CHAPTE R
4
Divide by a
Two-Digit Divisor
connectED.mcgraw-hill.com
The
BIG Idea
Investigate
How can I divide
by two-digit
divisors accurately?
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information about
division.
e
a
Estimat
e by
ts Divido-Digit
Quotien
Tw isor
iv
h
D
wit
it
Two-Dig
Divisiors
Adjust
Quotients
Audio
e
Dividter
Grea bers
Num
Foldables
Practice
Self-Check Practice
eGames
Worksheets
Assessment
Review Vocabulary
r that is being divided
dividend dividendo a numbe
19 19 is the dividend.
3 Review Vocabulary
English
divisor
quotient
158
Español
divisor
cociente
When Will I Use This?
Your Turn!
You will solve thhiis teerrr.
problem in the chap
Divide by a Two-Digit Divisor 159
Are You Ready
for the Chapter?
Text Option
You have two options for checking
Prerequisite Skills for this chapter.
Take the Quick Check below.
Estimate each product. Tell whether the estimate is greater than
or less than the actual product.
1. $224 × 12
2. 372 × 36
3. 488 × 85
4. 515 × 41
5. 688 × 59
6. 729 × 82
7. Raul purchases 13 packs of straws for
his restaurant from Company A. About
how many straws does he have in all?
Company
Number of Straws
per Pack
A
225
B
310
Multiply.
8. 14 × 3
9. 36 × 5
11. 125 × 5
12. 368 × 7
10. 76 × 4
13. 2,576 × 8
14. A musical was sold out for three straight shows. If 825 tickets were
sold at each performance, how many tickets were sold in all?
Multiply.
15. 15 × 12
16. 16 × 14
17. 28 × 43
18. 75 × 62
19. 132 × 24
20. 372 × 89
21. The teacher purchased 13 packs of crayons.
There are 24 crayons in each pack. How
many crayons are there in all?
Online Option
160
Take the Online Readiness Quiz.
Divide by a Two-Digit Divisor
Multi-Part
Lesson
1
Divide by a Two-Digit Divisor
PART
A
Main Idea
I will estimate
quotients with twodigit divisors.
Get ConnectED
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.
Also addresses GLE 0506.1.7.
B
C
D
Estimate Quotients
with Two-Digit Divisors
You can use rounding and compatible numbers to estimate
quotients when dividing by two-digit divisors. By estimating first,
you can determine the reasonableness of your results.
FLIERS The school principal has 812 fliers
to pass out equally to 19 different
teachers. About how many fliers will
each teacher receive?
Estimate 812 ÷ 19.
Step 1
Round the divisor to the nearest
ten and round the dividend to
the nearest hundred.
Step 2 Divide mentally.
812 ÷ 19
800
20
800 ÷ 20 = 40
So, each teacher would receive about 40 fliers.
CAMPING Camp Hickory has 425 campers. If there are
64 counselors, about how many campers will be assigned
to each counselor?
Estimate 425 ÷ 64.
Step 1
Round the divisor to
the nearest ten.
425 ÷ 64
425 ÷ 60
Step 2 Change the dividend to
420 because 42 and 6
are compatible numbers.
420 ÷ 60
Step 3 Divide mentally.
420 ÷ 60 = 7
So, about 7 campers will be assigned to each counselor.
Lesson 1A Divide by a Two-Digit Divisor 161
Use Rounding and
Compatible Numbers
Estimate 234 ÷ 41.
Step 1
Another way to
write 234 ÷ 41 is
4.
23
41 Round the divisor to the
nearest ten.
234 ÷ 41
234 ÷ 40
Step 2
Change the dividend to a number
that is compatible with 40. Notice
it is easy to divide 240 by 40.
240 ÷ 40
Step 3
Divide mentally.
240 ÷ 40 = 6
So, 234 ÷ 41 is about 6.
Check 6 × 40 = 240 and 240 ≈ 234 Estimate. Show your work.
Estimate
work See Examples 1–3
1 3
1. 31 312
2. 91 730
3. 24 943
4. 43 847
5. 129 ÷ 42
6. 642 ÷ 83
7. 208 ÷ 51
8. 597 ÷ 28
9. A classroom of 28 students used 612 pencils over the school year. If
each student used the same number of pencils, about how many
pencils did each student use?
10. A box of cereal contains 340 grams. If there are 12 servings, about
how many grams are there in one serving? Show how you estimated.
Explain why your answer is reasonable.
11. There are 598 goldfish divided equally among 23 fish tanks.
About how many goldfish are in each tank?
12. Suppose the number of goldfish in Exercise 11 increased to 605,
would your estimate change? Explain.
13.
E
TALK MATH Is it possible to have more than one estimate for a
division problem? Explain. Give an example.
162
Divide by a Two-Digit Divisor
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Begins on page EP2.
Estimate.
E
ti t Sh
Show your work.
k See Examples 1–3
14. 23 400
15. 52 653
16. 59 300
17. 38 244
18. 32 619
19. 34 272
20. 84 812
21. 26 425
22. Sudi has collected 643 stamps and
wants to place them all in an album.
Each page of the album holds
82 stamps. He estimates that he needs
80 pages. How can you tell his
estimate is wrong?
23. A school bus holds 42 people.
Suppose 381 students ride the bus to
school. About how many buses are
needed? Explain why your estimate
is reasonable.
Use the information to solve the problem.
