U.S. Traditional Long Division
with Decimal Dividends
Algorithm
Objective To extend long division to problems in which
Project
Projject
a decimal is divided by a whole number.
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Core State
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Focal Points
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Teacher’s
Lesson Guide
Doing the Project
Recommended Use After Lesson 45 and Algorithm Project 7
Materials
Key Concepts and Skills
Math Journal 1 or 2, pp. 29P and 30P
• Apply multiplication facts in carrying out long division. Student Reference Book, pp. 54E and 54F
[Operations and Computation Goal 2]
• Use long division to solve division problems with decimal dividends. [Operations and Computation Goal 3]
• Estimate products and quotients. [Operations and Computation Goal 6]
• Find average speeds, given times and distances. [Operations and Computation Goal 7]
Key Activities
Students extend the whole-number long division algorithm to decimal dividends.
Extending the Project
Ex
Students use long division to rename fractions as decimals.
For additional practice, students solve division problems, first using the focus algorithm
(partial-quotients division) and then using any algorithm they choose.
Materials
Math Journal 1 or 2, p. 31P
Student Reference Book, pp. 42, 43, 54E,
54F, 54I, and 54J
Online Additional Practice, pp. 31A–31C
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Algorithm Project 8
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U.S. Traditional Long Division with Decimal Dividends
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Student Page
Date
1 Doing the Project
PROJECT
8
Time
Long Division with Dollars and Cents
Algorithm Project 8
Emma’s work for a math problem looked like this:
► Long Division with Dollars
WHOLE-CLASS
DISCUSSION
1.
What problem was
Emma trying to solve?
2
6 $ 1 7
⫺ 1 2
5
⫺ 4
$17.35 / 6
and Cents
(Math Journal 1 or 2, p. 29P; Student Reference Book, pp 54E and 54F)
2.
.
.
8 9
3 5
3
8
5 5
⫺ 5 4
1
$2.89 R$0.01 Was she correct? yes
Sample answer: I multiplied the
divisor and the quotient, and then added the
remainder: (6 * 2.89) + 0.01 = $17.35.
What answer did Emma get?
How do you know?
Have students solve Problems 1–3 on journal page 29P. When
most students have finished, write Emma’s long division work from
the journal page introduction on the board or a transparency. Ask
questions such as the following:
Where does the 53 in the fourth line of Emma’s method come
from? The 53 refers to 53 dimes, 50 dimes from the $5 left
over after the whole dollars were shared and 3 dimes in the
original dividend: 50 dimes + 3 dimes = 53 dimes.
Where does the 48 in the fifth line of Emma’s method come
from? The 48 is the number of dimes shared when each of
6 shares gets 8 dimes: 6 * 8 dimes = 48 dimes.
3.
Use Emma’s method to solve $47.95 / 5. Show your work.
$9.59
Solve using U.S. traditional long division. Show your work on a separate sheet of paper.
4.
$142.24 / 8
6.
$5.00 ÷ 3
$17.78
$1.66 R$0.02
5.
$28.75 / 25
7.
$783 / 4
$1.15
$195.75
Math Journal, p. 29P
29P-31P_EMCS_S_MJ2_G5_P08_576434.indd 29
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What is the 1 at the very bottom? It is the remainder; it
represents $0.01 that is left over after $17.35 is divided by 6.
Have students make up a number story that fits 17.35 / 6. Ask
volunteers to share their number stories and explain what should
be done with the remainder in each case. Emphasize that what to
do with the remainder depends on the problem situation.
Have partners complete journal page 29P. Students may find the
examples on Student Reference Book, pages 54E and 54F helpful.
► Long Division with Decimal
NOTE Extending whole-number long
division to money in dollars-and-cents
notation is relatively straightforward. One
of the most useful characteristics of our
base-10 place-value number system is that
many whole-number algorithms can be
easily adapted to work with decimals.
WHOLE-CLASS
DISCUSSION
Dividends
(Math Journal 1 or 2, p. 30P)
Student Page
Date
PROJECT
8
Have students solve Problems 1 and 2 on journal page 30P. For
Problem 2, remind students that a decimal point and trailing 0s
can be attached to the dividend: 224 = 224.000 . . . and that a table
of easy multiples of 12 might be helpful. Problem 2 involves a
division that will never come out evenly and introduces students to
a process that repeats forever. This idea is explored further in
Part 2 of this project.
Time
Long Division with Decimal Dividends
Algorithm Project 8
Use long division to solve these problems. Give your answers to the nearest hundredth.
1.
A garden snail travels 7.95 feet in 3 minutes. What
is the snail’s average speed in feet per minute?
