Conversions among Fractions,
Decimals, and Percents
Objectives To reinforce the use of a data table; and to reinforce
renaming fractions as percents using a calculator and renaming
decimals as percents.
www.everydaymathonline.com
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Practice
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Teaching the Lesson
Family
Letters
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Management
Common
Core State
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Ongoing Learning & Practice
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
Key Concepts and Skills
Updating the World Tour
• Read and use large numbers. Math Journal 2, pp. 329–331, 336,
and 337
Student Reference Book, pp. 276,
277, 281, 288, 289, 297, and 302–305
Math Masters, pp. 419 and 420
(optional)
Students continue the World Tour.
Rounding Percents
Angle Addition and Subtraction
5-Minute Math™, pp. 93 and 181
calculator
Students practice conversions among
fractions, decimals, and percents.
[Number and Numeration Goal 1]
• Explore repeating and terminating decimals. [Number and Numeration Goal 5]
• Use a calculator to rename fractions as
percents; rename decimals as percents
by multiplying by 100. [Number and Numeration Goal 5]
• Compare two quantities with like units
using division. [Operations and Computation Goal 4]
• Round to the nearest whole-number percent. [Operations and Computation Goal 6]
• Use a data table. [Data and Chance Goal 2]
Key Activities
Students look up country population and
land area data and convert these to percents
of the world population and land area.
Students complete the percent column of the
Equivalent Names for Fractions table on
journal pages 342 and 343.
Ongoing Assessment:
Informing Instruction See page 746.
Math Journal 2, pp. 260A and 260B
Students practice finding unknown
angle measures.
Math Boxes 9 5
Math Journal 2, p. 260
Students practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 4. [Operations and Computation Goal 4]
Study Link 9 5
Math Masters, p. 288
Students practice and maintain skills
through Study Link activities.
Materials
Math Journal 2, pp. 342 and 343
Student Reference Book, pp. 271 and 281
Study Link 94
calculator classroom world map slate
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 62, 63, 153, 154
744
Unit 9
Fractions, Decimals, and Percents
READINESS
Math Masters, p. 289
Students use a curved number-line model
to round percents.
EXTRA PRACTICE
5-Minute Math
Mathematical Practices
SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8
Content Standards
Getting Started
4.NF.6, 4.MD.7
Mental Math
and Reflexes
Math Message
1 3 5 7
Use your calculator to rename these fractions as percents: _
, _, _, _.
8 8 8 8
Write fractions on the board. For each
fraction, students write the equivalent
decimal and percent on their slates.
Have students explain their strategies
problems. Suggestions:
for the
55 0.55, 55%
_
100
71
_
0.71, 71%
100
67
_
0.67, 67%
100
Study Link 9 4 Follow-Up
Review answers. Have students share the strategies they used to solve
Problems 3–6. For example:
84
84
42
Problem 3: _
=_
(multiply numerator and denominator by 2); _
= 84%
50
100
100
2 0.10, 10%
_
20
12
_
0.48, 48%
25
15
_
5, 500%
3
25
1
1
Problem 6: _
=_
(divide numerator and denominator by 25); _
= 20%
5
5
125
Ask if any student can describe a solution strategy to solve Problems 7 and 8
without a calculator. For example:
5 0.05, 5%
_
23
1
1
Problem 7: _
=_
(divide numerator and denominator by 23); _
= 25%
92
4
4
100
5
_
0.5, 50%
10
1
_ 0.25, 25%
4
3
3
12
Problem 8: _
=_
(divide numerator and denominator by 4); _
= 30%
40
10
10
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Go over the answers: _18 = 12.5%; _38 = 37.5%; _58 = 62.5%;
7
_
= 87.5%. Students may have renamed the fractions as percents
8
in one of two ways.
Use the percent key. For example, to rename _38 as a percent,
TI-15: 3 ÷ 8
Casio fx-55: 3
Display: 37.5
8
Display: 37.5
Divide numerator by denominator, and multiply by 100. For
example, divide 3 by 8 (= 0.375) and multiply by 100 (= 37.5).