A Big Book
24. Estimate the number of pages Antwan needs to read each day.
25. REASONING Explain how you can use mental math to estimate
320 ÷ 82.
26. WHICH ONE DOESN’T BELONG? Which of these equations is
NOT a reasonable estimate for 533 ÷ 57?
540 ÷ 60 = 9
27.
E
500 ÷ 50 = 10
550 ÷ 55 = 10
420 ÷ 60 = 7
WRITE MATH Explain when it would be useful to estimate.
Lesson 1A Divide by a Two-Digit Divisor 163
Multi-Part
Lesson
1
Divide by a Two-Digit Divisor
PART
A
Main Idea
B
C
D
Divide by a
Two-Digit Divisor
I will explore dividing
by two-digit divisors
using models.
Materials
base-ten blocks
Gary is saving up to buy a guitar that costs $180.
Suppose he saves for 12 months. How much money
does he need to save each month?
Find 180 ÷ 12. Use base-ten blocks to find the quotient.
Step 1
Model 180 using base-ten blocks.
Step 2
Regroup the hundred block into tens. Divide the
tens equally into 12 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.
There are
18 tens.
There are still 6 tens that need to
be divided.
164
Divide by a Two-Digit Divisor
Step 3
Regroup the remaining tens as ones. Divide the ones
equally into 12 groups.
There are 60 ones.
Each group contains 1 ten and 5 ones or 15. So, each month
Gary needs to save $15.
Check Use multiplication to check your answer.
$15 × 12 = $180 About It
1. In the Explore Activity you started by placing 1 ten in each group. What does
that show about the place value of the first digit of the quotient?
2. What would happen if the cost of the guitar was $192? Would the
amount to save each month increase or decrease? Explain.
3. Suppose Jamie chose to save for 13 months instead of 12 months.
Will the amount he needs to save per month increase or decrease?
Explain your answer.
and Apply It
Use models to find each quotient.
4. 117 ÷ 13
5. 136 ÷ 17
6. 231 ÷ 11
7. 105 ÷ 15
8. 208 ÷ 13
9. 273 ÷ 13
10.
E
TALK MATH How can you use multiplication to check your
answers for Exercises 4–9?
Lesson 1B Divide by a Two-Digit Divisor 165
Multi-Part
Lesson
1
PART
Divide by a Two-Digit Divisor
A
Main Idea
I will divide up to a
three-digit number by
a two-digit divisor.
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
Divide by a
Two-Digit Divisor
In this lesson, you will learn how to divide by a two-digit divisor.
Use estimation to help place the first digit in the quotient.
FOOD A full sheet cake serves
76 people. How many sheet
cakes are needed to serve
836 people? Check your
answer for reasonableness.
Find 836 ÷ 76.
Estimate 800 ÷ 80 = 10. So, the first digit is in the tens place.
Step 1
Write 836 ÷ 76 as 76 836 .
Step 2
Divide the tens.
1
76 836 Divide: 83 ÷ 76
-76
−−− Multiply: 76 × 1
7 Subtract: 83 - 76
Compare: 7 < 76
Step 3
11
76 836
-76
−−−−
76
-76
−−−
0
Divide the ones.
Bring down the ones.
Divide: 76 ÷ 76
Multiply: 1 × 76
Subtract: 76 - 76
Compare: 0 < 76
Check for Reasonableness Compare to the estimate, 10.
Since 11 is close to 10, the answer is reasonable. So, 11 cakes are needed to serve 836 people.
As with division by a one-digit divisor, it is possible to have
a remainder when you divide by a two-digit divisor.
166
Divide by a Two-Digit Divisor
Division with a Remainder
Find 751 ÷ 30.
Estimate 750 ÷ 30 = 25
n
You can check divisio
with a remainder.
Multiply the quotient
and the divisor. Then
add the remainder.
25
×
−
−−30
750
750
1
+
−−−−
751
Step 1 Write 751 ÷ 30 as 30 751 .
Step 2 Divide the tens.
Step 3 Divide the ones.
2
30 751 75 ÷ 30
-60
−−− 2 × 30
15 75 - 60
25 R1
30 751
Bring down the ones.
-60
−−−−
151 151 ÷ 30
5 × 30
-150
−−−−
1 151 - 150
15 < 30
1 < 30
Check for Reasonableness Compare to the estimate, 25.
Since 25 R1 is close to 25, the answer is reasonable.
So, 751 ÷ 30 is 25 R1.
MEASUREMENT Mackenzie volunteered 204 hours last
year. If she volunteered the same number of hours each
month, how many hours did she volunteer each month?
Find 204 ÷ 12.
Estimate 200 ÷ 10 = 20
Step 1 Write 204 ÷ 12 as 12 204 .
Step 2 Divide the tens.
Step 3 Divide the ones.
1
12 204 20 ÷ 12
-12
−−− 1 × 12
8 20 - 12
17
12 204
-12
−−−−
84
-84
−−−
0
8 < 12
Bring down the ones.
84 ÷ 12
7 × 12
84 - 84
Check for Reasonableness Compare to the estimate, 20.
Since 17 is close to 20, the answer is reasonable.
So, Mackenzie volunteered an average of 17 hours each month.
Lesson 1C Divide by a Two-Digit Divisor 167
Divide
Divide. See Examples 11–33
1. 16 176
2. 23 759
5. Mr. Calzada buys flags for his store.
Each flag costs $28. How many flags
can he buy for $350?
