CHAPTE R
3
Divide by a
One-Digit Divisor
connectED.mcgraw-hill.com
The
BIG Idea
Investigate
How can I accurately
divide by one-digit
numbers when the
division problem is
shown in various ways?
Animations
Vocabulary
Math Songs
Multilingual
eGlossary
Personal Tutor
Virtual
Manipulatives
Make this Foldable
to help organize
information about
division.
Division
Learn
Audio
Lesson 1
Divide by a
One-Digit
g
Divisor.
Foldables
Practice
Self-Check Practice
eGames
Worksheets
Assessment
Review Vocabulary
ciones A group
Fact Family familia de opera
same numbers.
of related facts using the
3 × 5 = 15
5 × 3 = 15
15 ÷ 5 = 3
× ÷
15 ÷ 3 = 5
Key Vocabulary
English
102
quotient
dividend
divisor
Español
cociente
dividendo
divisor
When Will I Use This?
Your Turn!
You will solve thhiis teerrr.
problem in the chap
Divide by a One-Digit Divisor 103
Are You Ready
for the Chapter?
Text Option
You have two options for checking
Prerequisite Skills for this chapter.
Take the Quick Check below.
Multiply.
1. 12 × 7
2. 42 × 8
3. 51 × 9
4. 7 × 18
5. 3 × $75
6. 3 × $89
7. Turner’s bookshelf has 6 shelves. Each shelf has 17 books.
How many books are on the bookshelf?
Round each number to its greatest place value.
8. 36
11. $33,103
9. $451
10. 7,499
12. $271
13. $5,001
14. There are 7,209 students at the amusement park.
Approximately how many students are at the park?
Divide.
15. 8 ÷ 2
16. 15 ÷ 5
17. 27 ÷ 3
18. 28 ÷ 4
19. 48 ÷ 6
20. 54 ÷ 9
21. Three people spent a total of $24 for lunch.
If they divide the total cost evenly, how much
does each person pay?
Online Option
104
Item
Pizza
$12
Salads
$6
Drinks
$6
Take the Online Readiness Quiz.
Divide by a One-Digit Divisor
Cost
Multi-Part
Lesson
1
PART
Divide by a One-Digit Divisor
A
Main Idea
I will understand
how division and
multiplication are
related.
Vocabulary
V
ffact family
B
C
D
E
Relate Division
to Multiplication
A fact family is a group of related facts that use the same
numbers. You can use fact families to relate multiplication
and division.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
SPI 0506.2.4 Solve problems
involving the division of twoand three-digit whole numbers
by one- and two-digit whole
numbers.
B
BASKETBALL
Sheryl is putting away
20
2 basketballs after practice.
She places the balls on a rack that
has 5 shelves. How many basketballs
can she put on each shelf?
Use a fact family.
5 × 4 = 20
4 × 5 = 20
× ÷
20 ÷ 5 = 4
20 ÷ 4 = 5
So, 20 ÷ 5 = 4.
Sheryl can put 4 basketballs on each shelf.
Write a Fact Family
Write a fact family for the counters shown.
W
There are 5 rows, 9 columns, and a total of 45 counters.
45 ÷ 9 = 5
9 × 5 = 45
45 ÷ 5 = 9
5 × 9 = 45
Lesson 1A Divide by a One-Digit Divisor 105
You can also use mental math to help you divide basic facts.
Use Related Facts
GIFT BAGS Ellie is creating gift
bags for her party guests. She bought
a total of 56 pencils that she wants
to divide equally among the 7 gift bags.
How many pencils will go in each bag?
Check for
reasonableness by
er
comparing your answ
in
ed
to what was ask
the question.
Find 56 ÷ 7. You can use a related
multiplication fact to help you divide.
56 ÷ 7 = Think What number times 7 is 56?
7 × = 56
Write a related multiplication fact.
7 × 8 = 56
So, Ellie will put 8 pencils in each gift bag.
set. See Examples 1 and 2
Write a fact family for each set
1.
2.
3. 9, 8, 72
4. 6, 7, 42
Divide. Use a related multiplication fact. See Example 3
5. 48 ÷ = 6
6. 40 ÷ 5 = 7. 18 ÷ 3 = 8. 12 ÷ 6 = 9. ÷ 7 = 3
10. 63 ÷ 9 = 11. There are 3 students playing a board game. The game contains
18 game pieces. If each student receives the same number of
game pieces, how many pieces should each student receive?
12.
E
TALK MATH Explain how multiplication facts can help
you divide.
106
Divide by a One-Digit Divisor
EXTRA
%
)# E
# T4 IC
!C
2A
PR
0
Begins on page EP2.
Write
W
it a ffactt ffamily
il ffor each
h set.
t See Examples 1 and 2
13.
14.
15. 9, 4, 36
16. 6, 6, 36
Divide. Use a related multiplication fact. See Example 3
17. 64 ÷ 8 = 18. 45 ÷ 9 = 19. ÷ 9 = 9
20. ÷ 8 = 4
21. 40 ÷ = 8
22. 63 ÷ = 7
Orange blossoms have 5 petals and are some of
the most fragrant flowers.
23. How many petals would there be in a
group of 7 orange blossoms?
24. If you count 40 petals in all, what is the
number of orange blossoms?
25. How many petals would there be in a
group of 11 orange blossoms?
26. OPEN ENDED Write a real-world division problem that can be
solved by using fact families.
27. REASONING Can the number 12 be part of more than one fact
family? Explain.
28. WHICH ONE DOESN’T BELONG? Identify the equation that does
not belong with the other three. Explain.
54 ÷ 9 = 6
29.
E
54 ÷ 6 = 9
9 × 3 = 27
6 × 9 = 54
WRITE MATH Describe how you would find 42 ÷ 7.
Lesson 1A Divide by a One-Digit Divisor 107
Multi-Part
Lesson
1
Divide by a One-Digit Divisor
PART
A
B
C
D
E
Division Models
Main Idea
You can use base-ten blocks to help you divide.
I will explore division
using models.
Materials
base-ten blocks
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
GLE 0506.2.5 Develop fluency
in solving multi-step problems
using whole numbers, fractions,
mixed numbers, and decimals.
In art class, three students share 48 markers evenly. How
many markers will each student have?
Find 48 ÷ 3.
Step 1
Model 48 using base-ten blocks.
Step 2
Divide the tens into 3 equal groups.
Step 3
Regroup the remaining tens block into 10 ones.
You now have 18 ones.
Step 4
Divide the ones.
There are 16 in each group. So, 48 ÷ 3 = 16.
Use multiplication to check your answer.
16 × 3 = 48 108
Divide by a One-Digit Divisor
Model Remainders
M
Find 56 ÷ 5.
Step 1
Model 56 using base-ten blocks.
Step 2
Divide the tens into 5 equal groups.
Step 3
Divide the ones.
There is one left over.
When you divide 56 into 5 groups, there are 11 in each group with
one left over.
and Apply It
Find each quotient using models. Tell how many are left over.
1. 44 ÷ 4
2. 39 ÷ 3
3. 54 ÷ 3
4. 63 ÷ 3
5. 32 ÷ 5
6. 57 ÷ 8
7. 64 ÷ 5
8. 45 ÷ 8
9. Kendrick has 42 craft sticks to make 3 identical crafts. How many sticks will he use for
each craft?
10.
E
WRITE MATH Will 32 ÷ 3 have any left over? Explain.
Lesson 1B Divide by a One-Digit Divisor 109
Multi-Part
Lesson
1
PART
Divide by a One-Digit Divisor
A
Main Idea
I will carry out division
with and without
remainders.
Vocabulary
V
dividend
B
C
D
E
Divide a Two-Digit Dividend
by a One-Digit Divisor
In division, the dividend is the number that is being divided.
The divisor tells you how many groups.
divisor
dividend
quotient
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
GLE 0506.2.5 Develop fluency
in solving multi-step problems
using whole numbers,
fractions, mixed numbers, and
decimals. SPI 0506.2.4 Solve
problems involving the division
of two- and three-digit whole
numbers by one- and two-digit
whole numbers. Also addresses
GLE 0506.1.1.
3 36
36 ÷ 3
remainder
divisor
The result of the division problem is called the quotient .
BABYSITTING Mindy babysat on the weekend for 3 hours.
If she made $36, how much did she make each hour?
Find 36 ÷ 3.
Step 1 Model 36.
3 36
Step 2 Divide the tens.
1
3 36 1 ten
- 3 in each
−−− group.
0
Step 3 Divide the ones.
12
3 36 2 ones
- 3 in each
−−−− group.
06
-6
−−−
0
So, 36 ÷ 3 = 12. Mindy made $12 every hour she babysat.
110
Divide by a One-Digit Divisor
A remainder is the number, or part left, after you divide. We use
R to represent the remainder.
Divide with Remainders
BASEBALL Caleb is putting his baseball cards in an album.
He has 57 cards and can put 4 cards on each page.
How many full pages will Caleb have? Will there be
any cards left?
You need to find 57 ÷ 4.
Step 1 Rewrite as 4 57 . Then divide the tens.
Divide. 5 ÷ 4 = 1
Put 1 in the quotient over the tens place.
Multiply. 4 × 1 = 4
Subtract. 5 - 4 = 1
Compare. 1 < 4
1
4 57
4
−−−−
1
Step 2 Divide the ones.
14 R1
4 57
-4
−−−−
17
- 16
−−−−
1
57
Write 57 ÷ 4 as 4 t.
en
to find the quoti
Bring down the ones.
Divide. 17 ÷ 4 = 4
Put 4 in the quotient over the ones place.