Remind students that multiplying a decimal by 100 can be
done by moving the decimal point two digits to the right.
Students may use either method, but they should be able to
use both.
Adjusting the Activity
ELL
3 5
Ask students to explain how _18 , _8 , _8 , and _78 could be renamed as
percents without using a calculator. Record the steps on the board.
1
_
8
is half of _14 . Because _14 = 25% and half of 25% is 12.5%, _18 = 12.5%.
3
_
8
equals _14 + _18 , which is 25% + 12.5%, or 37.5%.
5
_
8
and _78 are renamed in the same way.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Lesson 9 5
745
Student Page
World Tour
Facts About the World
Social Studies Link Use the classroom world map to
identify Russia and China. Russia has the largest land area
of any country in the world. China has the largest population of
any country in the world. Tell students that in this lesson they
will investigate population and land area data and use their
calculators to convert these to percents of the world population
and land area.
Population is the number of people who
live in a certain region. Population growth is
the change in the population every year after
all births and deaths are accounted for.
The population growth rate is the increase
(or decrease) in population per year, written as
a percent.
The world’s population is now increasing by about 200,000
people per day, or about 75 million people per year. Over the last
40 years, the world’s population has about doubled. It reached
the 6 billion mark in 1999. World population is expected to reach
about 9 billion people by the year 2050.
Ask students to use the Student Reference Book to find the
population of China and the total world population.
The Continents
Percent
of World
Population
Percent of
Land Area
Area
(sq miles)
North America
509,000,000
8.0%
8,300,000
14.8%
South America
367,000,000
5.8
6,800,000
12.1
Europe
799,000,000
12.5
4,100,000
7.3
3,797,000,000
59.5
16,700,000
29.8
874,000,000
13.7
11,500,000
20.5
32,000,000
0.5
3,300,000
5.9
Asia
Africa
Australia
Antarctica
World Totals
0
6,378,000,000
(about 6.4 billion)
PROBLEM
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
LV
VIN
IIN
NG
(Student Reference Book, pp. 271 and 281)
A country is a territory and the people who live
there under one government. The number of
countries in the world often changes as countries
split apart or join with other countries. At this
time, there are about 200 countries in the world.
Population*
WHOLE-CLASS
ACTIVITY
as Percents
Continents are large land masses. There are
seven continents on the Earth, although Europe
and Asia are sometimes thought of as one
continent. Most continents contain many
countries, but there are no countries at all
in Antarctica.
Continent
Renaming Fractions
0.0
5,400,000
9.6
100.0%
56,100,000
100.0%
Write these populations on the board. Point out that the world
population has been rounded to the nearest million.
Ask students to round China’s population to the nearest million.
Record this estimate on the board.
*Data are for the year 2004. World population growth rate for the year 2004: about 1.2% per year
Student Reference Book, p. 271
Ask students what fraction of the world’s population lives in
China. Write this fraction on the board.
Population
Population
Rounded
China
1,298,848,000
1,299,000,000
World
6,378,000,000
6,378,000,000
Fraction
1,299,000,000
_
6,378,000,000
Have students use their calculators to rename this fraction as a
percent. They should use both methods and get the same answer:
Use the percent key.
TI-15: 1299000000 ÷ 6378000000
show 20.36688617.