3. 809 ÷ 62
6.
E
4. 925 ÷ 42
TALK MATH Explain how estimation
is used to help you place the first digit
in the quotient.
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Divide.
Di
id See Examples
l 1–3
7. 15 210
8. 27 837
9. 34 594
11. 840 ÷ 24
12. 546 ÷ 44
13. 939 ÷ 27
10. 12 155
14. 790 ÷ 29
15. A boat travels 384 miles in 24 hours.
What is the average distance the boat
travels in 1 hour?
16. Dreanne has 288 pictures. Her album
holds 12 pictures on each page. How
many pages does she need?
17. In 31 days Gwen sleeps 248 hours. If
she sleeps the same number of hours
each night, how many hours does she
sleep per night?
18. How many payments of $46 does
Will need to make for a bed that
costs $644?
Use the information to solve the problem.
A Big Book
19. How many pages does Antwan need to read each day to finish his
294-page book in 3 weeks?
168
Divide by a Two-Digit Divisor
20. OPEN ENDED Write a real-world division problem that has
a two-digit quotient that is greater than 40 but less than 50.
21. NUMBER SENSE Without calculating, predict whether 630 ÷ 42
will have a 1 or a 2 in the first digit of the quotient. Explain.
22. CHALLENGE Find the quotient of 1,686,366 ÷ 27.
23.
E
WRITE MATH What are two different ways to check the
reasonableness of your quotient?
Test Practice
24. A hotel has 21 floors and a total of
861 rooms. Suppose there are the
same number of rooms on each floor.
Which expression would describe
how many rooms are on the 21st
floor?
25.
26. The principal is placing trophies
onto 12 shelves. Suppose an equal
number of trophies need to be
placed on each shelf. How many
trophies can be placed on the first
shelf?
A. 21 ÷ 861
F. 12
B. 861 ÷ 21
G. 6
C. 861 × 21
H. 5
D. 861 ÷ 5
I. 4
GRIDDED RESPONSE Jalisa’s
teacher assigned a 364-page book
for her to read. Jalisa has 14 days to
read the book. If she reads the same
number of pages each day, how
many pages will she need to read
each day to finish the assignment
on time?
Trophies
Type
Amount
Academic
25
Sports
35
27. A group of friends equally split the
dinner bill shown. If each person
paid $16, how
many friends
paid?
A. 7 friends
B. 12 friends
C. 14 friends
Chicken Tacos.......$82
Drinks.....................$28
Salads.....................$52
Desserts..................$33
Tip...........................$29
Total......................$224
D. 16 friends
Lesson 1C Divide by a Two-Digit Divisor 169
Multi-Part
Lesson
1
Divide by a Two-Digit Divisor
PART
A
B
C
D
Problem-Solving Strategy:
Solve a Simpler Problem
Main Idea I will solve problems by solving a simpler problem.
TTo serve 240 people, you would need to
buy 20 cakes from Bryan’s Bakery. Each cake
b
serves the same number of people. How
many people could you serve if you
bought 25 cakes?
Understand
What facts do you know?
20 cakes can serve 240 people.
What do you need to find?
How many people can be served
by 25 cakes?
Plan
You can solve the problem by solving
a simpler problem.
Solve
Step 1 Find how many people are served by 1 cake.
240 ÷ 20 = 12 Each cake serves 12 people.
Step 2 Find how many people can be served by 25 cakes.
25 cakes
12
1 cake
12 × 25 = 300
So, 25 cakes will serve 300 people.
Check
Since 300 ÷ 25 = 12, and 12 is the amount of people served by one cake,
the answer is correct. 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 0506.1.2 Apply and adapt a variety of
appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
170
1
Divide by a Two-Digit Divisor
Refer to the problem on the previous page.
1. Explain why you first found how many
people just 1 cake would serve.
3. Look back at Exercise 2. Check your
answer. How do you know it is
reasonable? Explain.
2. How many people could be served by
8 cakes?
4. Explain when you would use the solve
a simpler problem strategy to solve a
problem.
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Solve. Use the solve a simpler problem strategy.
5. Algebra Working separately,
3 teenagers can mow 3 lawns in
3 hours. At this rate, how many lawns
can 6 teenagers mow in 9 hours?
6. Measurement
Darby is cutting
ribbons for
balloons. Each
ribbon needs to
be 3 feet long. How long will it take
Darby to make the cuts if each cut
takes 3 seconds?
9. Josh watches 720 television shows in
one year. If he watches the same
number of shows each month, how
many shows does he watch in
5 months?
10. Charity and her friend each want to
buy a piece of pizza, a drink, and an
ice cream cone. Charity has $10 to pay
for her and her friend’s meal. Does she
have enough money? Explain.
7. Find the sum of the whole numbers
from 1 through 10. Use this sum to
help you find the sum of the whole
numbers from 1 through 20.
8. Kodi wants to buy a new tennis racket.
So far, she has saved $25 plus $7 from
each of her two babysitting jobs. How
much more money does she need to
buy the tennis racket shown below?
Pizza
$3.00
Drink
$1.00
Ice cream cone
$2.00
11. Algebra At the beach, 4 children
working separately made 8 sandcastles
in an hour. At this rate, how many
sandcastles can 12 children make in
1
a _ hour?
2
$6
5
12.