Multiply. 4 × 4 = 16
Subtract. 17 - 16 = 1
Compare. 1 < 4
The remainder is 1.
57 ÷ 4 = 14 R1
So, there will be 14 full pages and 1 card will be left over.
Check for Reasonableness 14 × 4 = 56 and 56 + 1 = 57. Divide
Fill in each with the correct number to find 85 ÷ 5.
7
17
5 85
5
−−−−
35
35
−−−−
0
5 8 5
-5
−−−−
5
- −−−−−
0
Divide: 8 ÷ 5 = 1
Subtract: 8 - 5 = 3
Multiply: 7 × 5 = 35
So, 85 ÷ 5 = 17.
Lesson 1C Divide by a One-Digit Divisor 111
Divide. Use multiplication to check your answer. See Examples 1–3
1.
2.
5
6. 7 96
R
4.
6 7 4
-6
−−−−−
4 5
3 - −−−−−
5
-1
−−−−−
0
5 6 5
-5
−−−−
5
- −−−−−
0
5. 3 63
3.
-1 −−−−
1 R
5 5
4 -
−−−−−
- −−−−−
2
7. 68 ÷ 5
8. 39 ÷ 2
9. Five students volunteered to carry boxes. There are 62 boxes. Is it
possible for each student to carry the same number of boxes and
have all the boxes carried? Explain.
E
10.
TALK MATH Why is the remainder always less than the divisor?
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Divide.
Di
id Use
U multiplication
lti li ti
to
t check
h k your answer. See Examples 1–3
11.
3 4 2
-3
−−−−
2
- −−−−−
0
12.
7
6 8
4 - −−−−−
8
-2
−−−−−
0
13.
R
2 3 3
-2
−−−−−
-1 −−−−
1
14.
1 R
5 7 7
-
−−−−−
- −−−−−
28
15. 2 16. 5 65
17. 60 ÷ 4
18. 51 ÷ 3
19. 7 85
20. 3 41
21. 64 ÷ 5
22. 70 ÷ 6
23. Maranda practiced a total of 52 hours
in 4 weeks to prepare for a piano
recital. If she practiced the same
number of hours each week, how
many hours did she practice each
week?
112
Divide by a One-Digit Divisor
24. Lance is putting
ng
75 photos in
a scrapbook.
If he puts
5 photos on
each page, how
many pages will he need?
25.
HIKING
Alberto and Darcy are hiking in the
Great Smoky Mountain National Park. One trail
is about 68 miles long. Alberto and Darcy split
the trip into 4 days of hiking. How many
miles will they walk each day?
26. OPEN ENDED A two-digit dividend is divided by a one-digit
divisor. The remainder is 2. Find possible values for the dividend
and divisor.
27. NUMBER SENSE Use the digits 3, 6, and 9 one time each to write
a division problem that contains a two-digit dividend. Write the
division problem with the greatest quotient.
28. REASONING The following fact families show the relationship
between multiplication and division.
18 ÷ 3 = 6
18 ÷ 0 = ?
3 × 6 = 18
0 × ? = 18
Explain why it is not possible to divide by zero.
29.
E
WRITE MATH Explain the meaning of a remainder in a division
problem.
Test Practice
30. A box of granola bars has 26 bars. If
7 friends split the bars evenly, how
many bars will be left?
A. 3
C. 5
B. 4
D. 6
31. An airplane that can hold
63 passengers is separated into
3 sections. Each section holds the
same number of passengers. Which
division sentence correctly describes
the situation?
F. 63 ÷ 21 = 3
H. 63 ÷ 21 = 5
G. 63 ÷ 3 = 21
I. 21 ÷ 3 = 7
Lesson 1C Divide by a One-Digit Divisor 113
Multi-Part
Lesson
1
Divide by a One-Digit Divisor
PART
A
Main Idea
I will use basic
facts and patterns to
divide multiples of
10, 100, and 1,000
mentally.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
GLE 0506.2.5 Develop fluency
in solving multi-step problems
using whole numbers,
fractions, mixed numbers, and
decimals. SPI 0506.2.4 Solve
problems involving the division
of two- and three-digit whole
numbers by one- and two-digit
whole numbers. Also addresses
GLE 0506.1.5.
B
C
D
E
Division Patterns
You can use basic facts and patterns to divide by multiples of 10.
Divide Multiples
of 10
B
BUTTERFLIES
A monarch butterfly
ccan fly 240 miles in 3 days.
Suppose it flies the same distance
each day. How many miles
can it fly each day?
Since 240 is a multiple of 10, use the
basic fact and continue the pattern.
24 ÷ 3 = 8
basic fact
240 ÷ 3 = 80
24 tens divided by 3 equals 8 tens
2,400 ÷ 3 = 800 24 hundreds divided by 3 equals 8 hundreds
24,000 ÷ 3 = 8,000 24 thousands divided by 3 equals 8 thousands
So, the butterfly can fly 80 miles each day.
Divide Multiples of 10
Find 600 ÷ 3 mentally.
Since 600 is a multiple of 10, you can use the basic fact and
continue the pattern.
6÷3=2
6 ones divided by 3 equals 2 ones.
60 ÷ 3 = 20
6 tens divided by 3 equals 2 tens.
600 ÷ 3 = 200
6 hundreds divided by 3 equals 2 hundreds.
So, 600 ÷ 3 = 200.
114
Divide by a One-Digit Divisor
MEASUREMENT A cow eats
900 pounds of hay over
a period of 30 days.
How many pounds of hay
would the cow eat each day
at this rate?
You need to find 900 ÷ 30.
Use the fact family of 3, 3, and 9 to help represent the
problem.
3×3=9
t
In multiplication, coun
the number of zeros in
each factor. Write the
zeros to the right of
the product of the
basic fact.
9÷3=3
30 × 3 = 90
90 ÷ 30 = 3
30 × 30 = 900
900 ÷ 30 = 30
This pattern suggests that you can cross out the same number
of zeros in the dividend and the divisor to make division easier.
/ ÷ 30
/
900
Cross out the same number of zeros in both the
dividend and divisor.
90 ÷ 3 = 30
Divide. THINK: 9 tens ÷ 3 = 3 tens.
So, 900 ÷ 30 = 30.
The cow eats 30 pounds of hay each day.
Divide mentally
mentally. See Examples 11–33
1. 500 ÷ 5
2. 320 ÷ 8
3. 200 ÷ 10
4. 420 ÷ 70
5. 800 ÷ 2
6. 150 ÷ 30
7. 270 ÷ 90
8. 5,600 ÷ 70
9. 2,100 ÷ 30
10. A sailfish grabbed a fishing line and
dragged it 300 feet in just 3 seconds.
On average, how many feet did the
fish drag the line each second?
11.
E
TALK MATH Explain how you
know that the quotients 48 ÷ 6 and
480 ÷ 60 are equal without doing
any computation.
Lesson 1D Divide by a One-Digit Divisor 115
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Divide
Di
id mentally.
ll See Examples 1–3
12. 800 ÷ 2
13. 900 ÷ 3
14. 150 ÷ 5
15. 140 ÷ 7
16. 450 ÷ 9
17. 280 ÷ 4
18. 180 ÷ 60
19. 240 ÷ 30
20. 4,200 ÷ 70
21. 1,800 ÷ 30
22. 2,000 ÷ 400
23. 2,400 ÷ 300
24. A group of 10 people bought tickets to a reptile exhibit and paid a
total of $130. What was the price of one ticket?
25. Measurement The fastest team in a wheelbarrow race traveled
100 meters in about 20 seconds. On average, how many meters
did the team travel each second?
26. Measurement Daniela has a 160-ounce bag of potting
soil. She puts an equal amount of soil in each pot shown.
How much soil will she put in each pot?
27. A video store took in $450 in DVD rentals during one day.
If DVDs rent for $9 each, how many DVDs were rented?
28. OPEN ENDED Write a real-world division problem that can be
solved by using basic facts or patterns.
29. NUMBER SENSE Write two different division problems that both
have a quotient of 50.
30. FIND THE ERROR Sonia is finding 5,400 ÷ 90 mentally. Find her
mistake and correct it.
5,40/0/ ÷ 90/
54 ÷ 9 = 6
31.
E
WRITE MATH Describe how placing zeros at the end of basic
division facts helps you divide mentally. Write an example.
116
Divide by a One-Digit Divisor
Test Practice
32. An elementary school has 320 students.
All of the students are going on a
field trip. If 40 students can ride a
bus, how many buses are needed?
34. There are 560 people in the
auditorium. There are 70 rows of
seats. Which number sentence
describes the number of seats in
each row?
A. 56 × 7 = 392
School Bus
B. 560 ÷ 70 = 8
School
S
ch
hool
l
B
Bus
us
A. 5
C. 7
C. 560 ÷ 8 = 70
B. 6
D. 8
D. 560 ÷ 70 = 80
33. Petra and 5 of her friends have to
hand out the number of fliers shown
for the school play. If each person
passes out the same number of fliers,
how many fliers will Petra hand
out?
F. 15
H. 90
G. 20
I. 540
35.
SHORT RESPONSE Write two
division sentences using the
numbers below.
4, 17, 68
Divide. Use multiplication to check your answer. (Lesson 1C)
36. 3 45
37. 4 72
38. 6 72
39. 5 69
40. A fisherman caught 42 fish over 3 days. If he caught
the same number of fish each day, how many fish
did he catch in one day? (Lesson 1C)
Write a fact family for each set of numbers. (Lesson 1A)
41. 9, 6, 54
42. 28, 4, 7
43. 18, 6, 3
44. 56, 7, 8
Lesson 1D Divide by a One-Digit Divisor 117
Multi-Part
Lesson
1
Divide by a One-Digit Divisor
PART
A
B
C
D
E
Problem-Solving Strategy:
Guess, Check, and Revise
Main idea I will solve problems by using the guess, check, and revise strategy.