Student Page
World Tour
REGION 4 Asia and Australia
Australia
Area: 2,967,900 sq mi
Population: 19,913,000
Capital: Canberra (Pop. 373,000)
Languages: English, aboriginal
languages
Monetary unit: Australian Dollar
Bangladesh
Area: 55,600 sq mi
Population: 141,340,000
Capital: Dhaka (Pop. 11,560,000)
Languages: Bangla, English
Monetary unit: Taka
China
Area: 3,705,400 sq mi
Population: 1,298,848,000
Capital: Beijing (Pop. 10,848,000)
Languages: Mandarin, Gan, Wu,
Haka, Yue, Minbei, Xiang, Minnan
Monetary unit: Renminbi (Yuan)
India
Area: 1,269,300 sq mi
Population: 1,065,071,000
Capital: New Delhi
(Pop. 12,441,000)
Languages: Hindi, English,
14 regional languages
Monetary unit: Rupee
Iran
Area: 636,000 sq mi
Population: 67,503,000
Capital: Tehran (Pop. 7,190,000)
Languages: Farsi, Kurdish,
Turkic, Luri
Monetary unit: Rial
Japan
Area: 145,900 sq mi
Population: 127,333,000
Capital: Tokyo (Pop. 34,997,000)
Language: Japanese
Monetary unit: Yen
Russia
Area: 6,592,800 sq mi
Population: 143,782,000
Capital: Moscow
(Pop. 6,468,000)
Languages: Russian, many
others
Monetary unit: Ruble
Canada
Area: 3,851,800 sq mi
Population: 32,508,000
Capital: Ottawa (Pop. 1,093,000)
Languages: English, French
Monetary unit: Dollar
Costa Rica
Area: 19,700 sq mi
Population: 3,957,000
Capital: San José
(Pop. 1,085,000)
Language: Spanish
Monetary unit: Colon
Cuba
Area: 42,800 sq mi
Population: 11,309,000
Capital: Havana (Pop. 2,189,000)
Language: Spanish
Monetary unit: Peso
El Salvador
Area: 8,100 sq mi
Population: 6,588,000
Capital: San Salvador
(Pop. 1,424,000)
Language: Spanish
Monetary unit: Colon
Guatemala
Area: 42,000 sq mi
Population: 14,281,000
Capital: Guatemala City
(Pop. 951,000)
Languages: Spanish, Mayan
languages
Monetary unit: Quetzal
Haiti
Area: 10,700 sq mi
Population: 7,656,000
Capital: Port-au-Prince
(Pop. 1,961,000)
Languages: French, Haitian
Creole
Monetary unit: Gourde
Jamaica
Area: 4,200 sq mi
Population: 2,713,000
Capital: Kingston (Pop. 575,000)
Languages: English, Jamaican
Creole
Monetary unit: Jamaican Dollar
Thailand
Area: 198,500 sq mi
Population: 64,866,000
Capital: Bangkok
(Pop. 6,486,000)
Languages: Thai, English
Monetary unit: Baht
Turkey
Area: 301,400 sq mi
Population: 68,894,000
Capital: Ankara (Pop. 3,428,000)
Languages: Turkish, Arabic,
Kurdish
Monetary unit: Lira
Vietnam
Area: 127,200 sq mi
Population: 82,690,000
Capital: Hanoi (Pop. 3,977,000)
Languages: Vietnamese,
Chinese, French, English
Monetary unit: Dong
REGION 5 North America
Mexico
Area: 761,600 sq mi
Population: 104,960,000
Capital: Mexico City
(Pop. 18,660,000)
Languages: Spanish, Mayan
dialects
Monetary unit: New Peso
Panama
Area: 30,200 sq mi
Population: 3,000,000
Capital: Panama City
(Pop. 930,000)
Languages: Spanish, English
Monetary unit: Balboa
United States of America
Area: 3,717,800 sq mi
Population: 293,028,000
Capital: Washington, D.C.
(Pop. 563,000)
Languages: English, Spanish
Monetary unit: Dollar
Student Reference Book, p. 281
746
Unit 9 Fractions, Decimals, and Percents
Casio fx-55: 1299 ÷ 6378
20.366886.
Display will
Display will show
Divide numerator by denominator, and multiply by 100.
1299000000 ÷ 6378000000
0.2036688617.
0.2036688617 Æ 100
Display will show
Display will show 20.36688617.
