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Chapter 8Multiply by Two-Digit Numbers
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Lesson 8-1 Multiply by TensLesson 8-2 Estimate ProductsLesson 8-3 Problem-Solving Strategy: Act
It OutLesson 8-4 Multiply Two-Digit NumbersLesson 8-5 Multiply Three-Digit Numbers
by Two-Digit NumbersLesson 8-6 Problem-Solving Investigation:
Choose a StrategyLesson 8-7 Multiply Greater Numbers
8Multiply by Two-Digit Numbers
Five-Minute Check (over Chapter 7)Main IdeaCalifornia StandardsExample 1Example 2
8-1 Multiply by Tens
8-1 Multiply by Tens
Standard 4NS3.3 Solve problems involving the multiplication of multidigit numbers by two-digit numbers.
8-1 Multiply by Tens
Standard 4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.
There are 35 packs of markers in an art classroom. Each pack contains 50 markers. How many markers are there in all?
You need to find 35 × 50.
8-1 Multiply by Tens
8-1 Multiply by Tens
One Way: Use Properties
35 × 5035 × (10 × 5)35 × (5 × 10)
(35 × 5) × 10175 × 10
1,750
Write the problem.Think of 50 as 10 × 5.Commutative PropertyAssociative PropertyMultiply. 35 × 5 = 175 Mental Math.
8-1 Multiply by Tens
Another Way: Paper and Pencil
3550×
Step 1 Multiply the ones.
0
Step 2 Multiply the tens.
3550×
01,75
Answer: So, there are 1,750 markers in all.
A store has 20 children’s bicycles in stock that cost $159 each. How much do all of the bicycles cost altogether?
Step 1 Multiply the ones.
8-1 Multiply by Tens
×$159
200
Step 2 Multiply the tens.
8-1 Multiply by Tens
×$159
200$3,18
Answer: So, all of the bicycles cost $3,180.
Check
8-1 Multiply by Tens
20 × $159 Write the problem.(2 × 10) × $159 Think of 20 as 2 × 10.(10 × 2) × $159 Commutative Property10 × (2 × $159) Associative Property
10 × $318 Multiply. 2 × $159 = $318.$3,180 Mental Math
So, the answer is correct.
Think of 20 × 159 as 2 × 10 × 159.
Five-Minute Check (over Lesson 8-1)Main IdeaCalifornia StandardsExample 1Example 2
8-2 Estimate Products
8-2 Estimate Products
Standard 4NS3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.
Standard 4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
Kaylee is awake for about 16 hours each day. About how many hours is she awake in 3 weeks?
There are 21 days in 3 weeks. So, estimate 16 × 21. Round each factor to its greatest place. Then multiply.
8-2 Estimate Products
Step 1 Round each factor to the nearest ten.
×1621 ×
2020
Step 2 Multiply.
8-2 Estimate Products
Answer: So, Kaylee is awake for about 400 hours in 3 weeks.
×2020
400
8-2 Estimate Products
A. 400
B. 425
C. 450
D. 500
A koala sleeps for about 19 hours a day. About how many hours does one sleep in 3 weeks?
A company bought 53 computers for $909 each. About how much did they spend in all? You need to estimate $909 × 53.
Step 1 Round each factor to its greatest place.
8-2 Estimate Products
×90953 ×
90050
Step 2 Multiply.
Answer: So, the company spent about $45,000.
8-2 Estimate Products
×90050
45,000
8-2 Estimate Products
A. $45,000
B. $48,000
C. $53,000
D. $56,000
A school bought 57 laptops for $837 each. About how much did the school spend in all?
Five-Minute Check (over Lesson 8-2)Main IdeaCalifornia StandardsExample 1: Problem-Solving Strategy
8-3 Problem-Solving Strategy: Act It Out
8-3 Problem-Solving Strategy: Act It Out
• I will solve a problem by acting it out.
8-3 Problem-Solving Strategy: Act It Out
Standard 4MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
8-3 Problem-Solving Strategy: Act It Out
Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.
8-3 Problem-Solving Strategy: Act It Out
Sonoda has 6 coins in his bank. The coins equal 65¢. What combination of coins does he have in his bank?