E
WRITE MATH Write a real-world
problem that can be solved using the
solve a simpler problem strategy. Trade
with a partner and solve.
Lesson 1D Divide by a Two-Digit Divisor 171
Mid-Chapter
Check
Estimate. Show your work. (Lesson 1A)
412
1. 43 2. 81 630
124
3. 31 4. 59 542
5. 987 ÷ 11
6. 921 ÷ 88
16. MULTIPLE CHOICE A package of
construction paper holds 525 pieces
of paper with 15 different colors. If
there are the same number of pieces
of paper per color, how many pieces of
paper of each color are there? (Lesson 1C)
7. MULTIPLE CHOICE There were
815 ants in 11 ant farms. If the same
number of ants were in each ant farm,
about how many ants were in one
farm? (Lesson 1A)
525
sheets
A. 50
B. 80
F. 35
H. 75
C. 100
D. 150
G. 50
I.
8. The Mitchell family is making payments
on the refrigerator shown. If they pay
$41 every month, how many months
will it take to pay for the refrigerator?
(Lesson 1C)
540
17. Addison has 512 beads to make
16 necklaces. How many beads can
she put on each necklace, if each
necklace gets the same number of
beads? (Lesson 1C)
18. Working separately, 5 carpenters can
make 10 chairs in 2 days. How many
chairs can 10 carpenters make in
4 days? (Lesson 1D)
Divide. (Lesson 1C)
9. 14 616
10. 22 814
11. 25 975
12. 62 682
13. 529 ÷ 43
14. 651 ÷ 28
15. A movie theater has 576 seats arranged
in 36 equal rows. How many seats are
in each row?
172
Mid-Chapter Check
19. Marcy and her friend working
separately can make 8 greeting
cards in 32 minutes. How many
greeting cards can Marcy and her
friend make in 48 minutes?
(Lesson 1D)
20.
E
WRITE MATH Suppose you estimate
323 ÷ 14 as 300 ÷ 10 = 30. Would
your estimate be larger or smaller than
the exact answer? Explain. (Lesson 1A)
Lowest Number Wins!
Divide by Two-Digit Divisors
You will need: number cubes,
index cards
Get Ready!
Players: 2, 3, or 4 players
Get Set!
Game Sheet
÷
Each player makes a game
sheet like the one shown at
the right.
Go!
Each player rolls a number
cube and writes the number
rolled in one of the blanks
on his or her game sheet.
All players find their
quotients. The player with
the least quotient earns one
point. In case of a tie, those
players each earn one point.
The first person to earn
5 points wins.
Game Time Lowest Number Wins!
173
Multi-Part
Lesson
2
PART
Divide Greater Numbers
A
Main Idea
I will adjust the
quotient when the
estimated digit is too
high or too low.
B
C
Adjust Quotients
When you estimate which digit to place in the quotient, your
estimate might be too small or too large. So, you need to adjust
the quotient.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
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 0506.2.3.
BDB
DMP3 Player Galina’s mother bought
ought herr
a new MP3 player. The total cost
st of
the MP3 player was $144. The store
allowed her to make monthly
payments of $16. How many
payments will she need to make?
e?
Find 144 ÷ 16.
Step 1
Estimate by using
compatible numbers.
144 ÷ 16
Step 2 Try the estimate.
140 ÷ 20 = 7
7
16 144
- 112
32
Step 3 Adjust. Try 8.
Step 4 Adjust again. Try 9.
8
Since 16 = 16,
16 144
the estimated
- 128 digit is too low.
16
9
16 144
- 144
0
Since 32 > 16,
the estimated
digit is too low.
144 ÷ 16 = 9
Check for Reasonableness The estimate, 7, is less than the actual
quotient because the dividend was rounded down to 140. So, Galina’s mother will need to make 9 payments.
174
Divide by a Two-Digit Divisor
Division with a
Remainder
s
It may take several trie
to find the best
estimate for dividing
by a two-digit number.
SPORTS CARDS Neil wants
to sell his sports cards. He
has collected 1,252 sports
cards over the past several
years. If he sells his cards
in packs of 32, how many
packs will he be able to sell?
Find 1,252 ÷ 32.
Step 1 Estimate by using
compatible numbers.
1,252 ÷ 32
Step 2
Try the estimate.
4
Since 128 > 125,
32 1,252 the estimated digit
- 1 28 is too high.
1,200 ÷ 30 = 40
Step 3
Adjust. Try 3.
Step 4
3
32 1,252 29 < 32
Continue
- 96 dividing.
29
Bring down the 2
ones. Divide. Try 9.
39 R4
32 1,252
- 96
292
- 288
4 4 < 32
1,252 ÷ 32 = 39 R4
Check for Reasonableness 39 R4 ≈ 40 Neil can sell 39 packs with 4 cards remaining.
Divide. Check each answer
Divide
answer. See Examples 1 and 2
1. 34 306
2. 53 1,272
3. 62 548
4. 71 5,243
5. 115 ÷ 23
6. 1,728 ÷ 72
7. 183 ÷ 19
8. 3,489 ÷ 42
9. A crew went net fishing to catch shrimp. They caught 486 shrimp
in 54 minutes. How many shrimp did they catch per minute?
10.
E
TALK MATH Explain how you know when a digit you try in the
quotient is too small.
Lesson 2A Divide Greater Numbers
175
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Divide.
