**

**PART**

**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.
**glencoe.com**

**Multipy Decimals**

**A**

**Multi-Part Lesson**

**1-1**

**PART**

**B**

**C**

**D**

**E**

**40 ** **Chapter 1 **Multiply and Divide Decimals

**Main Idea**

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.*

**Multiply Decimals by Decimals**

**PLANETS**The table shows the

** Mercury ** **0.3**
** Venus ** **0.9**
** Mars ** **0.3**
** Earth ** **1**
** Jupiter ** **2.3**
** Saturn ** **1**
** Uranus ** **0.8**
** Neptune ** **1.1**
**Planet** **Weight**
**(pounds)**

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**

**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. ** **Estimate** 4.2**×** 6.7 4**×** 7 or 28

4.2 one decimal place

× 6.7 one decimal place

294 + 252

28.14 two decimal places

The product is 28.14. Compared to the estimate, the product is reasonable.

** Find 3.6 × 0.05. ** **Estimate** 3.6**×** 0.05 4 **×** 0 or 0

3.6 one decimal place

× 0.05 two decimal places

0.180 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.

**a.** 5.7 × 2.8 **15.96 b. **4.12 × 0.05** 0.206 ** **c.** 0.014 × 3.7 **0.0518**

034_043_C1L1_891639.indd 40 1/21/09 9:01:03 AM

040_043_C1L1E_891640.indd 40

**AL**

** Alternate Teaching **

**Strategy**

**If**

students have trouble
multiplying decimals by decimals,

**Then**

use one of these reteach
options:

**1 **

**1 ***Quick Review Math Handbook, *

pp. 131 –132

**2 **

**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.

** Formative Assessment**

Use the Check Your Progress exercises after each Example to determine students’ understanding of concepts.

**PRACTICE**

**3**

** Formative Assessment**

Use Exercises 1–10 to check for understanding. Then use the table on the next page to

customize assignments for your students.

**Foc**

**us on Mathematical Content**

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.

**Lesson 1-1 **Multiply Decimals **41**

Find 8.3 × 2.9. 24.07 Find 5.3 × 0.12. 0.636 Find 2.4 × 0.013. 0.0312

** 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.

**INTERACTIVE WHITEBOARDREADY**

**IWB**

**Annex a Zero**

** Find 1.4 × 0.067.**

0.067 three decimal places

× 1.4 one decimal place

268 + 67

0.0938 Annex a zero to make four decimal places.

**d.** 0.04 × 0.32 **0.0128 e. **0.26 × 0.205** 0.0533 f.** 1.33 × 0.06 **0.0798**

** 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 30** × **12 or 360

28.45 two decimal places

× 11.5 one decimal place

14225 2845 + 2845

327.175 The product has three decimal places.

The car could travel 327.175 miles. Since 327.175 ≈ 360, the answer is reasonable.

**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.

**Multiply. ** **3. 29.87127**
**Examples 1–3**
**(pp. 40–41) _{ 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**

**55**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**

**Example 4**

**(p. 41)**

** 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**

**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.

**indicates multi-step problem**

**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.**

**Lesson 1-1 **Multiply Decimals **41**

034_043_C1L1_891639.indd 41 1/28/09 3:54:34 PM
**1 1**
**.**
**8**
**5 9 0**
**0 5 9 0**
**5**
**X**
040_043_C1L1E_891640.indd 41
040_043_C1L1E_891640.indd 41 3/2/09 11:14:45 AM3/2/09 11:14:45 AM

**Odd/Even Assignments**

Exercises 11–24 are structured so that students practice the same concepts whether they are assigned odd or even problems.

**Common Error **Students may have
trouble remembering the order of
operations in Exercises 29–31. Remind
them to multiply before adding and
subtracting.

**!**

_{ Exercise Alert!}

_{ Exercise Alert!}

**FIND THE DATA **

In Exercise 36, students
should use the Data File on pp. 2–5 to write
a real-world problem.
**Focus Question Follow-Up**

**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.

**• **

**• ** **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.

**• **

**• ** **Do you think those same rules apply to **
**dividing by a decimal? **Sample answer:
I think they will be the opposite.

**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.
**AL** **OL**

**ELL**

**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
fi gure is 21.39 + 9 or 30.39 in2_{.}

**Differentiated Homework Options**

**Level** **Assignment** **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

**42 Chapter 1 **Multiply and Divide Decimals

**42 ** **Chapter 1 **Multiply and Divide Decimals

= **Step-by-Step Solutions **begin on page R1.

**Extra Practice **begins on page EP2.

**Multiply.**
**Examples 1–3**
**(pp. 40–41) _{ 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**

**22.**0.45 × 0.05

**0.0225**

**Example 4**

**(p. 41)**

** 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** ** 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.)

** a. ** Who walked farther? **Junnie**

** b. ** How much farther did that person walk? **0.62 mile farther**

**ALGEBRA** **Evaluate each expression if ****a****= 1.3, ****b****= 0.042, and ****c****= 2.01.**

** 29.** *ab*+*c* **2.0646 ** **30.** 6.023*a*-*c* **5.8199**
** 31.** 3.25*c*+*b* **6.5745 ** **32.** _{abc}**0.109746**

**33. MEASUREMENT **Find the area of the figure at

3 in. 6.9 in.