2.65 feet/minute
(unit)
2.
In 2004, Andrew Otto set a record for the men’s
course of the Davis 12-hour Challenge bicycle race
in Winters, California. He rode 224 miles in 12 hours.
What was Otto’s average speed in miles per hour?
18.67 miles/hour
(unit)
3.
In 2000, Sandy Earl set a record for the women’s
course of the Davis 12-hour Challenge. She rode
214 miles in 12 hours. What was Earl’s average
speed in miles per hour?
17.83 miles/hour
(unit)
Sources: Encyclopaedia Britannica, www.britannica.com
Davis Bike Club, www.davisbikeclub.org
Math Journal, p. 30P
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Algorithm Project 8
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Student Page
Date
Time
PROJECT
When most students have finished, have volunteers copy their
work on the board or a transparency and explain their solutions.
Ask questions such as the following:
Renaming Fractions as Decimals
8
Algorithm Project 8
Read Student Reference Book, page 541 with a partner. Then use
long division to rename the fractions below as decimals.
1.
4
_
=
9
−
0.4 or 0.44444
2.
Problem 1
−
0.5 or 0.55555
5
_
=
9
3.
7
_
=
9
5.
3
__
=
11
−
0.7 or 0.77777
2
4. __
11
−−
0.27 or 0.272727
6.
=
7
__
=
11
−−
0.18 or 0.181818
Why does dividing 7.95 by 3 give the average speed in feet per
minute? Feet per minute means feet in 1 minute. At the
average speed, the snail would go 7.95 feet in 3 minutes;
7.95 / 3 gives the distance traveled in 1 minute.
,#.*[i
−−
0.63 or 0.636363
&b^c
&b^c
&b^c
4
7.95 feet / 3 minutes = ? feet / 1 minute
7.
8.
What pattern do you notice when you
rename ninths as decimals?
Sample answer: For
ninths less than 1, the
decimal is simply the
numerator repeated
forever.
What pattern do you notice when you
rename elevenths as decimals?
Sample answer: For
elevenths less than
1, multiply the
numerator by 9 and
then repeat this 2-digit
number forever.
Problem 2
Math Journal, p. 31P
29P-31P_EMCS_S_MJ2_G5_P08_576434.indd 31
3/8/11 11:38 AM
What does the digit 2 in the quotient mean? If 7 feet are
shared into 3 equal parts, then each part would get 2 feet
with 1 foot left over.
Why does dividing 224 by 12 give the average speed in miles
per hour? Miles per hour means miles in 1 hour. At the
average speed, Otto would go 224 miles in 12 hours. 224 / 12
gives the distance traveled in 1 hour.
'')b^
Go to www.everydaymathonline.com
to access the additional practice
pages.
&]g &]g &]g &]g &]g &]g &]g &]g &]g &]g &]g &]g
4
224 miles / 12 hours = ? miles / 1 hour
Have partners complete journal page 30P.
2 Extending the Project
Online Master
Name
Date
PROJECT
Time
Online
Additional
Practice
Partial-Quotients Division
8
► Using Long Division to Rename
Algorithm Project 8
Fractions as Decimals
Use partial-quotients division to solve each problem.
1.
Leah spent $28.25 on lunch for five days. If she spent
the same amount each day, how much did each lunch
cost?
$
2.
PARTNER
ACTIVITY
(Student Reference Book, pp. 54I and 54J; Math Journal 1 or 2, p. 31P)
5.65
Have students solve Problems 1–8 on journal page 31P.
Jackson spent $32.46 on gifts for three of his friends.
How much did he spend on each friend?
$10.82
3.
$28.42 / 7
$4.06
Answer:
5.
$5.92 / 4
$1.48
Answer:
4.
Answer:
6.
► Solving Division Problems
$229.50 / 9
$25.50
(Online Additional Practice, pp. 31A–31C; Student Reference Book,
pp. 42, 43, 54E, 54F, 54I, and 54J)
Online practice pages 31A–31C provide students with additional
practice solving division problems. Use these pages as necessary.
$157.26 / 6
Answer:
$26.21
Online Additional Practice, p. 31A
EM3cuG5OP_31A-31D_P08.indd 31A
A42
Algorithm Project 8
INDEPENDENT
ACTIVITY
4/1/10 5:35 PM
Encourage students to use the focus algorithm (partial-quotients
division) to solve the problems on practice page 31A. Invite them
to use any algorithm they wish to solve the problems on the
remaining pages. Students may find the examples on Student
Reference Book, pages 42, 43, 54E, 54F, 54I, and 54J helpful.
U.S. Traditional Long Division with Decimal Dividends
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