Understand
What facts do you know?• Sonoda has 6 coins.• The value of the 6 coins is 65¢.
What do you need to find?• Find the coins Sonoda has in his bank.
8-3 Problem-Solving Strategy: Act It Out
Plan
8-3 Problem-Solving Strategy: Act It Out
You can use play money to act out different combinations of 65¢.
Solve
8-3 Problem-Solving Strategy: Act It Out
One way to make 65¢ is with 2 quarters, 1 dime, and 1 nickel. But, that is the only 4 coins. You need two more coins.
Solve
Take 1 quarter and exchange it for 2 dimes and 1 nickel. The value stays the same, and the number of coins increases to 6.
Answer: So, Sonoda has 1 quarter, 3 dimes, and 2 nickels.
8-3 Problem-Solving Strategy: Act It Out
Check
Look back at the problem.
So, the answer is correct.
1 quarter + 3 dimes + 2 nickels
8-3 Problem-Solving Strategy: Act It Out
= (1 × 25 ) + (3 × 10 ) + (2 × 5 )
= 65= 25 + 30 + 10
Five-Minute Check (over Lesson 8-3)Main IdeaCalifornia StandardsExample 1Example 2
8-4 Multiply Two-Digit Numbers
8-4 Multiply Two-Digit Numbers
Standard 4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use the relationships between them to simplify computations and to check results.
8-4 Multiply Two-Digit Numbers
Preparation for Standard 4NS3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.
How far can a truck travel in 14 hours if it is traveling an average of 57 miles per hour?
8-4 Multiply Two-Digit Numbers
8-4 Multiply Two-Digit Numbers
One Way: Partial Products
5714×28
20070
500+
Multiply 4 × 7.Multiply 4 × 50.Multiply 10 × 7.Multiply 10 × 50.Add partial products.798
8-4 Multiply Two-Digit Numbers
Another Way: Paper and Pencil
5714×
228
Step 1 Multiply the ones.2
8-4 Multiply Two-Digit Numbers
Another Way: Paper and Pencil
Step 2 Multiply the tens.
5714×
228
2
570
8-4 Multiply Two-Digit Numbers
Another Way: Paper and Pencil
Step 3 Add the products.
5714×
228
2
570+798
Answer: So, the truck can travel 798 miles in 14 hours at 57 miles per hour.
8-4 Multiply Two-Digit Numbers
A. 368
B. 378
C. 935
D. 945
How far can a car travel in 15 hours if it is traveling an average of 63 miles per hour?
The Jones family spends an average of $48 a month going to the movies. How much does the family spend in 3 years?
Estimate 50 × 40 = 2,000.
8-4 Multiply Two-Digit Numbers
Step 1 Multiply the ones.
×$48
36288
Step 3 Add the products.
8-4 Multiply Two-Digit Numbers
×$48
36288
1,440+1,728
Answer: So, the Jones family spends $1,728 in 3 years.
Check for Reasonableness
8-4 Multiply Two-Digit Numbers
Since 1,728 is close to the estimate of 2,000, the answer is reasonable.
Check
1,200 + 240 + 240 + 48 = 1,728
8-4 Multiply Two-Digit Numbers
A. $3,456
B. $3,157
C. $2,456
D. $2,157
Lauren spends about $72 a month on gas for her car. How much does she spend on gas in 4 years?
Five-Minute Check (over Lesson 8-4)Main IdeaCalifornia StandardsExample 1Example 2
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
• I will multiply a three-digit number by a two-digit number.
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Standard 4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use the relationships between them to simplify computations and to check results.
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Standard 4NS3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.
Antonio spends 194 minutes taking piano lesson each month. How many minutes does he spend taking piano lesson in a year?
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Step 1 Multiply 194 by 2.
Estimate 12 × 194 10 × 200 = 2,000.
×194
12388
Step 2 Multiply 194 by 1 ten.
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
×194
12388
1,940
1
Step 3 Add the products. ×
19412
3881,940
1
+2,328
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Answer: So, Antonio spends 2,328 minutes taking piano lessons in a year.
Check for Reasonableness
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Since 2,328 is close to the estimate, 2,000. So, the answer is correct.
