2-4
Interpreting the Quotient
Going Deeper
Essential question: How do you solve problems by interpreting the quotient?
Standards for
Mathematical Content
Highlighting
the Standards
MCC6.NS.3 Fluently add, subtract, multiply, and
divide multi-digit decimals using the standard
algorithm for each operation.
This lesson offers an ideal opportunity to
address Standard 4 (Model with mathematics).
A key part of the modeling process is
interpreting results in the context of the
problem. Point out to students that it is not
enough to know how to divide decimals
and correctly express the remainder. When
a division problem arises from a real-world
context, it is essential to reread the problem
and interpret the quotient as needed.
Prerequisites
Dividing decimals by decimals
Math Background
When solving real-world problems with division,
students will often need to use the context to
determine if the quotient needs to be rounded up or
down. In some cases, a quotient with a remainder
is appropriate. For example, if an 18-inch ribbon is
cut into 5 pieces, the length of each piece is given
by 18 ÷ 5, or 3.6 inches. Here, the remainder is
simply the decimal part of the length.
CLOS E
IN TRO DUC E
Essential Question
How do you solve problems by interpreting the
quotient?
Possible answer: When a real-world problem
requires division, first calculate the quotient and
any remainder. Then decide whether an exact
answer is required or if the situation calls for
rounding up or down to the next whole number.
Summarize
Have students write three original division problems:
one in which an exact answer is needed, one in
which the quotient should be rounded up, and one
in which the quotient should be rounded down.
TEACH
t
1
EXPLORE
PR ACTICE
Questioning Strategies
• In part A, what division problem models the
situation? 62 ÷ 8
Where skills are
taught
• What is the quotient? What is the remainder?
The quotient is 7 R6; the remainder is 6.
1 EXPLORE
Where skills are
practiced
EXS. 1–6
• What does the remainder tell you? If you pack the
loaves of bread into 7 boxes, there will still be 6
loaves left over.
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Lesson 4
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Present the following problem: “The pages of
a photo album can each hold 4 photos. If you
have 25 photos to place in the album, how many
pages will you need?” Students should find that
they need 7 pages. Ask students to explain how
they arrived at this answer. If necessary, help
them understand that (25 ÷ 4 = 6 R1) and that the
remainder of 1 means that an additional page is
needed for the leftover photo.
Name
Class
2-4
Date
Notes
Interpreting the Quotient
Going Deeper
Essential question: How do you solve problems by interpreting the quotient?
Many real-world situations require an exact answer to a problem. But in some
cases, you may need to round your answer up or down for it to make sense in
the given situation.
video tutor
MCC6.NS.3
1
EXPLORE
Interpreting Quotients
Choose the best answer to each problem. Explain your answer.
A
At a bakery, 8 loaves of bread can be packaged in one box for transport. The bakery has an
order for 62 loaves of bread to deliver to a grocery store today. How many boxes are needed
for the shipment?
7 boxes
7.75 boxes
8 boxes
8 boxes; Sample answer: 7 boxes are not enough because 62 ÷ 8 = 7.75.
The choice of 7.75 boxes does not make sense since you cannot have a
partial box.
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B
For a woodworking project, D’Andre needs several pieces of wood that are each 14 inches
long. How many 14-inch pieces can he cut from a board that is 78.5 inches long?
5 pieces
5.6 pieces
6 pieces
5 pieces; Sample answer: 78.5 ÷ 14 is about 5.6 so the board is not long enough
to cut 6 pieces. The choice of 5.6 pieces does not make sense since the partial
piece is shorter than the required 14 inches.
REFLECT
1a.
Reasoning Explain how your reasoning in A was different than your reasoning in B.
Sample answer: In A, it was necessary to round the exact quotient up. In B,
the exact quotient needed to be rounded down.
TRY THIS!
1b. How many 6-ounce servings can you pour from a 33.6-ounce container?
5 servings
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practice
1. A florist is placing flowers in vases to be sold in her shop. Each vase will hold
9 flowers and she has an assortment of 85 flowers to use. How many vases can
she fill completely?
9 vases; Sample answer: Since 85 ÷ 9 = 9 R4, she can fill 9 vases completely. There
will be 4 flowers left over, leaving her 5 flowers short of filling another vase.
2. Two bags of apples weigh 8.2 pounds and cost $7.36. How many bags of apples will
fit in a box with a 50 pound weight limit?
12 bags; Sample answer: 8.2 ÷ 2 = 4.1 so one bag of apples weighs
4.1 pounds. 50 ÷ 4.1 is about 12.2. The box will contain only full bags.
3. A company sells recycled golf balls through their online store. The golf balls are sold
in packages of 6 balls. The company recently received a shipment of 200 golf balls for
packaging. How many packages can be completely filled from this shipment?
33 packages. Sample answer: Since 200 ÷ 6 = 33 R2, 33 packages can be
completely filled. There will be 2 golf balls left over.
4. Heather wants to burn back-up copies of some digital music on her computer.
She has 140 songs to be copied. If each CD she uses will hold 18 songs, how many
CDs will she need?