The Bactrian camel has two humps, while the
Dromedary camel has just one. Toby counted
20 camels with a total of 28 humps. How many
camels of each type are there?
Understand
What facts do you know?
• Bactrian camels have two humps.
• Dromedary camels have one hump.
• There are 20 camels with 28 humps.
What do you need to find?
• How many camels of each type are there?
Plan
You can use the guess, check, and revise strategy to solve the problem.
Use combinations of 20 total camels to guess.
Solve
Guess:
10 Bactrian camels and 10 Dromedary camels
Check:
10 × 2 = 20 humps
10 × 1 = 10 humps
Revise:
Try fewer Bactrian camels and more Dromedary camels.
Guess:
7 Bactrian camels and 13 Dromedary camels
Check:
7 × 2 = 14 humps
13 × 1 = 13 humps
Revise:
Try more Bactrian camels and less Dromedary camels.
Guess:
8 Bactrian camels and 12 Dromedary camels
Check:
8 × 2 = 16 humps
12 × 1 = 12 humps
20 humps + 10 humps = 30 humps
Too high.
14 humps + 13 humps = 27 humps
Too low.
16 humps + 12 humps = 28 humps
This guess is correct. So, there are 8 Bactrian camels and 12 Dromedary camels.
Check
Look back at the problem. 8 + 12 = 20 camels and 16 + 12 = 28 humps.
So, the answer is correct.
GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,
and reasonableness of the solution. GLE 0506.2.3 Develop fluency with division of whole numbers.
Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division.
118
1
Divide by a One-Digit Divisor
Refer to the problem on the previous page.
1. Are there any other combinations of
each type of camel that Toby could
have seen? Explain your reasoning.
3. Explain how the guess, check, and
revise method helped you solve this
problem.
2. Suppose you saw 18 camels with a
total of 22 humps. How many of each
type did you see?
4. Explain why you should record your
guesses and their results in the solve
step of the problem-solving plan.
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Solve. Use the guess, check, and revise strategy.
5. Ruben sees 14 wheels on a total of
6 bicycles and tricycles. How many
bicycles and tricycles are there?
6. Conner spent $66 on rookie cards and
Hall of Famer cards. How many of each
type of card did he buy?
Baseball Card
Cost
Rookie
4 for $6
Hall of Famer
2 for $9
7. A teacher is having three students take
care of 28 goldfish during the summer.
He gave some of them to Alaina. Then
he gave twice as many to Miguel. He
gave twice as many to Kira as he gave
to Miguel. How many fish did each
student get?
9. Jerome bought 2 postcards and
received $1.35 in change in quarters
and dimes. If he got 6 coins back, how
many of each coin did he get?
10. The sum of two numbers is 30. Their
product is 176. What are the two
numbers?
11. A tour director collected $258 for tour
packages. Tour package A costs $18
and tour package B costs $22. How
many of each tour package were
sold?
12. Ticket prices for a science museum
are shown in the table. If $162 is
collected from a group of 12 people,
how many adults and students are in
the group?
8. Measurement Bike path A is 4 miles
long. Bike path B is 7 miles long. If
April biked a total of 37 miles, how
many times did she bike each path?
13.
E
WRITE MATH Refer to Exercise 10.
How did you use the guess, check, and
revise strategy to find the numbers?
To assess mastery of SPI 0506.2.8, see your Tennessee Assessment Book.
119
Mission:
Division
Dividing Whole Numbers
Get Ready!
Players: 2, 3, or 4 players
Get Set!
Each player makes a game
sheet like the one shown at
the right.
Make a spinner as shown.
Go!
The first person spins the
spinner. Each player writes
the number in one of the
blanks on his or her game
sheet. A zero cannot be
placed as the divisor.
The next person
n spins, and
each player writes
tes that
number in a blank.
nk.
The next player
spins and each
player fills in their
game sheet. A
player loses if
he or she
cannot use all
the numbers.
120
Divide by a One-Digit Divisor
isor
You will need: spinner, index
dex cards
All players find their
quotients. The player with
the greatest quotient earns
one point. In case of a tie,
each of those players earn
one point.
1
0
2
9
3
4
8
7
6
The first person to earn
5 points wins.
Game Sheet
÷
5
Mid-Chapter
Check
Divide. Use a related multiplication
fact. (Lesson 1A)
1. 36 ÷ = 9
2. 42 ÷ 6 = 3. 54 ÷ 9 = 4. 18 ÷ 3 = 5. ÷ 6 = 6
6. ÷ 9 = 8
7. Measurement The length of a
rectangle can be found by dividing the
area by the width. Find the length of
the rectangle below. (Lesson 1C)
area = 39 sq cm
3 cm
Divide mentally. (Lesson 1D)
16. 400 ÷ 2
17. 240 ÷ 6
18. 3,500 ÷ 5
19. 420 ÷ 60
20. 4,800 ÷ 800
21. 1,200 ÷ 300
22. MULTIPLE CHOICE A total of
180 students went on a field trip.
There were 3 buses. If each bus had
the same number of students on it,
how many students were on each
bus? (Lesson 1D)
F. 6
8. MULTIPLE CHOICE Suki received $87
for working 3 days. If she made the
same amount each day, how much did
Suki earn each day? (Lesson 1C)
A. $20
C. $25
B. $29
D. $30
G. 36
H. 54
I.
60
Solve. Use the guess, check, and revise
strategy. (Lesson 1E)
Divide. (Lesson 1C)
9. 2 48
10. 5 85
11. 4 63
12. 7 81
13. 78 ÷ 5
14. 96 ÷ 4
15. Measurement The table shows the
heights of the three tallest cacti. Find
the height of each cactus in yards.
(Hint: 1 yard = 3 feet) (Lesson 1C)
Cactus
Height
Saguaro
Organ-pipe
Opuntia
75 ft
48 ft
33 ft
23. The sum of two numbers is 70. Their
quotient is 13. What are the two
numbers?
24. Rory has $1.30 in coins. If there is a
total of 15 coins, how many quarters,
dimes, nickels, and pennies does
he have?
25.
E
WRITE MATH Can the remainder in
a division problem ever equal the
divisor? Explain.
Mid-Chapter Check 121
Multi-Part
Lesson
2
PART
Divide Three- and Four-Digit Dividends
A
Main Idea
I will estimate
quotients using
rounding and
compatible numbers.
B
C
D
E
F
Estimate Quotients
To estimate a quotient, you can use compatible numbers , or
numbers that are easy to divide mentally. Look for numbers that
are part of fact families.
Vocabulary
V
compatible numbers
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
GLE 0506.2.5 Develop fluency
in solving multi-step problems
using whole numbers,
fractions, mixed numbers, and
decimals. SPI 0506.2.4 Solve
problems involving the division
of two- and three-digit whole
numbers by one- and two-digit
whole numbers. Also addresses
GLE 0506.1.2.
Use a Compatible
Dividend
DOGS A dog’s heart beats
365 times in 3 minutes. About
how many times does a dog’s
heart beat in 1 minute?
365 ÷ 3
Change 365 to
360 because 360 and
3 are compatible
numbers.
360 ÷ 3 = 120 Divide.
So, a dog’s heart beats about 120 times a minute.
Check for Reasonableness 120 × 3 = 360. Find a Compatible Divisor
Estimate 3,200 ÷ 9.
E
3,200 ÷ 9
3,200 ÷ 8
Change 9 to 8 because
32 and 8 are compatible numbers.
3,200 ÷ 8 = 400
Divide mentally.
So, 3,200 ÷ 9 is about 400.
Check for Reasonableness 8 × 400 = 3,200. 122
Divide by a One-Digit Divisor
Use Rounding and Compatible Numbers
Estimate 208 ÷ 8.
E
To round 208 to the
nearest ten, look at the
number to the right of
8
the tens place. Since
is 5 or greater, round
210
up. 208
Step 1 Round the dividend to the
nearest ten.
208 ÷ 8
Step 2 Change the divisor to a
number that is compatible
with 210. Notice it is easy to
divide 210 by 7.
210 ÷ 8
210 ÷ 8
210 ÷ 7
210 ÷ 7 = 30
Step 3 Divide mentally.
So, 208 ÷ 8 is about 30.
DOGS Six dogs equally share a 45-pound bag of dog
food each week. About how much does each dog eat
each week?
One Way:
Use 45 and 5.
Another Way:
45 ÷ 6
45 ÷ 6
45 ÷ 5 = 9
48 ÷ 6 = 8
Use 48
and 6.
So, each dog eats about 8 or 9 pounds of dog food
each week.
Estimate
Estimate. Show your work
work. See Examples 11–44
1. 850 ÷ 9
2. 635 ÷ 8
3. 545 ÷ 5
4. 431 ÷ 2
5. 374 ÷ 9
6. 541 ÷ 6
7. 120 ÷ 5
8. 610 ÷ 7
9. An E-mail contained 250 characters.
The 4-line E-mail contained the same
number of characters on each line.
About how many characters were on
each line? Show how you estimated.
10.
E
TALK MATH Explain how you
could use compatible numbers to
estimate 272 ÷ 4.
Lesson 2A Divide Three- and Four-Digit Dividends 123
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Estimate.