Ongoing Assessment: Informing Instruction
Watch for students who notice that, because both numbers are in millions, it is
sufficient to divide 1,299 by 6,378. If students’ calculators, such as the Casio
fx-55, cannot display these large numbers, encourage them to use this strategy.
Help students summarize. Round percent answers to the nearest
whole-number percent. In 20.366886179, the digit in the tenths
place is less than 5, so the number is rounded down to 20%. About
20 of every 100 people in the world live in China. Because 20%
equals _15 , about 1 of every 5 people in the world live in China.
Student Page
Repeat this last routine to calculate the percent of the world’s land
area that is in Russia. Russia’s area is about 6,592,800 square
miles. The world’s land area is about 57,900,000 square miles. The
fraction of the world’s area that belongs to Russia is about
6,593,000 ÷ 57,900,000 = 0.1138687392. Multiply 0.11 ∗ 100 =
11%. So about 11% of the world’s area belongs to Russia.
Date
Time
Equivalent Names for Fractions
Fraction
Equivalent Fractions
Decimal
Percent
0
0%
1
100%
ᎏ0ᎏ
2
ᎏ1ᎏ
2
2 3
ᎏᎏ, ᎏᎏ
4 6
ᎏ2ᎏ
2
ᎏ1ᎏ
3
ᎏ2ᎏ
3
Completing the Equivalent
ᎏ1ᎏ
4
INDEPENDENT
ACTIVITY
Names for Fraction Table
ᎏ3ᎏ
4
ᎏ1ᎏ
5
ᎏ2ᎏ
5
ᎏ3ᎏ
5
(Math Journal 2, pp. 342 and 343)
ᎏ4ᎏ
5
Students should already have filled in the equivalent fractions and
decimals columns of the table on journal pages 342 and 343. Now
they will fill in the percents column.
On the first page of the table, students find the percents by
using the percent key. If the calculator display shows an
answer with more than 3 digits, they record only the first 3
digits. For example, for the fraction _56 , the percent answer will
be displayed on the calculator as 83.33333333, but only 83.3
should be recorded in the table.
ᎏ1ᎏ
6
ᎏ5ᎏ
6
ᎏ1ᎏ
8
ᎏ3ᎏ
8
ᎏ5ᎏ
8
ᎏ7ᎏ
8
Math Journal 2, p. 342
On the second page of the table, students can find the percents
without using a calculator and without making any actual
computations. The decimal names are already recorded in the
table. Students need only multiply the decimal by 100 (move
the decimal point two digits to the right) to rename the decimal
as a percent. As before, ask students to record only the first
3 digits for any percent name.
Student Page
Date
Time
Equivalent Names for Fractions
Fraction
Equivalent Fractions
continued
Decimal
Percent
ᎏ1ᎏ
9
ᎏ2ᎏ
9
ᎏ4ᎏ
9
ᎏ5ᎏ
9
ᎏ7ᎏ
9
ᎏ8ᎏ
9
ᎏ1ᎏ
10
ᎏ3ᎏ
10
ᎏ7ᎏ
10
ᎏ9ᎏ
10
ᎏ1ᎏ
12
ᎏ5ᎏ
12
ᎏ7ᎏ
12
11
ᎏ
ᎏ
12
Math Journal 2, p. 343
Lesson 9 5
747
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Finding Unknown Angle Measures
95
Without using a protractor, find the measure of the unknown angle. Write an equation to show how
you solved the problem. Use a variable to represent the unknown angle measure.
Sample equations are given.
1.
2.
D
°
20
30°
H
A
E
B
50 °
20 + 30 = x
F
Measure of ∠HEF =
Equation:
3.
4.
P
K
Q
x°
70°
x°
25 °
70 - 45 = x
Equation:
92 °
26 + x = 118
Measure of ∠PNO =
Equation:
They update the Route Map by drawing a line segment to
connect Brasília, Brazil, and Beijing, China.
X
6.
R
S
Social Studies Link Students follow the established World
Tour routine.
N
J
Measure of ∠KJL =
5.