8 CDs. Sample answer: Since 140 ÷ 18 = 7 R14, Heather needs an 8th CD to
copy the last 14 songs.
5. Emilio has a collection of 246 sports cards. He is buying a binder with plastic
sleeves for organizing his cards. Each sleeve will hold 8 cards. How many sleeves
will he need to hold his entire collection?
31 sleeves. Sample answer: Since 246 ÷ 8 = 30 R6, Emilio needs a 31st sleeve
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Solve each problem. Explain your answer.
to hold the last 6 cards.
6. Brittany is making tote bags. She spent $18.75 on fabric that costs $5 per yard.
If she uses 0.5 yard of the fabric for each bag, how many bags can she make?
7 bags. Sample answer: 18.75 ÷ 5 = 3.75 so she bought 3.75 yards of fabric.
3.75 ÷ 0.5 = 7.5 but she would not make half of a bag.
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Lesson 4
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36
Lesson 4
Add i t i o na l P r ac ti c e
Assign these pages to help your students practice
and apply important lesson concepts. For
additional exercises, see the Student Edition.
Answers
Additional Practice
1. B
2. H
3. A
4. H
5. 6 costumes
6. 11 weeks
7. 6 costumes
8. $2.19
Problem Solving
1. $3.35
2. 6 vans
3. 5 necklaces
4. $0.57
5. B
6. J
7. A
8. H
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Module 2
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Lesson 4
Name
Class
Notes
2-4
Date
Name ________________________________________ Date __________________ Class__________________
Decimals Practice
Additional
LESSON
7
Practice B: Interpreting the Quotient
Circle the letter of the correct answer.
1. You spent a total of $6.75 for
15 yards of ribbon. How much
did the ribbon cost per yard?
2. Buttons come in packs of 12. How
many packs should you buy if you
need 100 buttons?
A $0.50
F 10
B $0.45
G 8
C $1.35
H 9
D $1.45
J 12
3. Your sewing cabinet has
compartments that hold 8 spools
of thread each. You have 50 spools
of thread. How many compartments
can you fill?
4. You spent a total of $35.75 for velvet
cloth. Each yard of the velvet costs
$3.25. How many yards did you buy?
F 10
G 10.5
A 6
H 11
B 7
J 11.5
C 5
D 8
5. You used a total of 67.5 yards of
cotton material to make costumes
for the play. Each costume used
11.25 yards of cloth. How many
costumes did you make?
6. You are saving $17.00 each week to
buy a new sewing machine that costs
$175.50. How many weeks will you
have to save to have enough money
to buy the sewing machine?
________________________________________
________________________________________
7. Sequins come in packs of 75. You
use 12 sequins on each costume. If
you have one pack of sequins, how
many costumes can you make?
8. You pay $26.28 for a subscription to
Sewing Magazine. You get an issue
every month for a year. How much
does each issue cost?
________________________________________
________________________________________
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Module 2
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Write the correct answer.
Practice and Problem Solving
20
Holt McDougal Mathematics
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CS10_MSM_C1_HPWSE.indb 20
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Name ________________________________________ Date __________________ Class __________________
Decimals
Problem
Solving
LESSON
7
Problem Solving: Interpreting the Quotient
2. There are 45 choir members going
to the recital. Each van can carry
8 people. How many vans are
needed?
1. Five friends split a pizza that costs
$16.75. If they shared the bill equally,
how much did they each pay?
________________________________________
3. Tara bought 150 beads. She needs
27 beads to make each necklace.
How many necklaces can she make?
________________________________________
4. Cat food costs $2.85 for five cans.
Ben only wants to buy one can. How
much will it cost?
________________________________________
________________________________________
Circle the letter of the correct answer.
5. Tennis balls come in cans of 3.
The coach needs 50 tennis balls
for practice. How many cans should
he order?
6. The rainfall for three months was
4.6 inches, 3.5 inches, and
4.2 inches. What was the average
monthly rainfall during that time?
A 16 cans
F 41 inches
B 17 cans
G 12.3 inches
C 18 cans
H 4.3 inches
D 20 cans
8. Mei needs 135 hot dog rolls for the
class picnic. The rolls come in packs
of 10. She wants to know how many
packs to buy. What should she do
after she divides?
A Drop the decimal part of the
quotient when he divides.
F Drop the decimal part of the
quotient when she divides.
B Drop the decimal part of the
dividend when he divides.
G Drop the decimal part of the
dividend when she divides.
C Round the quotient up to the next
highest whole number to divide.
H Round the quotient up to the next
highest whole number.
D Use the entire quotient of his
division as the answer.
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Book 1.indb 20
Module 2
J Use the entire quotient of her
division as the answer.
3820
© Houghton Mifflin Harcourt Publishing Company
J 4.1 inches
7. Tom has $15.86 to buy marbles that
cost $1.25 each. He wants to know
how many marbles he can buy. What
should he do after he divides?
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Write the correct answer.
Practice
Problem
Solving
Holtand
McDougal
Mathematics
3/15/12 3:08:22 AM
4/27/11 2:46:24 AM
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Lesson 4