E
ti t Sh
Show your work.
k See Examples
l 1–4
11. 397 ÷ 4
12. 432 ÷ 7
13. 753 ÷ 9
14. 253 ÷ 5
15. 554 ÷ 6
16. 360 ÷ 7
17. 791 ÷ 2
18. 151 ÷ 3
19. 289 ÷ 9
20. 477 ÷ 9
21. 230 ÷ 7
22. 244 ÷ 8
23. 660 ÷ 7
24. 860 ÷ 3
25. 639 ÷ 7
26. 486 ÷ 6
Solve. Show your work.
27. A grocery store employee puts 8 bagels in each bag. If she has
385 bagels, about how many bags does she need?
28. Measurement Jani drives 240 miles in 4 hours. About how
many miles does she drive each hour?
29. There were 317 marbles divided equally among 8 bowls.
About how many marbles were in each bowl?
30. Measurement Emilio has 5 bags of birdseed.
Each bag has about 28 ounces of birdseed. If he
divides the birdseed equally into 3 containers, about
how much birdseed will he put in each container?
31. The table shows how much each fifth grade
room earned from a bake sale. The money is
going to be given to 6 different charities. If each
charity is given an equal amount, about how much
will each charity receive? Show how you estimated.
32. OPEN ENDED Write a division problem and show two different
ways that you can estimate the quotient using compatible
numbers.
33. NUMBER SENSE Without calculating, predict whether 617 ÷ 7
is greater than or less than 100. Explain your reasoning.
34.
E
WRITE MATH Write a real-life problem in which you estimate
the quotient of two numbers.
124
Divide by a One-Digit Divisor
Test Practice
35. Which of the following is the most
reasonable estimate for the number
of Calories in one serving of milk?
Servings
of Milk
Calories
5
430
36. A train traveled 300 miles in
5 hours. How far did the train travel
each hour on average?
F. 60 mi
G. 150 mi
H. 600 mi
A. between 8 and 9
I. 1,500 mi
B. less than 80
C. between 80 and 90
37.
D. more than 90
SHORT RESPONSE Mrs. Chong
bought 480 bookmarks. If each box
contains 60 bookmarks, how many
boxes did she buy? Explain your
reasoning.
Solve. Use the guess, check, and revise strategy. (Lesson 1E)
38. Stacie counts 26 legs in a barnyard with horses and chickens.
If there are 8 animals, how many are horses?
Divide mentally. (Lesson 1D)
39. 400 ÷ 2
40. 180 ÷ 3
41. 630 ÷ 70
42. 2,500 ÷ 500
Divide. Use estimation to check. (Lesson 1C)
43. Miss Carbone read a book to her class. The book contained
54 pages and she read the same number of pages each day.
If it took her 3 days to read the book, how many pages did
she read each day?
44. BAR DIAGRAM Frankie paid $18 to rent a paddleboat. If
the cost of renting is $6 per hour, for how many hours did
Frankie rent the paddleboat?
Divide. Use a related multiplication fact. (Lesson 1A)
C04 005A 105939 A
45. 24 ÷ 4
46. 32 ÷ 8
47. 56 ÷ 8
48. Samuel swam a total of 48 laps over 4 days. He swam
the same number of laps each day. How many laps did
Samuel swim each day? (Lesson 1A)
Lesson 2A Divide Three- and Four-Digit Dividends 125
Multi-Part
Lesson
2
MP-Title
-TitlThreee
Divide
and Four-Digit Dividends
PART
A
Main Idea
I will explore division
using models.
B
C
D
E
F
Division Models with
Greater Numbers
You can also use base-ten blocks to divide greater numbers.
Materials
base-ten blocks
At the fair, you need tickets to ride the rides. Three friends
share 336 tickets equally. How many tickets will each
friend receive? Find 336 ÷ 3.
Step 1
Model 336 using base-ten blocks.
Step 2
Divide the hundreds into 3 groups.
Step 3
Divide the tens blocks into 3 groups.
Step 4
Divide the ones blocks into 3 groups.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
Also addresses GLE 0506.1.4.
So, 336 ÷ 3 = 112.
Use multiplication to check your answer. 112 × 3 = 336 126
Divide by a One-Digit Divisor
Model Remainders
Find 319 ÷ 2.
F
Step 1
Model 319 using base-ten blocks.
Step 2
Divide the hundreds into 2 groups.
Step 3
Divide the remaining ten and the ones into 2 groups.
There is one left over.
When you divide 319 into 2 groups, there are 159 in each
group with one left over. So, 319 ÷ 2 = 159 R1.
Use multiplication to check your answer.
159 × 2 = 318 + 1 = 319 and Apply It
Use models to find each quotient.
1. 344 ÷ 2
2. 469 ÷ 7
3. 255 ÷ 5
4. 364 ÷ 4
5. 373 ÷ 4
6. 567 ÷ 5
7. 383 ÷ 3
8. 582 ÷ 4
9.
E
WRITE MATH If you are dividing a three-digit even
number by two, will you ever have a remainder? Explain.
Lesson 2B Divide Three- and Four-Digit Dividends 127
Multi-Part
Lesson
2
MP-Title
-TitlThreee
Divide
and Four-Digit Dividends
PART
A
Main Idea
I will divide using the
distributive property
and partial quotients.
B
C
D
E
F
Distributive Property
and Partial Quotients
The Distributive Property allows you to divide each
place-value position by the same factor.
Vocabulary
V
partial quotients
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
J
Jesse
has 369 beads to be split evenly
among 3 necklaces. How many beads
can Jesse put on each necklace?
Find 369 ÷ 3 using the
Distributive Property and a bar diagram.
Step 1
Model 369 as (300 + 60 + 9).
300
Step 2
Divide each section by 3.
Write each quotient above the bar.
3
Step 3
60 9
100
20 3
300
60 9
Add the quotients.
100 + 20 + 3 = 123
So, 369 ÷ 3 = 123.
Jesse can put 123 beads on each necklace.
Check 123 × 3 = 369. 128
Divide by a One-Digit Divisor
Partial quotients is a method of dividing where you break the
dividend into sections that are easy to divide.
Use Partial Quotients
There are 738 students in Manuel’s school. There are 6 grade
levels in his school, with each grade having the same number
of students. How many students are in the fifth grade?
Find 738 ÷ 6 by using partial quotients.
Step 1
Divide the hundreds. Since
6 × 100 is 600, and 600 is close
to 738, divide 600 by 6. 100 is
a partial quotient. Subtract.
Step 2
Divide the tens. Since
6 × 20 = 120, and 120 is
close to 138, divide 120
by 6. 20 is a partial quotient. Subtract.
Step 3
Divide the ones. There are only 18 left
and 6 × 3 = 18. 3 is a partial quotient.
Step 4
Add the partial quotients.
100 + 20 + 3 = 123
6 738
- 600
−−−−
138
- 120
−−−−
18
- 18
−−−−
0
100
20
3
So, 738 ÷ 6 = 123.
There are 123 students in the fifth grade.
Check 123 × 6 = 738. and Apply It
Divide. Use the Distributive Property.
1. 248 ÷ 2
2. 488 ÷ 4
3. 963 ÷ 3
5. 352 ÷ 4
6. 176 ÷ 8
Divide. Use partial quotients.
4. 654 ÷ 6
7.
E
WRITE MATH Suppose you are finding 296 ÷ 4 using partial
quotients. Is 50 or 70 a more reasonable partial quotient? Explain.
Lesson 2C Divide Three- and Four-Digit Dividends 129
Multi-Part
Lesson
2
Divide Three- and Four-Digit Dividends
PART
A
Main Idea
I will divide up to a
four-digit number by
a one-digit number.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
SPI 0506.2.4 Solve problems
involving the division of twoand three-digit whole numbers
by one- and two-digit whole
numbers.
B
C
D
E
F
Divide Three- and
Four-Digit Dividends
To divide a greater dividend by a one-digit divisor, use the same
process as dividing a two-digit dividend by a one-digit divisor.
RIDES In a 4-hour period,
852 people rode the Thunder
der
Canyon ride. If the same
number of people rode
the ride each hour, how
many people rode the
ride in the first hour?
Find 852 ÷ 4.
Estimate 852 ÷ 4
900 ÷ 4 = 225
Step 1 Divide the hundreds.
Step 2
2
4 852 Divide: 8 ÷ 4
-8
Multiply: 2 × 4
−−−
0
Subtract: 8 - 8
21
4 852
-8
−−−
Divide: 5 ÷ 4
05
-4
Multiply: 1 × 4
−−−
1
Subtract: 5 - 4
Compare: 0 < 4
Step 3 Divide the ones.
213
4 852
-8
−−−
05
-4
−−−
12
- 12
−−−−
0
Divide the tens.
Compare: 1 < 4
Divide: 12 ÷ 4
Multiply: 3 × 4
Subtract: 12 - 12
Compare: 0 < 4
So, 213 people rode Thunder Canyon in the first hour.
Check 213 × 4 = 852. 130
Divide by a One-Digit Divisor
Divide by a One-Digit Number
Find 2 856 .
Estimate 900 ÷ 2 = 450
Step 1
Step 2
Step 3
Divide the hundreds. Divide the tens.
Divide the ones.
4
2 856 8 ÷ 2
-8
4×2
−−−
8-8
0
0<2
428
2 856
-8
−−−−
05
-4
−−−−
16 16 ÷ 2
- 16 8 × 2
−−−−
0 16 - 16
0<2
42
2 856
-8
−−−−
05 5 ÷ 2
- 4 2×2
−−−
1 5-4
1<2
The quotient is 428.
Compare to the estimate.
Divide a Four-Digit Number
Find 7,946 ÷ 6.
To check division with
a remainder, first
multiply the quotient
and the divisor. Then
add the remainder.