Di
id Ch
Check
k each
h answer. See Examples
l 1 and
d2
11. 41 328
12. 81 4,536
13. 47 133
14. 28 2,146
15. 26 208
16. 98 784
17. 37 1,554
18. 58 5,336
19. 413 ÷ 57
20. 242 ÷ 34
21. 2,712 ÷ 64
22. 3,425 ÷ 75
23. Brianna made 26 bracelets to sell for a fundraiser. She used a total
of 208 beads to make the bracelets. How many beads did she use
for each bracelet, if each bracelet has an equal amount of beads?
Alaska Coastline
Geography
Alaska has the longest coastline in
the United States.
24. Traveling at 60 miles per hour, how many
hours would it take to travel along the Pacific
Coast?
Coast
Miles
Pacific
5,580
Arctic
1,060
25. Alaska has about 31,383 miles of shoreline. A boat
travels 33 miles per hour. How long will it take the
boat to travel the length of the shoreline?
26. CHALLENGE Find 56,212 divided by 52.
27. FIND THE ERROR Emma estimated the first digit in the
quotient of 2,183 ÷ 42 as 4. She adjusted the quotient
to 3. What did she do wrong? Explain.
4
42 2,183
- 1 68
50 50 > 42
I’ll try 3.
28.
176
E
WRITE MATH Explain what it means to adjust a quotient.
Divide by a Two-Digit Divisor
Alaska
Alaska
Test Practice
29. Antonio chooses cell phone plan A. It
costs him $25 a month. How many
minutes does he get per dollar?
Monthly Cell Phone Plans
Plan
Minutes
A
450
B
700
30. Tyree printed 144 pictures from his
vacation. He is going to make
12 photo albums to give to his
friends. Which is the best estimate
for the number of pictures that will
be in each album?
F. less than 5
G. between 5 and 9
A. 21 minutes per dollar
H. between 10 and 20
B. 16 minutes per dollar
I. more than 20
C. 25 minutes per dollar
D. 18 minutes per dollar
31.
SHORT RESPONSE Sheila
played a total of 680 minutes for
the entire soccer season. If she
played an equal amount of time for
20 games, how many minutes did
she play each game?
Solve. Use the solve a simpler problem strategy. (Lesson 1D)
32. Sixty people can receive a slice of pizza if 5 pizzas are
purchased. How many people can receive a slice of pizza if
7 pizzas are purchased?
Divide. (Lesson 1C)
33. 18 396
34. 38 418
35. 472 ÷ 29
36. 957 ÷ 53
559
38. 72 39. 37 246
319
40. 43 Estimate. (Lesson 1A)
37. 18 409
41. A football team scored 384 points for the season. If there
were 16 games, about how many points were scored in
each game? (Lesson 1A)
42. James wants to buy a new bike that costs $239. If he wants
to save the same amount each month for a year, about how
much should he save each month? (Lesson 1A)
Lesson 2A Divide Greater Numbers
177
Multi-Part
Lesson
2
PART
Divide Greater Numbers
A
Main Idea
I will divide greater
numbers by multi-digit
divisors.
B
C
Divide Greater Numbers
You can use the standard algorithm or a calculator to divide
greater numbers.
Get ConnectED
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
0506.1.8, GLE 0506.2.3.
BDB
DCONCERTS At a recent rock concert,
$22,500 was made from front row
ticket sales. If the cost of a single
front row ticket was $75, how many
people purchased front row tickets?
Find 22,500 ÷ 75.
Estimate
21,000 ÷ 70 = 300
Step 1 Place the first digit.
3
75 22,500
- 22 5
0
225 ÷ 75
75 × 3
225 - 225
0 < 75
Step 2 Divide the tens.
30
75 22,500
- 22 5
00
-0
0
0 ÷ 75
75 × 0
0-0
0 < 75
Step 3 Divide the ones.
300
75 22,500
- 22 5
00
-0
00
-0
0
0 ÷ 75
75 × 0
0-0
0 < 75
So, 300 people purchased front row tickets.
Check for Reasonableness 300 = 300. 178
Divide by a Two-Digit Divisor
Determine
Reasonable Answers
..
To round 306.1447 .
ole
wh
to the nearest
number, look at the
digit in the tenths
PHONE BOOKS A city phone book
has 46,534 names and 152 pages.
If each page has about the same
number of names per page, how
many names are on each page?
Sean divided 46,534 by 152. He got
36 for the quotient. Is the quotient
reasonable?
Step 1 Estimate.
46,534 ÷ 152
place.
45,000 ÷ 150 = 300
306.1 rounds to 306.
45 and 15 are compatible.
Since the estimate is 300,
Sean’s quotient is NOT reasonable.
Step 2
Find the quotient using a calculator.
Type the following into your calculator.
4
6
5
3
4
1
5
2
Enter
The answer in your display screen is 306.1447 . . .
306.1447 . . .
306
So, there would be about 306 names on each page.
Estimate. Then divide.
Estimate
divide Check for reasonableness.
reasonableness See Examples 1 and 2
1. 25 47,800
2. 32 64,000
3. 87,232 ÷ 64
4. Turtles and tortoises have long life spans. A tortoise can live for
54,750 days. How many years can a tortoise live?
Estimate. Then divide using a calculator. If needed, round the quotient
to the nearest whole number.
5. 75 29,775
8.
E
6. 638 24,987
7. 66,396 ÷ 772
TALK MATH Explain how estimation is used before, during,
and after dividing greater numbers.