O
°
45°
M
118°
26
U
Y
T
Z
W
∠SRU is a right angle.
∠YZW is a straight angle.
Measure of ∠TRU = 60°
Measure of ∠XZY = 33°
30 °
90 - 60 = x
INDEPENDENT
ACTIVITY
(Math Journal 2, pp. 329–331, 336, and 337;
Student Reference Book, pp. 276, 277, 281, 288, 289, 297, and 302–305;
Math Masters, pp. 419 and 420)
116 °
57 + 59 = x
Measure of ∠DAB =
Equation:
L
Updating the World Tour
G
57°
59°
C
They use the World Tour section of the Student Reference Book
to locate facts about China and Beijing, and they fill in the
Country Notes pages for this country and capital.
147 °
180 = 33 + x
Measure of ∠TRS =
Measure of ∠XZW =
Equation:
Equation:
Students who are also keeping a Route Log update that as well.
Math Journal 2, p. 260A
260A-261B_EMCS_S_MJ2_G4_U09_576426.indd 260A
3/6/11 7:49 AM
Angle Addition and Subtraction
INDEPENDENT
ACTIVITY
(Math Journal 2, pp. 260A and 260B)
Students practice using addition and subtraction to find unknown
angle measures.
Math Boxes 9 5
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 260)
Mixed Practice Math Boxes in this lesson are linked
with Math Boxes in Lessons 9-7 and 9-9. The skill in
Problem 6 previews Unit 10 content.
Student Page
Date
Time
LESSON
Finding Unknown Angle Measures
95
Ongoing Assessment:
Recognizing Student Achievement
continued
Find the value of x. Write an open sentence to show how you solved the problem.
Sample equations are given.
7.
H
(x + 100)°
35°
G
F
45
110 + 35 = x + 100
145 °
Measure of ∠EFG =
x=
Equation:
8.
Use Math Boxes, Problem 4 to assess students’ ability to divide a multidigit
whole number by a 1-digit divisor. Students are making adequate progress if
they express the quotient as a whole number with a whole-number remainder.
Some students may be able to express the remainder as a fraction.
110°
E
Math Boxes
Problem 4
[Operations and Computation Goal 4]
B
158°
°
A
(x +
22)
73°
D
Study Link 9 5
C
63
Equation: (x + 22) + 73 = 158
85 °
Measure of ∠ADB =
x=
INDEPENDENT
ACTIVITY
(Math Masters, p. 288)
Try This
9.
Angela used her protractor to measure ∠KJL and ∠NJM. She found the
two angles had the same measure. Angela said, “Without measuring, I
also know ∠KJM has the same measure as ∠NJL.”
K
M L
N
Home Connection Students use a table of data to
calculate the approximate percentage of marriages
that occurred each month in 2001.
J
Explain how Angela knows her statement is true.
Sample answer: There is only one angle in between
∠NJM and ∠KJL. So, the measure of ∠NJM + the
measure of ∠MJL is the same as the measure of ∠KJL
+ the measure of ∠LJM.
Math Journal 2, p. 260B
260A-261B_EMCS_S_MJ2_G4_U09_576426.indd 260B
748
3/6/11 7:49 AM
Unit 9 Fractions, Decimals, and Percents
Student Page
Date
3 Differentiation Options
PARTNER
ACTIVITY
Rounding Percents
Math Boxes
95
1.
READINESS
Time
LESSON
Calculate.
10% of 70 =
b.
5% of 60 =
c.
25% of
50
80
d.
5–15 Min
(Math Masters, p. 289)
e.
3.
To explore rounding percents to the nearest whole number,
have students plot numbers on a curved number line to see which
way the percent will “slide.” Ask students to describe how they
rounded their numbers. Encourage vocabulary such as top, bottom,
endpoint, middle, closer, and farther.
2.
a.
28
5-Minute Math
(6 + 2)∗ 4 = 32
(5 + 7)∗ 3 = 36
c. (1 + 8)∗(8 + 2)= 90
d. (1 + 7)∗(8 + 2)= 80
b.