1,324
× 6
−−−−
7,944
7,944
+ 2
−−−−
7,946 Step 1 Divide the thousands.
Step 2 Divide the hundreds.
1
6 7,946
-6
−−−
1
13
6 7,946
-6
−−−
19
- 18
−−−−
1
7
1
7
1
÷6
×6
-6
<6
19 ÷ 6
3×6
19 - 18
1<6
Step 3 Divide the tens.
Step 4 Divide the ones.
132
6 7,946
-6
−−−
19
- 18
14 ÷ 6
−−−−
2×6
14
- 12 14 - 12
−−−−
2
2<6
1,324 R2
6 7,946
-6
−−−
19
-18
−−−−
14
- 12
26 ÷ 6
−−−−
4×6
26
- 24
26 - 24
−−−−
2<6
2
The quotient is 1,324 R2.
Lesson 2D Divide Three- and Four-Digit Dividends 131
Divide. See Examples 11–33
Divide
1. 2 268
2. 5 595
3. 4 625
4. 3 410
5. 516 ÷ 3
6. 932 ÷ 6
7. 5,816 ÷ 5
8. 9,982 ÷ 7
9. Three adult kangaroos weigh 435 pounds. If each adult weighs
the same, how much would one adult kangaroo weigh?
10.
E
TALK MATH Does the quotient of 945 and 8 have two or
three digits? Explain how you know without solving.
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Divide.
i id See Examples 1–3
11. 5 755
12. 2 648
13. 3 493
14. 4 8,469
15. 3 945
16. 5 630
17. 4 97
18. 2 87
19. 515 ÷ 5
20. 595 ÷ 4
21. 766 ÷ 6
22. 969 ÷ 8
23. 428 ÷ 3
24. 590 ÷ 4
25. 9,350 ÷ 7
26. 6,418 ÷ 3
27. BAR DIAGRAM A state park has cable cars that
travel about 864 yards in 4 minutes. How many
yards do the cars travel per minute?
864 yards
1 min
? yd
28. Three new video game systems cost $645. If all
the game systems cost the same, what is the cost
of each game system?
29. On Monday, a concession stand manager ordered
985 popcorn bags. She splits the bags evenly among
5 concession stands. How many popcorn bags will
each concession stand receive?
30. Mr. Harris wants to divide his 36 students into
equal groups of 3 students each. How many groups
of 3 students can he make? How many students will
not be in a group of 3?
132
Divide by a One-Digit Divisor
1 min
1 min
1 min
31. OPEN ENDED Write a real-world division problem with a divisor of
4 that has no remainder. Then write a real-world division problem
with a divisor of 4 that has a remainder.
32. NUMBER SENSE Place the digits 2, 4, 7, and 8 in ÷ to
create a division problem with the greatest quotient.
33.
E
WRITE MATH Explain how estimation is useful when
solving division problems.
Test Practice
34. Use the table below to make a true
statement.
Weight of Whales
Mammal
Weight
Blue whale
144 tons
Gray whale
36 tons
35. Lauren poured an equal amount of
the solution below in each of 4 test
tubes. How much solution is in
each test tube?
A blue whale is about ________
heavier than a gray whale.
A. 3 times
C. 6 times
F. 30 mL
H. 105 mL
B. 4 times
D. 8 times
G. 100 mL
I. 110 mL
Divide. Use the partial quotients method. (Lesson 2C)
36. 368 ÷ 4
37. 725 ÷ 5
38. Enrique has 685 trading cards that he wants to place into
5 different albums. If each album will hold the same number
of cards, how many cards will fit in each album? (Lesson 2C)
39. There are 520 baseballs that will be shipped to nine sports stores.
Estimate the number of baseballs each store is to receive if they
each receive about the same number. (Lesson 2A)
Divide. Use a related multiplication fact. (Lesson 1A)
40. 63 ÷ 7
41. 25 ÷ 5
42. 40 ÷ 8
43. 18 ÷ 6
Lesson 2D Divide Three- and Four-Digit Dividends 133
Multi-Part
Lesson
2
PART
Divide Three- and Four-Digit Dividends
A
Main Idea
I will understand how
to place the first digit
in a quotient.
B
C
D
E
F
Place the First Digit
Sometimes you may have a three-digit dividend, but there are
not enough hundreds to divide. If so, the quotient should start
at the next place value position.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
GLE 0506.2.5 Develop fluency
in solving multi-step problems
using whole numbers, fractions,
mixed numbers, and decimals.
SPI 0506.2.4 Solve problems
involving the division of twoand three-digit whole numbers
by one- and two-digit whole
numbers. Also addresses GLE
0506.1.7.
R
Raven
received 135 E-mails over
3 weeks. If she received the same
number of E-mails each week, how
many E-mails did she receive in the
first week?
Find 135 ÷ 3.
Step 1
Divide the hundreds.
3 135
There are not enough hundreds to divide into three
groups. So, regroup the hundreds block into 10 tens.
Step 2
Divide the tens.
The first digit of
4
3 135 the quotient is in
- 12
the tens place.
−−−−
15
Step 3
Divide the ones.
45
3 135
- 12
−−−−
15
- 15
−−−−
0
So, 135 ÷ 3 = 45. Raven received 45 e-mails in the first week.
Check 45 × 3 = 135. 134
Divide by a One-Digit Divisor
Divide
Find 7 684 . Estimate 700 ÷ 7 = 100
Step 1
First estimate your
answer by rounding or
using compatible
numbers.
687 ÷ 7
700 ÷ 7 = 100
So, 687 ÷ 7 is
about 100.
Step 3
Step 2
Divide the hundreds. Divide the tens.
Divide the ones.
97 R5
7 684
- 63
−−−−
54
- 49
−−−−
5
9
7 684
- 63
−−−−
5
7 684
Since 7 > 6, look at
the tens. 7 < 68.
The first digit is in
the tens place.
So, 684 ÷ 7 = 97 R5.
Compare to the estimate. 97 R5 ≈ 100 The symbol ≈ means about or almost equal to.
Divide. Check your answer using multiplication
Divide
multiplication. See Examples 1 and 2
1.
2.
5 435
- −−−−−
256
4 - −−−−−
- −−−−−
8 629
- −−−−−
- −−−−−
4. 6 576
5. 5 385
8. 282 ÷ 3
9. 108 ÷ 9
R 3.
- −−−−−
6. 6 427
7. 4 217
10. 274 ÷ 4
11. 312 ÷ 4
12. There are 594 people standing in line to see a movie premiere. The
movie is playing in 6 theaters. If the same number of people will see
the movie in each theater, how many people will be in one theater?
13.
E
TALK MATH If the first digit in the dividend is less than the number
in the divisor, where will you begin writing your quotient?
Lesson 2E Divide Three- and Four-Digit Dividends 135
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Divide.
i id Ch
Check
k your answer using
i multiplication.
l i li i
See Examples 1 and 2
14.
15.
6 498
- −−−−−
16.
315
7 - −−−−−
- −−−−−
R 286
3 - −−−−−
- −−−−−
- −−−−−
17. 6 486
18. 9 738
19. 7 662
20. 6 392
21. 117 ÷ 9
22. 237 ÷ 3
23. 485 ÷ 5
24. 567 ÷ 9
25. 178 ÷ 6
26. 472 ÷ 7
27. 382 ÷ 5
28. 518 ÷ 6
29. There are 624 envelopes to be sorted into 8 different mail bags.
If the same number of envelopes will be in each bag, how many
envelopes will be in one bag?
Use the information to solve the problem.
30. How much food does one manatee eat in a day if the three
manatees eat the same amount?
31. WHICH ONE DOESN’T BELONG? Identify the expression that
does not have a two-digit quotient.
519 ÷ 6
32.
E
915 ÷ 7
439 ÷ 7
WRITE MATH Can you determine the number of digits in
the quotient of 637 ÷ 7 without dividing? Explain.
136
Divide by a One-Digit Divisor
812 ÷ 9
Multi-Part
Lesson
2
PART
Divide Three- and Four-Digit Dividends
A
Main Idea
I will solve division
problems that result in
quotients that have
zeros.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
GLE 0506.2.5 Develop fluency
in solving multi-step problems
using whole numbers, fractions,
mixed numbers, and decimals.
SPI 0506.2.4 Solve problems
involving the division of twoand three-digit whole numbers
by one- and two-digit whole
numbers. Also addresses GLE
0506.1.7.
B
C
D
E
F
Quotients with Zeros
Sometimes quotients will contain zeros.
ELECTRONICS Maya is saving
to buy a television. The television
costs $327. She plans to save
money for 3 months. How much
does Maya need to save each
month to buy the television?
C01
1-03
31A-112
112057
Find $327 ÷ 3.
Estimate 300 ÷ 3 = 100
Step 1
$3
27
Divide the hundreds.
1
3 327
-3
0
Step 2
Divide the tens.
10
3 327
-3
02
-0
2
Step 3
Notice there are not enough tens to
divide. Place a 0 in the quotient.
Divide the ones.
109
3 327
-3
02
-0
27
- 27
0
Regroup the two tens as twenty
ones. There are now 27 ones.
Maya needs to save $109 each month.
Compare to the estimate. $109 ≈ $100. Lesson 2F Divide Three- and Four-Digit Dividends 137
Quotients with Zeros
Find 523 ÷ 4.
Estimate 500 ÷ 4 = 125
Use the same strategy
to divide a three-digit
number that you used
to divide a two-digit
Step 1 Divide the hundreds.
1
4 523
-4
−−−−
1
number.
Step 2 Divide the tens.
13
4 523
-4
−−−
12
-12
−−−
0
Step 3 Divide the ones.