Lesson 2B Divide Greater Numbers
179
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
Estimate.
i
Then
h divide.
di id Check
Ch k for
f reasonableness.
bl
See Examples 1 and 2
9. 51 91,988
10. 17 14,637
11. 15,489 ÷ 64
36,712
12. 52 13. 93 43,803
14. 25,435 ÷ 42
15. There are 14,224 people inside a 56-story building. If the same
number of people are on each floor, how many people are on the
first floor?
Estimate. Then divide using a calculator. If needed, round the
quotient to the nearest whole number.
16. 28 26,208
17. 89 85,978
18. 52,056 ÷ 783
19. 812 39,789
20. 352 25,779
21. 36,719 ÷ 263
22. An average person speaks 35,000 words in one week. Does
the average person speak more or less than 2,500 words
per day?
23. BAR DIAGRAM If you pay for the golf clubs shown in 24 equal
payments, how much will you be paying each month?
In the first 26 weeks of life, a calf gainss
about 320 pounds. In the second 26 weeks,
it gains about 370 pounds.
About how many pounds does a
calf gain each week for each of
the following? Round to the
nearest pound.
24. during the first 26 weeks
25. during the second 26 weeks
180
Divide by a Two-Digit Divisor
$2,
47
2
26. OPEN ENDED Write a division problem that has an estimated
quotient of 500.
27. CHALLENGE The dividend below is missing a number. Place a
number into the dividend to make the division problem true.
8 31 R2
59 49,01
28.
E
WRITE MATH Is there a limit to the size of the dividend
that can be divided using the strategy learned in this lesson? Explain.
Test Practice
29.
SHORT RESPONSE Cale solved
875 ÷ 25 as shown. Explain the
mistake that Cale made and then
determine the correct answer.
34 R25
25 875
- 75
125
- 100
25
30. Lena’s mom is having an addition
built on their house for $15,650.
She has already paid $1,550. She
plans to pay the remaining amount
in 25 equal payments. How much is
one payment?
A. $500
B. $564
C. $592
D. $14,100
Solve. Use multiplication to check your answer. (Lesson 2A)
31. 27 216
32. 98 882
33. 37 1,591
34. Simon and his family drove 825 miles. They traveled at 55 miles
per hour. How much time did it take them? (Lesson 2A)
Estimate. Show your work. (Lesson 1A)
35. 18 496
36. 34 586
37. 12 330
Lesson 2B Divide Greater Numbers
181
Multi-Part
Lesson
2
PART
Divide Greater Numbers
A
B
C
Problem-Solving Investigation
Main Idea I will choose the best strategy to solve a problem.
ANNIE had 78 inches of plastic string to
make keychains. She used 12 inches for
one keychain. How many more keychains
will Annie be able to make if each
keychain is the same size?
Understand
What facts do you know?
• The roll of string is 78 inches long.
• Each keychain is 12 inches long.
• She has already used 12 inches of string.
What do you need to find?
How many more keychains Annie will be able to make.
Plan
Solve
Use the guess, check, and revise strategy.
Find how much string is left after Annie makes 1 keychain.
78 inches
12 inches
−−−−−−−−
66 inches
There are 66 inches of string left.
Use multiplication to find how many 12-inch keychains Annie
can make.
Guess
12
×
6
−−−
72
Check
72 > 66
Revise
12
×
5
−−−
60
She can make 5 more keychains with 6 inches of string left over.
Check
Is the answer reasonable? 66 ÷ 12 = 5 R6. 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.
182
Divide by a Two-Digit Divisor
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
• Guess, check, and revise.
• Solve a simpler problem.
• Use the four-step plan.
Use any strategy shown above to solve
each problem.
1. An aquarium at a pet store has
18 Black Neon Tetra fish in it. A
customer buys 12 Black Neon Tetra fish
at the same time the store clerk adds 7
more Black Neon Tetra fish to the tank.
How many Black Neon Tetra fish are in
the aquarium now?
2. A fifth grader takes the change from her
pocket and places it on the table. The
number of each coin she had in her
pocket is shown below.
Coin
Number
Quarter
2
Dime
4
Nickel
3
Penny
5
How many different combinations of
coins can she make with the coins she
has to have $0.45?
5. During the summer Ajay wants to read
the books shown. If it takes him 88 days
to read all of the books, and each book
takes him the same amount of time,
how long will it take him to read
1 book?
6. Mr. Reyes baked 4 batches of
muffins for his class. Each batch
had 12 muffins. If Mr. Reyes has
24 students, how many muffins will
each student receive?
7. Measurement Niko has a roll of
wrapping paper that had 40 inches on
it. He has already used 4 inches for one
gift. Does he have enough paper to
wrap three gifts that require 12 inches
of paper each? Explain.
8. At the soccer banquet everyone was
given the choice of chicken, beef, or
lasagna for dinner. If 212 people
attended the banquet, how many
people ordered lasagna?
3. The quotient of two numbers is 20.
Their sum is 84. What are the
two numbers?
Food
Number of
People
Chicken
55
Beef
110
Lasagna
4. Shelli sold 9 tickets for the school play
and collected $78. Upper-level tickets
cost $6. Ground-level tickets cost $10.
How many of each kind of ticket was
sold?
9.
E
WRITE MATH Refer to Exercise 3.
Explain how you used the guess,
check, and revise strategy to find the
numbers.