3.1 in. 6.1 in.

the right. Justify your procedure. **See margin.**
**34. ALGEBRA **Which of the three numbers

9.2, 9.5, or 9.7 is the correct solution of
2.65*t*= 25.705? Explain your answer.
**9.7; 2.65 × 9.7 = 25.705**

**35**

**35 GROCERY SHOPPING **Pears cost $0.98 per
pound and apples cost $1.05 per pound.

Mr. Bonilla bought 3.75 pounds of pears and 2.1 pounds of apples. How much did he pay for the pears and apples? Explain your answer.

** 36. FIND THE DATA **Refer to the Data File on pages 2–5. Choose some

data and write a real-world problem in which you would multiply
decimals. **See students’ work.**

**For each statement below, find two decimals ****a**** and ****b**** that make the **

**statement true. Then find two decimals ****a**** and ****b**** that make the **

**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.
**37. Sample answer: If **
**a****= 1.5 and ****b****= 0.2, **
**then ****ab****= 0.3, which **
**is less than 1; if **
**a****= 1.5 and ****b****= 0.8, **
**then ****ab****= 1.2, which **
**is ****not**** less than 1.**
**38. Sample answer: **
**If ****ab****= 0.63, then ****a****could be 0.9 and ****b****could be 0.7, which **
**are both less than 1; **
**if ****ab****= 0.5, then ****a****could be 0.5, which is **
**less than 1, but ****b****would be 1.0, which **
**is ****not**** less than 1.**
**Algebra**To show
multiplication with
variables, the variables
and/or numbers are
placed next to each
other.

*ab* means *a***×***b*
6.023*a* means
6.023**×***a*.

**$5.88; Each price is about $1. He bought about 6 pounds of fruit. 6 × 1 = 6 ≈ $5.88**

034_043_C1L1_891639.indd 42 1/28/09 3:54:47 PM

040_043_C1L1E_891640.indd 42

**ASSESS**

**4**

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.

** Formative Assessment**

Check for student understanding of concepts in Multi-Part Lesson 1-1.

**CRM** Chapter Quiz 1, p. 64

**Are students continuing to **
**struggle with multiplying **
**decimals by decimals?**

**If Yes ** _{ }**AL** _{ Reteach Worksheet }

**CRM** _{(p. 24)}

**If No ** **OL** _{ Skills Practice Worksheet }

**CRM** (p. 25)
**BL** _{ Enrich Worksheet }
**CRM** _{(p. 29)}
**BL** _{ Differentiated Instruction }
Option 1 (p. 27c)

**Practice**

**NGSSS**

**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

**Lesson 1-1 **Multiply Decimals **43**

**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.

**Multiply.** (Lesson 1-1C)

** 49.** 45 × 0.27 **12.15 50. **3.2 × 109 **348.8 51.** 24 × 5.6 **134.4 52. **2.94 × 16 **47.04**
** 53.** The distance around Earth at the equator is 24,805.94 mi

24,889.78 mi

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.**

**a.** Estimate how many miles you would travel if you
circled the equator 3 times. **about 75,000 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**
**Add or subtract.** (Lesson 0-3)

** 54.** _ 3
10+
5
_
10 ** **
**4**

**_ **

**_ 2 9+ 7 _ 9**

_{5}55.**1 56.**5 _ 8- 2 _ 8

**3**

**_ **

**_ 10 11- 7 _ 11**

_{8}57.

**3**

**_ **

_{11}**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**

** 40. NUMBER SENSE **Place the decimal point in the answer to make it
correct. Explain your reasoning. 3.9853 × 8.032856 = 32013341...

** 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.

**CHALLENGE** **Evaluate each expression.**

** 43.** 0.3(3 - 0.5) **0.75 ** **44.** 0.16(7 - 2.8) **0.672 ** **45.** 1.06(2 + 0.58) **2.7348**

** 46.** Describe two methods for determining where to

place the decimal point in the product of two decimals.
**See Ch. 1 Answer Appendix.**

**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.**

**48. 0.448 kilogram; The golf balls’ total mass is 12 × 0.046 or 0.552 kilogram.**
**Practice** _{MA.6.A.1.1, MA.6.A.1.2}

**NGSSS**

** 47.** What is the area of the rectangle? **D**

5.62 cm

1.4 cm

** A.** 14.04 cm2 _{C.}_{ 8.992 cm}2

** B.** 10.248 cm2 _{D.}_{ 7.868 cm}2

** 48.** **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.

**Lesson 1-1 **Multiply Decimals **43**

034_043_C1L1_891639.indd 43 10/1/10 3:21:42 PM

**NGSSS Practice**
exercises help students

solidify their knowledge using exercises in a format

similar to the state test.

040_043_C1L1E_891640.indd 43