Fractions and Decimals:
Part 2
Objective To provide experience with several graphic models
ffor renaming fractions as decimals.
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Practice
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Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Convert between fractions, mixed numbers,
and decimals. [Number and Numeration Goal 5]
• Order rational numbers. [Number and Numeration Goal 6]
• Order fractions and decimals on a
number line. [Number and Numeration Goal 6]
Key Activities
Students use the Probability Meter and
Fraction-Stick Chart to approximate decimal
equivalents for fractions. They begin filling in
a table of decimal equivalents.
Materials
Math Journal 1, pp. 142, 205, and the inside
back cover
Study Link 55
transparencies of Math Masters, pp. 137
and 138 slate straightedge
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Converting Improper Fractions
with Division
Math Journal 1, p. 143
Students review and practice
converting improper fractions to mixed
numbers using division.
Math Boxes 5 6
Math Journal 1, p. 144
Students practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Playing Number Top-It (3-Place
Decimals)
Student Reference Book, p. 327
Math Masters, p. 493
per partnership: 4 each of number cards 0–9
(from the Everything Math Deck, if available)
Students practice forming and
comparing decimals.
ENRICHMENT
Ongoing Assessment:
Recognizing Student Achievement
Writing Fraction and Decimal
Equivalents for a Shaded 100-Grid
Use Math Boxes, Problem 5. Math Masters, pp. 140 and 141
transparency of Math Masters, p. 141
Students write equivalent fractions and
decimals for the shaded portion of a 100-grid.
[Number and Numeration Goal 6]
Study Link 5 6
Math Masters, p. 139
Students practice and maintain skills
through Study Link activities.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, p. 93
Students compare fractions, decimals,
and percentages.
Advance Preparation
For Part 1, make transparencies of Math Masters, pages 137 and 138.
For the optional Enrichment activity in Part 3, make one transparency of Math Masters, page 141 for each
group of six students. Cut apart the transparency grids so that there is one per student.
Teacher’s Reference Manual, Grades 4–6 pp. 88, 89, 172
Lesson 5 6
319
Mathematical Practices
SMP1, SMP2, SMP3, SMP5, SMP6, SMP7
Content Standards
Getting Started
5.NBT.3a, 5.NBT.4, 5.NF.3
Mental Math and Reflexes
Math Message
Ask questions like the following. Students refer to the Probability Meter
on Math Journal 1, page 205 and respond by writing number
sentences.
How would you use the Probability
Meter on journal page 205 to show someone
1
what _
8 dollar is worth?
or _
?_>_
Which is greater, _
10
8 8
10
6
5
5
6
Study Link 5 5
Follow-Up
or _
?_>_
Which is greater, _
8
3 8
3
3
1
3
or _
?_>_
Which is greater, _
5 3
5
3
2
2
2
1
2
= 0.875
What fraction is equal to 0.875? _
8
7
Allow partners five minutes to
compare their answers and correct any errors.
= 0.625
What fraction is equal to 0.625? _
8
5
Ask volunteers to share their strategies for rounding
the area of Malta to the nearest tenth km2. Highlight
that rounding to the nearest tenth rounds 315.98 km2
to the nearest whole number—316.0 km2.
⎯? _
⎯
= 0.3
What fraction is equal to 0.3
3
1
= 0.05
What fraction is equal to 0.05? _
20
1
⎯? _
⎯
= 0.16
What fraction is equal to 0.16
6
1
⎯
= 0.83
What fraction is equal to 0.83? _
6
5
1 Teaching the Lesson
100%
1 .00
0.99
9 5%
0.95
9 0%
0.90
0.875
8 5%
0.85
0.83
8 0%
0.80
75%
0.75
C E R TA I N
E L
X I
T K
R E
E L
M Y
E
L
Y
V
E
R
Y
L
I
K
E
L
Y
9—
9
—
100
1
19
—
20
5
—
6
4, —
8
—
5 10
I
7 0%
K
0.70
6 5%
7
—
10
E
0.66
2
—
3
L
Y
0.65
5
—
8
3, —
6
—
5 10
0.625
6 0%
0.60
5 5%
0.55
50%
0.50
4 5%
0.45
40%
0.40
Ask volunteers to show how they used the Probability Meter to
1 dollar. Use their explanations to discuss the
find the value of _
8
meter’s decimal labels as dollar notation.
In dollar notation, hundredths are equivalent to pennies or cents:
1 is 0.25, or 25 cents. The fraction _
1 is directly opposite the
_
4
8
1
decimal 0.125. Point out that 0.12 is 12 cents and 0.005 is _
2
1
1
1
1
_
_
_
_
of 100 , or 2 of 1 cent, so 8 dollar is worth $0.125, or 12 2 cents.