130
4 523
-4
−−−
12
-12
−−−
03
- 0
−−−−
3
There are not enough
ones to divide. Place
0 in the ones place.
The remainder is 3.
So, 523 ÷ 4 = 130 R3.
Compare 130 R3 to the estimate. 130 R3 ≈ 125 Check using multiplication 130 × 4 = 520, 520 + 3 = 523
Divide. See Examples 1 and 2
Divide
1. 3 324
2. 2 418
3. 4 4,324
4. 840 ÷ 7
5. 842 ÷ 4
6. 420 ÷ 6
7. 613 ÷ 2
8. 692 ÷ 3
9. 9,163 ÷ 3
10. BAR DIAGRAM There are 630 minutes
of music to be put on 6 CDs. If the
same number of minutes fit on each
CD, how many minutes of music fit on
each CD?
138
Divide by a One-Digit Divisor
11.
E
TALK MATH Explain how to model
finding the quotient 416 ÷ 4 using
base-ten blocks.
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Divide.
Di
id See Examples
l 1 and
d2
12. 2 210
13. 3 627
14. 6 782
15. 5 530
16. 4 413
17. 9 817
18. 8 856
19. 2 6,461
20. 928 ÷ 3
21. 841 ÷ 4
22. 815 ÷ 2
23. 3,213 ÷ 3
24. There are 312 fish at the aquarium in
3 different fish tanks. Each tank has
the same number of fish. How many
fish are in each tank?
25. Kirk has watched 120 minutes of
television in the last 4 days. He
watched the same amount of television
each day. How many minutes of
television did he watch in 1 day?
Use the information to solve the problem.
26. How much does one manatee eat if the three manatees eat the
same amount?
27. OPEN ENDED Write two division problems that have zeros in the
quotient. One of the problems should have a remainder and the
other should not.
28. WHICH ONE DOESN’T BELONG? Identify the division problem
that does not belong with the other three. Explain.
621 ÷ 6
384 ÷ 3
719 ÷ 7
514 ÷ 5
29. NUMBER SENSE In problems like 714 ÷ 7, where the digit in the
greatest place of the dividend is the same as the divisor, will the
quotient always have a zero? If not, give an example.
30.
E
WRITE MATH Explain how to find the quotient of 936 ÷ 9.
To assess partial mastery of SPI 0506.2.4, see your Tennessee Assessment Book.
139
Multi-Part
Lesson
3
PART
Interpret the Remainder
A
B
C
D
E
Interpret the Remainder
Main Idea
I will explore
interpreting the
remainder in a
division problem.
Materials
connecting cubes
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
SPI 0506.1.3 Recognize the
unit associated with the
remainder in a division
problem or the meaning of the
fractional part of a whole
given in either decimal or
fraction form. SPI 0506.2.3
Select a reasonable solution to
a real-world division problem
in which the remainder must
be considered. Also addresses
GLE 0506.1.4, GLE 0506.1.6.
140
The following activities show you how to use remainders in
different kinds of problems.
A group of fifth graders collected 46 cans of food to
donate to 3 food banks. If each food bank is to get
an equal number of cans, how many cans do they
each receive?
Step 1
Use 46 connecting cubes to represent the cans of
food. Use three paper plates to represent the food
banks. Divide the cubes equally among the
three plates.
Step 2
Interpret the remainder.
Since each food bank is to get the same number of cans of
food, they will each receive 15 cans. There is one can left over.
Divide b
by a O
One-Digit
Di it Di
Divisor
i
A total of 35 students are going on a field trip to NASA’s Johnson
Space Center in Houston. If there needs to be an adult for every
8 students, how many adults are needed?
Use 35 connecting cubes to represent the students. Use paper plates
to represent the adults.
Place 8 cubes on as many plates as
possible. Place any leftover cubes on
a plate. Interpret the remainder.
There are 4 groups of 8 students.
They will each need an adult. There
are 3 students who are not enough
for a full group of 8. They will also
need an adult.
So, 4 + 1 or 5 adults are needed.
About It
1. In Activity 1, the remainder was dropped. Explain why.
2. In Activity 2, the quotient was “rounded up” to 5. Explain why.
and Apply It
State the solution and explain how to interpret the remainder in
each division problem.
3. Each picnic table at a park seats 6 people. How many tables will
83 people at a family reunion need?
4. Mrs. Malone has $150 to buy volleyballs for Lincoln Middle School.
How many can she buy at $9 each?
5.
E
WRITE MATH Suppose 2 friends want to share 5 cookies evenly.
Interpret the remainder in two different ways.
Lesson 3A Interpret the Remainder 141
Multi-Part
Lesson
3
PART
Interpret the Remainder
A
Main Idea
I will interpret the
remainder in a division
problem.
B
C
D
E
Interpret the Remainder
It is important to know what the remainder represents. In some
situations, the remainder may require you to increase the quotient.
Get ConnectED
GLE 0506.2.3
Develop fluency with division
of whole numbers. Understand
the relationship of divisor,
dividend, and quotient in terms
of multiplication and division.
SPI 0506.2.3 Select a
reasonable solution to a realworld division problem in
which the remainder must be
considered. SPI 0506.2.4 Solve
problems involving the division
of two- and three-digit whole
numbers by one- and two-digit
whole numbers. Also addresses
GLE 0506.2.5, SPI 0506.1.3.
TREES A state park has 257
evergreens to plant equally
in 9 areas. How many evergreens
are planted in each area? What
does the remainder represent?
Step 1 Divide.
28 R5
9 257
18
−−−−
77
72
−−−−
5
Step 2 Interpret the remainder, 5.
The remainder, 5, means there are 5 evergreens left over after
28 are planted in each of the 9 areas.
So, the park plants 28 evergreens in each area and
5 evergreens are left.
PARTY There are 174 guests invited to a dinner. Each table
seats 8 guests. How many tables are needed?
Step 1 Divide.
21 R6
8 174
16
−−−−
14
8
−−−
6
Step 2
Interpret the remainder, 6.
There are 6 guests left over, which is not enough for a full
table of 8. But, they also need a table.
So, a total of 21 + 1, or 22 tables are needed.
142
Divide by a One-Digit Divisor
Solve. Explain how you interpreted the remainder
remainder. See Examples 1 and 2
Solve
1. A tent is put up with 7 poles. How many tents can be put up
with 200 poles?
2. There are 50 students traveling in vans on a field trip. Each van
seats 8 students. How many vans are needed?
3. How many payments of $10 would it take
Samuel to purchase the scooter shown at the right?
4.
E
TALK MATH Discuss the different ways you
C04-01
16A
6A-105939
9
can interpret the remainder in a division problem.
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Solve.
S
l
E
Explain
l i h
how you iinterpreted
t
t d th
the remainder.
i d
See Examples
l 1 and
d2
5. Mrs. Hodges made 144 muffins for a bake sale.
She puts them into tins of 5 muffins each. How many
tins of muffins can she make?
6. Students on the softball team earned $295 from a carwash.
How many team banners shown can they buy?
7. Measurement How many 8-foot sections of fencing are
needed for 189 feet of fence?
$8.00
8. Valerie has 20 stuffed animals. She wants to store them in
plastic bags. She estimates she can fit three stuffed animals
in each bag. How many bags will she need?
9. Mrs. Flores is buying scrapbooks for her store. Her budget
is $350. How many of the scrapbooks shown can she buy?
SCRAPBOOK
10. Measurement How many 6-ounce cups can be filled from
4 gallons of juice? (Hint: 1 gallon = 128 ounces)
11. Measurement Water stations will be placed every 400 meters
of a 5-kilometer race. How many water stations are needed?
(Hint: 1 kilometer = 1,000 meters)
12. BAR DIAGRAM Three yards of fabric will be cut into pieces so
that each piece is 8 inches long. How many pieces can be cut?
(Hint: 1 yard = 36 inches)
Lesson 3B Interpret the Remainder 143
Food
Six friends decide to pack and share an
extra large submarine sandwich, which is cut into
20 equal size pieces. The cost of the submarine
sandwich is $21, not including tax.
13. How much would each friend pay if each one
paid the same amount? Explain how you
interpreted the remainder.
14. How many pieces would each friend receive if
each one receives the same amount? Explain
how you interpreted the remainder.
15. Three pieces will fit into one plastic bag. How
many plastic bags are needed to pack the
20 pieces? Explain how you interpreted
the remainder.
16. OPEN ENDED Write a real-world situation that could be described
by the division problem 38 ÷ 5 = 7 R3 in which it makes sense to
round the quotient up to 8.
17. CHALLENGE If the divisor is 30, what is the least three-digit
dividend that would give a remainder of 8? Explain.
CHALLENGE Consider each situation. In each case, decide whether
you would drop the remainder, round the quotient up, or represent
the quotient as a fraction or decimal to solve each problem. Explain
your reasoning. Then solve each problem.
18. Ernesto spent $50 on four identical photo frames. How much did he
spend on each frame?
19. Two friends share 3 cookies equally. How many cookies did each
friend get?
20. Measurement A piece of string 50 inches long will be cut into
pieces so that each piece is 4 inches long. How many full-length
pieces can be cut from the string?
21.
E
WRITE MATH Write a real-world division problem that can be
solved by interpreting the remainder. Does it make sense to
round up or down to the next whole number? Explain.
144
Divide by a One-Digit Divisor
Test Practice
22. Forty-six students are visiting a
dinosaur exhibit. A tour guide is
needed for each group of 6 students.
How many tour guides are needed?
23. Ms. Meir wants to divide 135 maps
as equally as possible among 4 zoo
guides. Which is a true statement?