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
A. 3,210
B. 3,814
C. 3,752
D. 3,852
Lui spends about 321 minutes a month writing to pen pals. How many minutes does he spend writing letters in a year?
Rai is paid $308 a week for her part-time job at the city library. What is Rai’s annual salary?
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Step 1 Multiply $308 by 2.
Estimate $308 × 52 300 × 50 = $15,000.
×$308
52$616
1
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Step 2 Multiply $308 by 50.
×$308
52$616
1
$15,400
4
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Step 3 Add the partial products.
×$308
52$616
1
$15,400
4
+$16,016
Answer: So, the product of $308 and 52 is $16,016.
Check for Reasonableness
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
Since $16,016 is close to the estimate, the answer is reasonable.
8-5 Multiply Three-Digit Numbers by Two-Digit Numbers
A. $22,088
B. $23,088
C. $21,088
D. $20,088
Monique gets paid $444 a week at her job. How much does she get paid in a year?
Five-Minute Check (over Lesson 8-5)Main IdeaCalifornia StandardsExample 1: Problem-Solving Investigation
8-6 Problem-Solving Investigation: Choose a Strategy
8-6 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
8-6 Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
8-6 Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.
GREGORY: I spent 4 hours at a school carnival. I spent 35 minutes eating and 45 minutes playing games. I also rode 12 rides, which took about 15 minutes each because I had to stand in lines.
YOUR MISSION: Determine if Gregory is correct in saying that he spent 4 hours at the carnival.
8-6 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?• Gregory spent 35 minutes eating.• He spent 45 minutes playing games.• He rode 12 rides, which lasted 15 minutes each.
What do you need to find?• Find if Gregory is correct in saying he spent
4 hours at the carnival.
8-6 Problem-Solving Investigation: Choose a Strategy
Plan
Find the total number of minutes spent on carnival activities and compare to 4 hours.
8-6 Problem-Solving Investigation: Choose a Strategy
Solve
8-6 Problem-Solving Investigation: Choose a Strategy
Gregory gave the amount of time spent at the carnival in hours. The amount of time spent on each activity was given in minutes. So, change hours to minutes. Then compare the two amounts of time.
Solve
8-6 Problem-Solving Investigation: Choose a Strategy
240 minutes
60 minutes60 minutes60 minutes
+ 60 minutes30
15× 12
+ 150180 230 minutes
35 minutes45 minutes
+ 180 minutes
time Gregory said he spent at carnival
time spent riding rides
time spent on carnival activities
Solve
8-6 Problem-Solving Investigation: Choose a Strategy
The amount of time Gregory said he spent at the carnival does not equal the amount of time he spent of carnival activities.
Answer: So, Gregory was not correct.
Check
Look back at the problem. Use subtraction to check the amount of time spent on carnival activities.
8-6 Problem-Solving Investigation: Choose a Strategy
133 – 55 – 46 – 32 = 0. So, Gregory was not correct.
Five-Minute Check (over Lesson 8-6)Main IdeaCalifornia StandardsExample 1Example 2
8-7 Multiply Greater Numbers
8-7 Multiply Greater Numbers
• I will multiply four- and five-digit numbers by a two-digit number.
8-7 Multiply Greater Numbers
Standard 4NS3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.
Standard 4MR2.1 Use estimation to verify the reasonableness of calculated results.
A science museum gets an average of 4,562 visitors every week. How many visitors does it get in a year?
Step 1 Multiply the ones. Regroup if necessary.
8-7 Multiply Greater Numbers
Estimate 52 × 4,562 50 × 5,000 = 250,000
×4,562
529,124
111
Step 2 Multiply the tens.
8-7 Multiply Greater Numbers
×4,562
529,124
111
228,100
32
Step 3 Add the partial products. Check for reasonableness.
8-7 Multiply Greater Numbers
×4,562
529,124
111
228,100
32
+237,224
Answer: So, the science museum gets 237,224 visitors a year.
Check for Reasonableness
8-7 Multiply Greater Numbers
Since the answer, 237,224, is close to the estimate, the answer is reasonable.
8-7 Multiply Greater Numbers
A. 427,700
B. 427,590
C. 426,790
D. 427,800
An amusement park gets an average of 8,225 visitors every week. How many visitors does it get in a year?