3 dollar worth? $0.375, or 37_
1 cents
● What is _
8
50–50
CHANCE
0.35
0.33
30%
0.30
25%
0.25
2 0%
0.20
0.16
1 5%
0.15
U
N
L
I
K
E
L
Y
V
E
R
Y
0.125
1 0%
0.10
5%
0.05
0%
0.01
0. 0 0
1 2 , 3 , 4 , 5 , 10
50
—
—, —
— — — —, —
2 4 6 8 10 20 100
2, —
4
—
5 10
3
—
8
0.375
3 5%
E
X
T
R
E
M
E
L
Y
1
—
3
3
—
10
2
1, —
—
4 8
U
N
L
I
K
E
L
Y
U
N
L
I
K
E
L
Y
1
—
6
1
—
8
1
—
10
1
—
20
—1—
100
0
Probability Meter
320
Unit 5
2
●
5 dollar worth? $0.625, or 62_
1 cents
What is _
●
7 dollar worth? $0.875, or 87_
1 cents
What is _
8
8
2
2
Writing Fractions as Decimals
WHOLE-CLASS
ACTIVITY
(Math Journal 1, p. 142; Math Masters, p. 137)
Use a transparency of Math Masters, page 137 to demonstrate
how the Fraction-Stick Chart can be used to approximate the
decimal names for fractions.
1
—
5
IMPOSSIBLE
WHOLE-CLASS
DISCUSSION
(Math Journal 1, p. 205)
9
—
10
7
—
8
6
3, —
—
4 8
L
Math Message Follow-Up
Fractions, Decimals, and Percents
Student Page
2?
Example: What decimal is about equal to _
3
Date
Time
LESSON
2 . Count the
Step 1: Use the thirds row, and locate the fraction _
3
1 bars from left to right: _
2 is the right edge of the second bar.
_
3
3
2 ; that is,
Step 2: Place one edge of a ruler or straightedge at _
3
1 piece and perpendicular to the
along the right edge of the second _
Writing Fractions as Decimals
5 6
䉬
1
4
0
1
2
1
4
1
6
6
1
1
1
3
1
4
0.2
0.3
1
9
1
12
1
16
0.4
1
10
1
12
1
16
1
10
1
12
1
16
0.5
3
1
8
1
9
1
9
1
16
0.6
1
16
1
9
1
10
1
10
1
12
1
12
1
16
0.7
1
7
1
6
1
7
1
7
1
8
1
12
1
16
1
16
0.3
1
8
1
9
1
10
1
12
1
16
0.4
1
9
1
10
1
12
1
16
1
12
1
16
1
16
0.6
1
8
1
9
1
10
1
12
1
16
1
9
1
10
0.5
1
7
1
8
1
9
1
10
1
12
1
16
1
6
1
7
1
8
1
9
1
10
1
5
1
6
1
10
1
12
1
16
0.7
1
12
1
16
0.8
1
16
0.9
1.0
5.
0.125
1
ᎏᎏ
3
––
9.
0.75
––
1.3
11.
3.875
⫽ 0.
1
ᎏᎏ
8
⫽ 0.
1 3
9
ᎏᎏ
12
⫽ 0.
7 5
1
1ᎏ3ᎏ
7
3 ᎏ8ᎏ
4.
0.6
0.8
6.
0.625
2.
0.916
苶
1.375
10.
8.
⫽ 1. 3 3
⫽ 3. 8 8
4
ᎏᎏ
5
6 7
⫽ 0. 8 0
5
ᎏᎏ
8
⫽ 0.
11
ᎏᎏ
12
⫽ 0.
2
ᎏᎏ
3
⫽ 0.
3
1 ᎏ8ᎏ
9 2
⫽ 1. 3 8
––
12.
9.83
6 3
9.8 3
5
9 ᎏ6ᎏ ⫽
1
7
1
7
1
8
1
9
1
10
1
16
1
7
1
8
1
6
1
6
1
6
1
7
1
8
1
5
1
10
1
12
1
16
0.8
1
12
1
16
1
16
0.9
1
8
1
9
1
10
1
12
1
16
Math Journal 1, p. 142
1.0
0
inches
0.1
1
6
1
7
1
5
1
5
1
6
1
6
1
1
7
7
1
1
1
8
8
8
1
1
1
9
9
9
1
1
1
10
10
10
1
1
1
1
12
12
12
12
1
1
1
1
1
16
16
16
16
16
1
4
1
5
2
1
6
0.0
1
4
1
5
1
6
0.2
1
4
1
5
3 3
4
0
ᎏᎏ ⫽ 0. 4
10
3.
7.