To assess mastery of SPI 0506.2.3, see your Tennessee Assessment Book.
183
Did you know you have between
206 and 300 bones in your body?
A healthy diet makes them strong
strong,
and calcium is an important part
of a healthy diet. Adults need only
1,000 milligrams of calcium each
Your bones
grow until you
are 30 years old.
184
Divide by a Two-Digit Divisor
day, but fifth graders should eat
or drink about 1,200 milligrams.
The calcium you eat or drink is
deposited in your bones. Therefore,
your bones are a “bank” for
calcium!
Use the information on the previous page to solve each problem.
1 If you eat 1 ounce of cheddar
cheese, how much calcium willl you
deposit in your bone bank? Solve
lve
mentally.
ou
u have 15
15 cups
cu
ups of
of ice
ic cream in
5 YYou
2 weeks.
w ek
we
ks.
s How
How much
muc
m
uch
h calcium
calc
ca
lciu
i m will
you
u consume
co
ons
nsum
ume in each
eac
e
acch cup?
cup?
2 Suppose you eat twelve cups of
yogurt in one week. How much
h
calcium will you eat in one day?
y?
nd a
3 Toni had a cup of skim milk and
cup of yogurt for breakfast. How
w
much calcium was in Toni’s
breakfast?
ld
4 How much more calcium would
a cup of carrots and a cup
of yogurt have than a
cup of skim milk?
Problem Solving in Health 185
Chapter Study
Guide and Review
Be sure the following Key
Concepts are noted in your
Foldable.
Vocabulary
compatible numbers
dividend
Estimate
Quotient
s
with
Two-Digit
Divisiors
Ad
Quo just
tient
s
Divide by a
Two-Digit
Divisor
divisor
quotient
Divide
Greater
Numbers
remainder
rounding
Key Concepts
Estimate Quotients with Two-Digit
Divisors (Lesson 1)
Find compatible numbers
for 315 and 59.
315 ÷ 59
300 ÷ 60
300 and 60 are
compatible because
30 ÷ 6 = 5.
Vocabulary Check
State whether each sentence is
true or false. If false, replace the
underlined word or number to make
a true sentence.
1. The answer to a division problem
is 534 R4. The R stands for
reduce.
Divide by Two-Digit Divisors (Lesson 1)
21
12 252
- 24
_____
12
12
−−−−
0
2. In the division sentence
500 ÷ 10 = 50, 50 is the
dividend.
Bring down the ones.
12 ÷ 12 = 1
1 × 12 = 12
12 - 12 = 0
3. Compatible numbers are
numbers that are easy to
divide mentally.
Adjust Quotients (Lesson 2)
Estimate 250 ÷ 50 = 5
6
48 251
288
−−−−
186
Since 288 > 251,
the estimated
digit is too high.
Adjust. Try 5.
5 R11
251
48 240
______
11
Divide by a Two-Digit Divisor
4. 810 ÷ 90 = 90
5. In the division sentence
616 ÷ 22 = 28, 22 is the
divisor.
Multi-Part Lesson Review
Lesson 1
Divide by Two-Digit Divisors
Estimate Quotients with Two-Digit Divisors
Estimate each quotient. Show your work.
634
6. 74 7. 49 311
8. 24 743
9. 84 647
EXAMPLE 1
Estimate 348 ÷ 53.
10. Tito purchased 11 tickets to a baseball
game for $374. About how much did
one ticket cost?
Divide by Two-Digit Divisors
(Lesson 1A)
348 ÷ 53
Round the divisor
to the nearest ten.
350 ÷ 50 = 7
Change the dividend
to a number that is
compatible with 5.
So, 348 ÷ 53 is about 7.
(Lesson 1C)
EXAMPLE 2
Divide.
928
11. 32 12. 71 923
13. 53 678
14. 23 578
15. Tonya saved $564 in one year. If she
saved the same amount each month,
how much did Tonya save in one
month?
Find 242 ÷ 22.
11
22 242
22
−−−−
22
22
−−−−
0
So, 242 ÷ 22 = 11.
Problem-Solving Strategy: Solve a Simpler Problem
Solve. Use the solve a simpler problem
strategy.
16. Bennett is placing
photographs in an
album. He will put
the same number of
photos on each of
the 13 pages. If he can put 4 pictures
in a row, how many rows will be on
each page?
(Lesson 1D)
EXAMPLE 3
A school rents 5 buses to take 215
students on a field trip. If each bus can
take the same number of students, how
many students will be on two buses?
Step 1 Find how many students fit on
one bus. 215 ÷ 5 = 43
Step 2 Multiply 43 by 2 to find the
number of students on 2 buses.
43 × 2 = 86
So, 86 students can fit on 2 buses.
Chapter Study Guide and Review 187
Chapter Study Guide and Review
Lesson 2
Divide Greater Numbers
Adjust Quotients
(Lesson 2A)
Divide. Check each answer.
EXAMPLE 4
378
17. 54 18. 39 273
Find 498 ÷ 83.
19. 54 2,816
20. 46 3,625
21. A jet ski costs $3,204. If you want to
make 36 equal payments, how much
is one payment?
Divide Greater Numbers
23. 76 85,400
Estimate. Then divide using a calculator.
If needed, round the quotient to the
nearest whole number.
24. 38 95,276
6
83 498
498
−−−−
0
(Lesson 2B)
Estimate. Then divide. Check for
reasonableness.