8-7 Multiply Greater Numbers
A web site gets an average of 23,146 hits each month. How many hits does it get in 15 months?
Step 1 Multiply the ones. Regroup if necessary.
Estimate 15 × 23,149 20 × 20,000 = 400,000
×23,149
15115,745
421
8-7 Multiply Greater Numbers
Step 2 Multiply the tens.
×23,149
15115,745
421
231,490
8-7 Multiply Greater Numbers
Step 3 Add the partial products.
+347,235
×23,149
15115,745
421
231,490
Answer: So, the website gets 347,235 hits in 15 months.
8-7 Multiply Greater Numbers
Check for Reasonableness
Since 347,235 is close to the estimate, the answer is reasonable.
8-7 Multiply Greater Numbers
A. 594,975
B. 595,864
C. 595,975
D. 594,323
Another web site gets an average of 19,225 hits a day. How many hits does the website get in a 31 day month?
8Multiply by Two-Digit Numbers
Five-Minute Checks
8Multiply by Two-Digit Numbers
Lesson 8-1 (over Chapter 7)Lesson 8-2 (over Lesson 8-1)Lesson 8-3 (over Lesson 8-2)Lesson 8-4 (over Lesson 8-3)Lesson 8-5 (over Lesson 8-4)Lesson 8-6 (over Lesson 8-5)Lesson 8-7 (over Lesson 8-6)
8Multiply by Two-Digit Numbers
(over Chapter 7)
A. 426
B. 405
C. 406
D. 425
Multiply. Check for reasonableness.203
× 2
8Multiply by Two-Digit Numbers
(over Chapter 7)
A. 1,283
B. 3,502
C. 1,273
D. 3,542
Multiply. Check for reasonableness.506
× 7
8Multiply by Two-Digit Numbers
(over Chapter 7)
A. 21,105
B. 21,095
C. 10,368
D. 21,405
Multiply. Check for reasonableness.3 × 7,035
8Multiply by Two-Digit Numbers
(over Chapter 7)
A. $32,743
B. $33,672
C. $13,097
D. $33,752
Multiply. Check for reasonableness.8 × $4,209
8Multiply by Two-Digit Numbers
(over Chapter 7)
A. 30,042
B. 30,108
C. 30,708
D. 30,048
Multiply. Check for reasonableness.6 × 5,008
8Multiply by Two-Digit Numbers
(over Lesson 8-1)
A. 807
B. 187
C. 870
D. 957
Multiply. 87
× 10
8Multiply by Two-Digit Numbers
(over Lesson 8-1)
A. 1,020
B. 912
C. 102
D. 1,054
Multiply. 34
× 30
8Multiply by Two-Digit Numbers
(over Lesson 8-1)
A. 5,240
B. 520
C. 5,265
D. 5,200
Multiply. 65
× 80
8Multiply by Two-Digit Numbers
(over Lesson 8-1)
A. $1,173
B. $115
C. $1,150
D. $1,138
Multiply. $23
× 50
8Multiply by Two-Digit Numbers
(over Lesson 8-1)
A. $6,480
B. $7,110
C. $711
D. $7,189
Multiply. $79
× 90
8Multiply by Two-Digit Numbers
(over Lesson 8-1)
A. $3,420
B. $3,042
C. $3,477
D. $3,480
Multiply. $57
× 60
8Multiply by Two-Digit Numbers
(over Lesson 8-2)
A. 1,400; more
B. 1,600; less
C. 1,600; more
D. 1,200; less
Estimate. Tell whether the estimate is more or less than the actual product.
39× 35
8Multiply by Two-Digit Numbers
(over Lesson 8-2)
A. 2,700; less
B. 2,400; less
C. 3,000; more
D. 2,700; more
Estimate. Tell whether the estimate is more or less than the actual product.
63× 44
8Multiply by Two-Digit Numbers
(over Lesson 8-2)
A. $4,300; less
B. $4,400; less
C. $4,800; more
D. $4,000; less
Estimate. Tell whether the estimate is more or less than the actual product.