1
3
1
1
4
1
5
––
0.3
0.4
1.
4
1
2
1
3
1
4
1
5
0.1
1
3
1
4
1
5
Use a straightedge and the above chart to fill in the blanks to the right of each
fraction below. Write a decimal that is equal to, or about equal to, the given
fraction. Directions for filling in the blank to the left of each fraction will be given
in the next lesson. Sample answers:
2
4
1
2
1
3
1
1
7
7
1
1
1
8
8
8
1
1
1
9
9
9
1
1
1
10
10
10
1
1
1
1
12
12
12
12
1
1
1
1
1
16
16
16
16
16
5
1
4
1
1
2
1
3
0.0
0
3
4
1
3
Decimal Number Line.
2
4
Step 3: Find where the straightedge crosses the number line. It
2 is about 0.67.
crosses at about 0.67, so _
3
Refer students to journal page 142. Ask them to use the chart and
number line on the page to mirror the steps as you demonstrate
5.
finding the decimal name for _
8
Ask students how they would use the chart to find the decimal
2 . Use their responses to emphasize that with mixed
name for 6_
3
numbers it is necessary to approximate only the fraction part. The
whole number part is unchanged when they write the decimal
2 is about 6.67.
name, so 6_
3
Teaching Master
Name
Date
LESSON
Time
Fraction-Stick Chart and Decimal Number Line
56
䉬
1
4
0
2
4
3
4
1
1
1
2
1
2
1
3
1
3
1
4
0.1
0.2
1
5
1
6
0.3
1
4
1
5
1
6
1
1
7
7
1
1
1
8
8
8
1
1
1
9
9
9
1
1
1
10
10
10
1
1
1
1
12
12
12
12
1
1
1
1
1
16
16
16
16
16
0.0
1
4
1
5
1
6
Assign students to complete the estimates for each problem on the
journal page. Circulate and assist. When most students have
finished, review the answers and strategies, and discuss any
problems that students found particularly difficult or interesting.
1
3
1
4
1
5
1
7
1
8
1
9
1
7
1
8
1
16
0.4
1
10
1
12
1
16
0.5
1
7
1
8
1
9
1
10
1
12
1
16
1
6
1
7
1
8
1
9
1
12
1
16
1
6
1
7
1
10
1
5
1
6
1
9
1
10
1
12
1
16
0.6
1
16
1
9
1
10
1
12
1
16
0.7
1
10
1
12
1
16
0.8
1
12
1
16
1
16
0.9
1
8
1
9
1
10
1
12
1
16
1.0
NOTE The Fraction-Stick Chart is a useful visual device but is not intended to
provide precise equivalencies between all fractions and decimals. In Lesson 5-7,
students will use their calculators to find decimal equivalents for fractions.
Math Masters, p. 137
Lesson 5 6
321
Teaching Master
Name
LESSON
56
䉬
Date
Filling In a Table of Decimal
Time
Table of Decimal Equivalents for Fractions
Equivalents for Fractions
Example: To find the decimal equivalent for ᎏ14ᎏ, use the row for the denominator 4.
Go to the column for the numerator 1. The box where the row and the
column meet shows the decimal 0.25.
(Math Journal 1, inside back cover; Math Masters, p. 138)
Numerator
1
2
3
4
1
1.0
2.0
3.0
2
0.5
1.0
1.5
5
6
7
Denominator
3
8
9
10
A partially completed table of decimal equivalents for fractions
appears on the inside back cover of the journal and on Math
Masters, page 138.
2.3
4
0.25
1.25
5
0.2
1.0
6
Use a transparency of Math Masters, page 138 to show students
how the table works. Each number across the top of the table
identifies the numerator of a fraction. Each number down the left
side of the table identifies the denominator of a fraction. The box
where a row and column meet is used to show the decimal
equivalent for that fraction.
1.6
7 0.142857
8
0.625
9
10
PARTNER
ACTIVITY
0.8
0.1
Have students complete rows 1, 2, 4, 5, and 10. The fractions for
the assigned rows are easy fractions. Most students will know their
decimal names or will be able to calculate them mentally. Students
will complete the rest of the rows in succeeding lessons.
Math Masters, p. 138
Numerator
2
3
4
5
6
7
8
9
10
1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
2
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
4
0.25
0.5
0.75
1.0
1.25
1.5
1.75
2.0
2.25
2.5
5
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Denominator
1
Inside back cover of Math Journal 1.
Completed rows 1, 2, 4, 5, and 10.
Student Page
Date
LESSON
56
Time
Converting Improper Fractions to Mixed Numbers
In the problems below, the hexagon shape has a value of 1.
Whole
Write the improper fraction name for each diagram.