F. All 4 guides will get 34 maps.
A. 7
G. Three guides will get 33 maps
and 1 guide will get 34 maps.
B. 8
H. Three guides will get 34 maps
and 1 guide will get 33 maps.
C. 40
D. 52
I. Two guides will get 33 maps and
2 guides will get 34 maps.
Divide. (Lesson 2F)
24. 432 ÷ 4
25. 763 ÷ 7
26. 840 ÷ 6
Estimate. Show your work. (Lesson 2A)
27. 360 ÷ 5
28. 619 ÷ 302
29. 643 ÷ 8
30. 411 ÷ 8
31. A penguin swam at 9 miles per hour. About how many hours would
it take for the penguin to travel 362 miles?
Solve. Use the guess, check, and revise strategy.
32. BAR DIAGRAM The teacher asked three students to
bring in cereal boxes for an art project. Dwayne brought
in 3 less than Mandy. Mandy had twice as many as
Steve. How many boxes did each student bring, if there
were a total of 22 boxes? (Lesson 1E)
Divide mentally. (Lesson 1D)
33. 640 ÷ 80
34. 3,600 ÷ 60
35. 450 ÷ 9
36. Jack owed $240 for a drum set that he needed to pay off in
6 months. How much will Jack need to pay each month in order
to pay for the drum set on time?
Lesson 3B Interpret the Remainder 145
Multi-Part
Lesson
3
PART
Interpret the Remainder
A
C
B
Problem-Solving Investigation
Main Idea I will identify extra information or missing information to solve a problem.
LILIA: On Tuesday, I was put in charge
of collecting book orders. The cost of
each book is $3. There were 7 orders
on Wednesday, 5 orders on Thursday, and
more orders on Friday and Monday.
YOUR MISSION: Find how many book orders
Lilia collected.
Understand
What facts do you know?
You know the cost of a book and the number of book orders on
Wednesday and Thursday.
What do you need to find?
You need to find the total number of book orders.
Plan
Is there any information that is not needed?
The cost of a book.
Is there any information that is missing?
Weds. Thurs.
7
5
Fri.
Mon.
?
?
The number of book orders that were collected on Friday
and Monday.
Solve
You do not have enough information to solve the problem.
Check
Read the question again to see if you missed any information.
If so, go back and rework the problem. If not, the problem cannot
be solved.
GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and
reasonableness of the solution. SPI 0506.1.4 Identify missing information and/or too much information in contextual
problems. Also addresses GLE 0506.1.6.
146
Divide by a One-Digit Divisor
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
• Use the four-step plan.
• Identify extra or missing information.
Solve each problem. If there is extra
information, identify it. If there is not
enough information, tell what information
is needed.
1. Jayden is downloading songs onto his
MP3 player. One song is 5 minutes
long, another is 2 minutes long, and a
third is between the lengths of the
other two songs. What is the total
length of all three songs?
2. BAR DIAGRAM Room 220 and Room
222 are having a canned food drive.
How many more cans has Room 222
collected than Room 220?
5. Mrs. Rollins raises prize chickens. Each
chicken eats the same amount of food.
Mrs. Rollins bought 100 pounds of
chicken food last week. How much
food did each chicken eat?
6. Paco studied his spelling words for
4 days. How many words did he study
each day if he studied the same
amount of words each day?
7. What is the cost
of the peaches
for a peach pie?
8. Measurement Rocco is slicing a loaf
of Italian bread for dinner. The bread
cost $2.99. He cuts the loaf into slices
that are 1 inch thick. If the loaf is
18 inches long, how many pieces of
bread did he cut?
9. Measurement The table shows the
number of miles the Wong family drove
each day on their vacation.
3. Karly is collecting money for a bowl-athon. Her goal is to collect $125. Last
year the bowl-a-thon raised $100. If she
charges $5 for each person, how many
people need to participate in the
bowl-a-thon?
Miles
Day 1
345
Day 2
50
Day 3
89
Day 4
279
How many more miles did they drive
on Day 1 than on Day 4?
10.
4. Measurement Sari made pancake
2
batter. She has 1_ cups of batter left.
3
How much batter did she use?
Day
E
WRITE MATH Write a problem that
has missing information. Explain how
to rewrite the problem so that it can
be solved.
To assess mastery of SPI 0506.1.3, SPI 0506.1.4, and SPI 0506.2.4, see your Tennessee
Assessment Book.
147
The Statue of Liberty has become a
symbol of freedom since its arrival
in the United States. The statue
stands on Liberty Island in the New
York harbor. It is 151 feet tall and
weighs about 448,000 pounds.
There are 354 stairs from the
bottom of the statue to the crown.
What a hike!
When immigrants came to New
York between 1886 and 1920, this
statue was one of the first things
they saw. Today, visitors can travel
to the Statue of Liberty by a ferry
or a yacht. The yacht, called the
Zephyr, can hold up to
600 passengers at one time.
Use the information given to solve each problem.
A total of 459 passengers rode
the Zephyr to Ellis Island. If the
passengers were evenly spread out
on the ferry’s three decks, how
many passengers were on each
deck?
If the Zephyr was completely filled,
how many people could fit evenly
on each deck?
How many adult tickets can be
purchased with $75? Tell how you
interpreted the remainder.
148
Divide by a One-Digit Divisor
How many child tickets can be
purchased with $25? Tell how you
interpreted the remainder.
How many senior tickets can be
purchased with $35? Tell how you
interpreted the remainder.
When school groups visit, one
teacher must accompany each
group of ten students. How many
teachers should accompany a class
of 25 students?
The Statue
of Liberty was
completed in France. Then
it was taken apart and all
350 pieces were shipped to
the United States
and rebuilt.
Statue of Liberty
Ferry Prices ($)
Adult
10
Child (4–12 yr)
4
Senior (+62 yr)
8
Problem Solving in Social Studies 149
Chapter Study
Guide and Review
Be sure the following
Key Concepts are noted in
your Foldable.
Vocabulary
dividend
Divisio
n
divisor
Lesson
1
Divide
b
One-D y a
ig
Divisor it
.
quotient
remainder
Vocabulary Check
Key Concepts
Divide a Two-Digit Number by a One-Digit
Divisor (Lesson 1)
32
64
2 6
6÷2
−−−
04 3 × 2
4 4÷2
−−−
0 2×2
Estimate Quotients (Lesson 2)
• You can use compatible numbers to
estimate quotients.
28 and 7 are
compatible numbers.
280 ÷ 7 = 40, so 283 ÷ 7 is about 40.
Interpret the Remainder (Lesson 3)
• When interpreting the remainder you
can drop the remainder, use only the
remainder, or add 1 to the quotient.
150
1. When you divide, the answer is
called the (dividend, quotient).
2. When you use 450 ÷ 9 to
estimate 437 ÷ 9, you are using
(rounding, compatible numbers).
3. The (divisor, remainder) is the
number left after a quotient is
found.
4. The quotient 1,040 ÷ 5 is
(208, 28).
283 ÷ 7
280 ÷ 7
Choose the correct term or number
to complete each sentence.
Divide by a One-Digit Divisor
5. The value of 360 ÷ 90 is (4, 40).
6. The better estimate for 6,217 ÷
186 is (30, 300).
7. An example of compatible
numbers for division is (9 and 45,
9 and 10).
Multi-Part Lesson Review
Lesson 1
Divide by a One-Digit Divisor
Relate Division to Multiplication
(Lesson 1A)
Divide. Use a related multiplication fact.
8. 32 ÷ = 8
10. 14 ÷ 7 = 9. 40 ÷ 5 = 11. ÷ 7 = 7
EXAMPLE 1
48 ÷ 8 = Think: 8 × = 48
8 × = 48 Write a related multiplication
fact.
8 × 6 = 48
So, 48 ÷ 8 = 6.
Divide a Two-Digit Number by a One-Digit Divisor
Divide. Use multiplication to check your
answer.
EXAMPLE 2
12. 3 93
13. 7 84
Step 1
Divide the tens.
14. 5 78
15. 2 47
1
7 79 7 ÷ 7
1×1
7
−−−
7-7
0
16. In 2 hours Cara read 48 pages. If she
read the same number of pages each
hour, how many pages did Cara read
in one hour?
Division Patterns
(Lesson 1C)
Find 79 ÷ 7.
0<7
So, 79 ÷ 7 = 11
Step 2
Bring down the ones.
Divide the ones.
11
7 79
7
−−−
09 9 ÷ 7
7 7×1
−−−
2 9-7
2<7
R2.
(Lesson 1D)
Divide mentally.
EXAMPLE 3
17. 420 ÷ 7
18. 300 ÷ 3
Find 15,000 ÷ 5 mentally.
19. 800 ÷ 20
20. 160 ÷ 8
Step 1 Write the basic fact.
21. 630 ÷ 10
22. 400 ÷ 50
23. Mara deposited a total of $240 in her
account in the past 6 weeks. If she
deposited the same amount each
week, what was the amount of each
deposit?
15 ÷ 5 = 3
Step 2 Continue the pattern.
150 ÷ 5 = 30
1,500 ÷ 5 = 300
15,000 ÷ 5 = 3,000
So, 15,000 ÷ 5 = 3,000.
Chapter Study Guide and Review 151
Chapter Study Guide and Review
Lesson 1
Divide by a One-Digit Divisor
(continued)
Problem-Solving Strategy: Guess, Check, and Revise
Solve. Use the guess, check, and revise
strategy.
24. The table shows admission costs to a
car exhibit.
Customer
Cost
Adult
Child
$5
$3
The cost of admission for 8 people is
$32. How many adults and children
are in the group?