$54× 81
8Multiply by Two-Digit Numbers
(over Lesson 8-2)
A. $5,400; more
B. $3,000; less
C. $6,000; more
D. $4,125; less
Estimate. Tell whether the estimate is more or less than the actual product.$274 × 16
8Multiply by Two-Digit Numbers
(over Lesson 8-2)
A. 63,000; less
B. 64,800; more
C. 70,000; more
D. 64,800; less
Estimate. Tell whether the estimate is more or less than the actual product.719 × 94
8Multiply by Two-Digit Numbers
(over Lesson 8-3)
A. 1 quarter, 4 dimes, 1 nickel, 3 pennies
B. 2 quarters, 1 dime, 2 nickels, 3 pennies
C. 3 dimes, 2 nickels, 3 pennies
D. 2 quarters, 2 dimes, 3 pennies
Solve. Use the Act it Out strategy. Carlos has 8 coins in his pocket. The total value of the coins is 73¢. What coins does Carlos have?
8Multiply by Two-Digit Numbers
(over Lesson 8-4)
A. 308
B. 34
C. 187
D. 200
Multiply. 17
× 11
8Multiply by Two-Digit Numbers
(over Lesson 8-4)
A. 840
B. 210
C. 720
D. 740
Multiply. 35
× 24
8Multiply by Two-Digit Numbers
(over Lesson 8-4)
A. 2,708
B. 590
C. 2,995
D. 2,714
Multiply. 59
× 46
8Multiply by Two-Digit Numbers
(over Lesson 8-4)
A. $2,248
B. $2,368
C. $640
D. $2,512
Multiply. $64
× 37
8Multiply by Two-Digit Numbers
(over Lesson 8-4)
A. $5,082
B. $4,242
C. $942
D. $4,642
Multiply. $77
× 66
8Multiply by Two-Digit Numbers
(over Lesson 8-4)
A. 1,936
B. 7,628
C. 1,104
D. 7,728
Multiply. 92
× 84
8Multiply by Two-Digit Numbers
(over Lesson 8-5)
A. 4,852
B. 1,612
C. 496
D. 1,602
Multiply. 124
× 13
8Multiply by Two-Digit Numbers
(over Lesson 8-5)
A. 6,482
B. 1,030
C. 5,810
D. 6,592
Multiply. 206
× 32
8Multiply by Two-Digit Numbers
(over Lesson 8-5)
A. 25,065
B. 24,865
C. 5,013
D. 22,635
Multiply. 557
× 45
8Multiply by Two-Digit Numbers
(over Lesson 8-5)
A. 47,948
B. 7,128
C. 47,952
D. 45,322
Multiply. 648
× 74
8Multiply by Two-Digit Numbers
(over Lesson 8-5)
A. 17,534
B. 62,469
C. 11,438
D. 62,909
Multiply. 817
× 77
8Multiply by Two-Digit Numbers
(over Lesson 8-5)
A. 13,902
B. 85,398
C. 74,398
D. 77,688
Multiply. 993
× 86
8Multiply by Two-Digit Numbers
(over Lesson 8-6)
A. Yes, it is reasonable because he spent exactly 3 hours completing his chores.
B. No, it is not reasonable because he spent over 3 hours completing his chores.
Use any strategy to solve. Nitin spent 55 minutes mowing the lawn, 48 minutes cleaning his room, 23 minutes vacuuming, and 32 minutes doing laundry. Is it reasonable to say that Nitin spent 3 hours on completing his chores?
8Multiply by Two-Digit Numbers
(over Lesson 8-6)
Use any strategy to solve. Nitin spent 55 minutes mowing the lawn, 48 minutes cleaning his room, 23 minutes vacuuming, and 32 minutes doing laundry. Is it reasonable to say that Nitin spent 3 hours on completing his chores?
C. No, it is not reasonable because he spent less than 3 hours completing his chores.
D. Yes, it is reasonable because he spent almost 3 hours completing his chores.
8Multiply by Two-Digit Numbers
(over Lesson 8-6)
Use any strategy to solve. Nitin spent 55 minutes mowing the lawn, 48 minutes cleaning his room, 23 minutes vacuuming, and 32 minutes doing laundry. Is it reasonable to say that Nitin spent 3 hours on completing his chores?
C. No, it is not reasonable because he spent less than 3 hours completing his chores.
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