=7
% of 25 = 20
38
39
Complete the table with equivalent names.
Fraction
Decimal
Percent
5
_
10
0.5
50%
20%
20
_
100
7
_
10
_2
0.20
5
0.7
70%
0.4
40%
61
5.
Insert parentheses to make each number
sentence true.
a.
% of 48 = 24
150
4.
Divide. Use a paper-and-pencil algorithm.
897 ÷ 6 =
149 R3,
or 149 _12
62
What is the height of the parallelogram?
Include the correct unit.
22
6.
23
Draw the mirror image of the figure shown
on the left of the vertical line.
?
SMALL-GROUP
ACTIVITY
EXTRA PRACTICE
7
3
9 in.
Area = 27 in2
5–15 Min
Height:
To offer students more experience with conversions among fractions,
decimals, and percents, see 5-Minute Math, pages 93 and 181.
27 / 9 = 3
3 in.
Number model:
135
106 109
Math Journal 2, p. 260
248-273_EMCS_S_MJ2_G4_U09_576426.indd 260
2/1/11 1:49 PM
Planning Ahead
Remind students to bring to school the second page of Study
Link 9-1 (Trivia Survey). Their survey results will be used in
Lesson 9-6.
Study Link Master
Teaching Master
Name
LESSON
9 5
Date
Name
Time
Date
STUDY LINK
Rounding Percents
9 5
The number lines below are curved like hills. You can use them to help you
round percents to the nearest whole-number percent.
Renaming Fractions as Percents
1.
Round 89.7% to the nearest whole-number percent.
Use a calculator to find the percent of the total number of marriages that
occurred each month. Round the answers to the nearest whole-number percent.
Think: Which whole-number percents are nearest to 89.7%?
Month
If I look at the number line, 89% is the whole-number percent to the left of 89.7%.
If I look at the number line, 90% is the whole-number percent to the right of 89.7%.
89.5%
Mark 89.7% on the curved number line.
89.7%
Would 89.7% slide down to 89% or 90%?
89.7% rounded to the nearest whole-number
percent is 90%.
1.
89%
Round 23.6% to the nearest whole-number percent.
Label the curved number line. Mark 23.6%.
23.6% would slide down to
24% .
23.6% rounded to the
nearest whole-number percent is
90%
23.5%
23.6%
24% . 23%
62 207
In 2001, there were about 2,317,000 marriages in the United States.
The table below shows the approximate number of marriages each month.
Example:
What number would be exactly halfway between 89% and 90%?
Time
24%
Approximate
Number of
Marriages
Approximate
Percent of
Total Marriages
January
147,000
6%
February
159,000
7%
7%
7%
8%
10%
11%
10%
10%
9%
8%
7%
March
166,000
April
166,000
May
189,000
June
237,000
July
244,000
August
225,000
September
224,000
October
217,000
November
191,000
December
152,000
Source: U.S. Department of Health and Human Services
2.
Round 92.1% to the nearest whole-number percent.
Label the curved number line. Mark 92.1%.
92.1% would slide down to
92% .
92.1% rounded to the
nearest whole-number percent is
92.
1%
92% . 92%
2.
92.5%
3.
July
According to the table, what is the most popular month for a wedding?
What is the least popular month for a wedding?
January
Describe how you used your calculator to find the percent for each month.
Sample answer: I divided the number of marriages for each
month by the total then multiplied by 100 and rounded.
93%
Practice
Name all the factors of each number.
4.
1, 3, 7, 9, 21, 63
5.
28
1, 2, 4, 7, 14, 28
Math Masters, p. 288
Math Masters, p. 289
278-303_EMCS_B_MM_G4_U09_576965.indd 289
63
2/1/11 2:36 PM
278-303_EMCS_B_MM_G4_U09_576965.indd 288
2/1/11 2:36 PM
Lesson 9 5
749