25. Will ran 120 minutes in two days. He
ran 20 more minutes the second day
than the first day. How many minutes
did he run each day?
Lesson 2
(Lesson 1E)
EXAMPLE 4
Orlando buys 10 T-shirts and spends a
total of $96. Long-sleeved shirts cost
$12. Short-sleeved shirts cost $8. How
many of each did he buy?
Use the guess, check, and revise strategy.
Guess: 5 $12 shirts, 5 $8 shirts
Check: 5 × 12 = 60, 5 × 8 = 40
$60 + $40 = $100 too high
Revise: Try fewer $12 shirts and more
$8 shirts.
Guess: 4 $12 shirts, 6 $8 shirts
Check: 4 × 12 = 48, 6 × 8 = 48
$48 + $48 = $96 So, he bought 4 shirts for $12 each and
6 shirts for $8 each.
Divide Three- and Four-Digit Dividends
Estimate Quotients
(Lesson 2A)
Estimate. Show your work.
EXAMPLE 5
26. 219 ÷ 2
27. 126 ÷ 4
Estimate 825 ÷ 2.
28. 724 ÷ 9
29. 182 ÷ 3
30. 621 ÷ 3
31. 127 ÷ 6
32. 541 ÷ 6
33. 452 ÷ 5
825 ÷ 2
800 ÷ 2
Change 825 to 800 because
8 and 2 are compatible.
800 ÷ 2 = 400
Divide mentally.
So, 825 ÷ 2 is about 400.
34. Three plane tickets to New York cost
$2,472. If each plane ticket costs the
same amount, about how much does
one ticket cost?
152
Divide by a One-Digit Divisor
Lesson 2
Divide Three- and Four-Digit Dividends
Divide Three- and Four-Digit Dividends
(continued)
(Lesson 2D)
EXAMPLE 6
Divide.
625
35. 5 36. 4 936
37. 3 431
38. 2 533
39. 512 ÷ 5
40. 893 ÷ 8
41. Carmen has 468 trading cards in
4 binders. If each binder has the same
number of cards, how many cards are
in each binder?
42. A cabinet with 4 shelves can hold 640
CDs. If the shelves each hold the same
number of CDs, how many CDs does
each shelf hold?
Find 696 ÷ 3.
Step 1
Divide the hundreds.
2
3 696 6 ÷ 3
3×2
6
−−−
6-6
0
0<3
Step 2
Divide the tens.
23
3 696
-6
09 9 ÷ 3
-9 3×3
0 9-9
0<3
Step 3
Divide the ones.
232
3 696
-6
09
-9
06 6 ÷ 3
-6 3×2
0 6-6
So, 696 ÷ 3 = 232.
Place the First Digit
(Lesson 2E)
Divide. Check your answer using
multiplication.
43. 285 ÷ 3
44. 117 ÷ 9
45. 6 433
46. 4 221
47. There are 455 chairs separated into
5 equal sections. How many chairs are
in each section?
EXAMPLE 7
Find 171 ÷ 3.
57
3 171
15
−−−−
21
21
−−−−
0
There are not enough
hundreds. Place the 5
in the tens place.
So, 171 ÷ 3 = 57.
Check 57 × 3 = 171 Chapter Study Guide and Review 153
Chapter Study Guide and Review
Lesson 2
Divide Three- and Four-Digit Dividends
Quotients with Zeros
(Lesson 2F)
Divide.
EXAMPLE 8
48. 8 848
49. 2 8,412
50. 3 627
51. 4 4,364
52. Malik swam 918 meters in 3 days.
If he swam the same distance each
day, how far did Malik swim in
one day?
Lesson 3
(continued)
Find 428 ÷ 4.
107
428
4 -4
02
0
−−−
28
28
−−−−
0
There are not enough
tens to divide equally
by 4. So, there is a
zero in the tens place
of the quotient.
So, 428 ÷ 4 = 107.
Interpret the Remainder
Interpret the Remainder
(Lesson 3B)
Solve. Explain how you interpreted
the remainder.
53. Joel has 48 oranges. He puts
7 oranges in a bag. How many bags
can he fill?
54. A factory received 1,268 sponges. Only
12 sponges fit in each box. How many
boxes did the factory receive?
EXAMPLE 9
A florist has 86 roses. She plans to put
5 roses in each box. How many boxes
can she fill?
17 R1
86
5 5
−−−
She can fill 17 boxes. The
36 remainder 1 means that
35 there is 1 rose left.
−−−−
1
Problem-Solving Investigation: Extra or Missing Information
Solve. If there is extra information, identify
it. If there is not enough information, tell
what information is needed.
55. How much higher is Mount Hayes
than Mount Olympus?
154
Mountain
Elevation (ft)
Mount Olympus
Mount Mitchel
Mount Hayes
2,429
6,684
4,216
Divide by a One-Digit Divisor
(Lesson 3C)
EXAMPLE 10
Gia studied 75 words over a certain
number of days. How many words did
she study each day if she studied the
same amount each day?
You cannot solve this problem because
you do not know how many days she
studied.
Practice
Chapter Test
Divide. Use a related multiplication fact.
1. 35 ÷ = 7
2. 42 ÷ 7 = Divide mentally.
3. 900 ÷ 100
4. 1,600 ÷ 800
5. 490 ÷ 7
6. 2,400 ÷ 3
17. A librarian has 88 new reference books.
She puts them on 5 shelves. She puts
an equal number of books on each
shelf. How many books are left over?
18. MULTIPLE CHOICE Mr. Torrez bought
a jar of beads that has 525 beads. If
he divides the beads equally among
5 bags, how many beads will be in
each bag?
7. Cedric is saving money to buy a new
skateboard that costs $350. If he saves
$70 each week, how many weeks will it
take him to save enough money to buy
the skateboard?
Estimate. Show your work.
8. 455 ÷ 5
9. 815 ÷ 4
10. MULTIPLE CHOICE Charlotte keeps her
coins in 3 separate cases. If each case
has the same number of coins, how
many coins are in each case?
Charlotte’s
Coins
Mark’s Coins
294
398
A. 92
C. 98
B. 95
D. 100
84
11. 3 12. 4 156
13. 5 632
14. 98 ÷ 7
15. 385 ÷ 5
16. 125 ÷ 9
H. 110
G. 105
I.
115
19. The Snack Shop sold 13 more hot
dogs on Saturday than it sold on
Sunday. A total of 59 hot dogs were
sold. How many were sold on
Saturday? Solve. Use the guess, check,
and revise strategy.
20. A pizza with 10 pieces will be divided
among three friends. How many pieces
will each friend receive? Explain how
you interpreted the remainder.
21.
Divide. Write answers with remainders.
F. 100
E
WRITE MATH A student group visits
a butterfly exhibit. They pay $12 for
each student, but receive a group
discount. The total cost after the
discount is $242. How many students
were in the group? Explain what
information is missing to solve this
problem.
Practice Chapter Test
155
Test Practice
GRIDDED RESPONSE There are 447 people
seated in the school auditorium. There are
3 sections in the auditorium each with the same
number of seats. If the auditorium is completely
filled, how many seats are there in each section?
When you divide, use
multiplication to check
your work.
Read the Test Item
You need to divide the number of people by the
number of sections to find how many seats there
are in each section.
Solve the Test Item
1 49
Divide 447 by 3.
149
3 447
3
−−−
14
12
−−−−
27
27
−−−−
0
The answer is 149. Fill in the grid.
Read each question. Then fill in the correct answer on the answer
sheet provided by your teacher or on a separate sheet of paper.
1. A food bank
Fruit
Amount
has apples
Apples
112
and oranges.
Oranges
94
The apples are
stored evenly in
4 bags. How many apples are there in
each bag?
156
A. 22
C. 26
B. 24
D. 28
Divide by a One-Digit Divisor
2. A grocery store has 96 cereal boxes on
8 shelves. If the same number of boxes
are on each shelf, how many boxes are
on one shelf?
F. 12
H. 50
G. 24
I. 768
3. There are 279 teachers in attendance at
a conference. The teachers are divided
into groups of 9. How many groups
are there?
4.
A. 23
C. 27
B. 25
D. 31
7. So far, 380 people have ridden in the
hot-air balloon. The balloon holds a
total of 4 people each time it goes up.
How many times has the hot-air
balloon gone up?
GRIDDED RESPONSE Sean has
120 CDs in his collection. The CDs are
stored in a book with 8 per page. How
many pages of the book are filled?
5. Kenya has 183 stickers in a book. If
each page contains about 9 stickers,
estimate how many pages she has in
her sticker book.
F. 10
H. 75
G. 50
I. 95
8. Use mental math to estimate the
quotient shown below.
814 ÷ 9
F. 10
H. 30
G. 20
I. 50
9.
6. Use mental math to estimate the
quotient shown below.
A. 90
C. 110
B. 100
D. 115
SHORT RESPONSE Chris spent $9
on lunch. He bought 3 different items.
What did Chris buy for lunch? Explain.
Prices
215 ÷ 30
Chicken Sandwich
$5
Salad
$3
Fries
$2
A. 5
C. 32
Vegetable
$2
B. 7
D. 112
Drink
$1
NEED EXTRA HELP?
If You Missed Question . . .
Go to Chapter-Lesson . . .
For help with . . .
1
2
3
4
5
6
7
8
9
3-2E
3-1C
3-2E
3-2E
3-2A
3-2A
3-2E
3-2A
3-1E
SPI 2.4 SPI 2.4 SPI 2.4 SPI 2.4 SPI 2.4 SPI 2.4 SPI 2.4 SPI 2.4 GLE 1.2
Test Practice 157