22. 25 25,600
Estimate 500 ÷ 100 = 5
Try the estimate.
5
Since 83 = 83,
the estimated
83 498
digit is too low.
415
−−−−
Adjust. Try 6.
83
So, 498 ÷ 83 = 6.
25. 68 34,658
EXAMPLE 5
Find 25,600 ÷ 64.
400
Estimate
64 25,600
30,000 ÷ 60 = 500
25 6
−−−−
00
0
−−−
00
0
−−−
0
So, 25,600 ÷ 64 = 400.
Problem-Solving Investigation: Choose the Best Strategy
Choose the best strategy to solve the
problem.
26. Sandra has 4 shirts and 3 pants. If she
wears a different combination of shirt
and pants each day, how many days
until she repeats an outfit?
(Lesson 2C)
EXAMPLE 6
Andre is using a rectangle, a triangle, and
a circle to create a pattern. How many
different ways can he arrange the shapes
to form a repeating pattern if he uses
each shape once?
27. How many ways are there to represent
$0.77 using at least two quarters and
only two pennies?
There are 6 ways to arrange the shapes.
188
Divide by a Two-Digit Divisor
Practice
Chapter Test
Estimate each quotient. Show your work.
638
1. 92 2. 19 411
433
3. 61 4. 54 989
13. MULTIPLE CHOICE Dario sold
three times as many wristbands as
headbands. If he sold 10 headbands,
how much money did he earn in all?
5. John bought 11 packages of tennis
balls for $132. About how much did
one package cost?
6. MULTIPLE CHOICE The table shows
the number of deer in a wildlife
preserve and the size of the preserve
in acres. Which is the best estimate for
the number of deer per acre?
Number of Deer
406
Number of Acres
38
A. 1
C. 100
B. 10
D. 1,000
Item
Cost
Headbands
$6
T-shirts
$12
Wristbands
$6
F. $60
H. $240
G. $180
I.
1,000
Divide.
448
14. 64 15. 89 534
16. 54 3,510
17. 36 2,649
18. 34 17,680
19. 47 44,652
Divide.
756
7. 42 8. 53 795
9. 43 822
10. 18 461
11. Trevon is making payments on a
computer that costs $1,548. If he
makes 12 equal payments, how much
is one of his payments?
12. Jillian read 336 pages in 42 days. If she
read the same amount each day, how
many pages did she read in one day?
Estimate. Then divide using a calculator.
If needed, round the quotient to the
nearest whole number.
20. 28 85,125
21. 18 72,598
22. 41 21,276
23. 13 21,740
24.
E
WRITE MATH Write a real-world
division problem that can be solved
using the act it out strategy.
Practice Chapter Test
189
Test Practice
Ms. Flores drove 360 miles. If she drove 45 miles
each hour, how many hours did she drive?
A. 5
C. 7
B. 6
D. 8
You can estimate using
compatible numbers or
rounding to check the
reasonableness of answers.
Read the Test Item
You need to divide the number of miles by
the speed she traveled to find how many
hours she drove.
Solve the Test Item
Divide 360 by 45 to find the number of
hours she drove.
8
45 360
360
−−−−
Check
45 × 8 = 360
0
The answer is D.
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. It costs $54 to purchase 6 movie
tickets. How much does it cost for
1 movie ticket?
2. The coach purchased 13 jerseys
for the basketball team for $312.
Which expression can be used to
find the cost of each jersey?
F. 13 × $312
G. $312 × 13
190
A. $5
C. $8
H. $312 ÷ 13
B. $6
D. $9
I. 13 ÷ $312
Divide by a Two-Digit Divisor
3. Find the quotient of the division
expression shown below.
7.
750 ÷ 250
4.
5.
A. 3
C. 75
B. 30
D. 300
GRIDDED RESPONSE The
principal has 322 certificates to give to
14 teachers. Each teacher receives the
same number of certificates. How many
certificates will 2 teachers receive
combined?
8. Brandy is purchasing prizes for her
party games. She spent $18 on stickers
and bracelets. How many of each prize
did she purchase?
SHORT RESPONSE It takes Javier
720 seconds to run two miles. Explain
how to find the number of minutes it
takes Javier to run two miles.
GRIDDED RESPONSE Lacey’s dad
bought the GPS system shown for his
car. He made 3 equal payments. What
was the amount of each payment in
dollars?
Prize
Cost
stickers
3 for $5
bracelets
2 for $4
A. 9 stickers and 2 bracelets
B. 6 stickers and 6 bracelets
C. 6 stickers and 4 bracelets
D. 9 stickers and 4 bracelets
9. Carlos looks at his car’s odometer
shown below to see the total distance
his car has traveled in 9 years. About
how many miles has the car traveled
each year?
$4
35
6. Erika sent 384 text messages in one
year. If she sent the same number of
messages each month, how many
messages did she send in December?
F. less than 9,000 miles
G. between 9,000 and 15,000 miles
F. 32
H. 45
H. between 15,000 and 20,000 miles
G. 40
I. 50
I. greater than 20,000 miles
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1
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3
4
5
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3-1A
4-1C
4-1A
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3-2D
4-1A
4-1D
3-1E
4-1A
SPI 2.4 SPI 2.4 GLE 2.3 GLE 2.3 SPI 2.4 GLE 2.3 GLE 1.2 GLE 1.2 GLE 1.2
Test Practice 191