Use division to find the mixed number.
Show your work.
hexagon
Improper Fraction
Mixed Number
9
_
2
1
4_
2
14
_
2
4_
3
4 R2
____
3 14
23
_
5
3_
6
___3 R5
6 23
Example:
Show your work.
4 R1
2
9
1.
3
2.
6
1
5_
3
3
Use division to convert the following improper fractions to mixed numbers
or whole numbers.
4.
30
_
5 =
6
5.
29
_
4 =
_1
74
6.
17
_
7 =
2 Ongoing Learning & Practice
5 R1
___
3.
16
_
Converting Improper Fractions
3 16
_3
3
14
_
Jenny said that she could convert _
3 to a mixed number by repeatedly subtracting 3 and
seeing what was left over. Tell whether you agree or disagree with this method, and explain why.
3
_
Sample answer: I agree. Each time Jenny subtracts 3 , she is
taking away a whole. If she writes the number of wholes she
subtracts and then writes the remainder as a fraction, she will
2
have the correct mixed number, 4 _
3.
322
Unit 5
(Math Journal 1, p. 143)
Students review and practice converting improper fractions to
mixed numbers using division.
Math Journal 1, p. 143
121-163_EMCS_G5_S_G5_SMJ_U05_57637X.indd 143
INDEPENDENT
ACTIVITY
with Division
27
Try This
7.
When students have written the decimal names, ask volunteers
to describe any patterns that they notice in the table. Sample
answers: The rows represent whole numbers, halves, thirds,
fourths, etc. The first column represents unit fractions. All boxes
on the diagonal from the upper left to the lower right have a value
of 1, with decimals greater than 1 in the boxes to the right of this
diagonal and less than 1 in the boxes to the left. Decimals become
larger as you move across rows and become smaller as you move
down columns.
8/29/11 10:19 AM
Fractions, Decimals, and Percents
Student Page
Math Boxes 5 6
Date
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 144)
Time
LESSON
Math Boxes
5 6
䉬
1.
Complete the table.
2.
Fraction
Decimal
Percent
7
ᎏᎏ
10
3
ᎏᎏ
8
0.7
0.375
1
ᎏᎏ
3
0.3
70%
38%
33%
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 5-8. The skill in Problem 6
previews Unit 6 content.
—
Estimate an answer for each problem.
Sample answers:
a.
20.6 ⫼ 4
Estimate
b.
184.38 ⫼ 9
Estimate
c.
15.503 ⫼ 7
Estimate
d.
872.16 ⫼ 8
Estimate
83 89
90
3.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 5
Use Math Boxes, Problem 5 to assess students’ ability to compare fractions.
Students are making adequate progress if they write the fractions correctly from
least to greatest.
[Number and Numeration Goal 6]
T
F
F
2 ⫽ 64
F
兹99
苶⫽9
3.5 ⬎ 0.35
2
b. ᎏᎏ
5
0.560
c.
0.099
d.
0.099 , 0.19 , 0.204 ,
0.265 , 0.560
1
3
⬍ ᎏᎏ
4
32 33
夹
9 32 66
Put the following fractions in order
from least to greatest.
,
3
ᎏᎏ
8
,
2
ᎏᎏ
3
,
4
ᎏᎏ
5
,
6.
9
ᎏᎏ
10
INDEPENDENT
ACTIVITY
(Math Masters, p. 139)
Determine whether the following sentences
are true or false. Write T or F.
a.
0.265
1
ᎏᎏ
4
4.
0.19
3 4 2 1 9
ᎏᎏ, ᎏᎏ, ᎏᎏ, ᎏᎏ, ᎏᎏ
8 5 3 4 10
Study Link 5 6
42
247–249
Put the following decimals in order
from least to greatest.
0.204
5.
5
20
2
108
Circle the letters for the pairs of
equivalent fractions.
a.
1 3
ᎏᎏ, ᎏᎏ
6 6
b.
15 3
ᎏᎏ, ᎏᎏ
25 5
c.
2 6
ᎏᎏ, ᎏᎏ
3 10
d.
2 10
ᎏᎏ, ᎏᎏ
7 35
e.
48 6
ᎏᎏ, ᎏᎏ
56 7
f.
4 65
ᎏᎏ, ᎏᎏ
9 135
59–61
66 67
Math Journal 1, p. 144
Home Connection Students practice converting between
decimals, fractions, and mixed numbers.
Study Link Master
䉬
1.
Games
Decimals, Fractions, and Mixed Numbers
Convert each decimal measurement to a mixed number.
Longest Road and Rail
Tunnels in the U.S.
Decimal Length
Number Top-It
63
83 89
Mixed-Number Length
79
Cascade Tunnel
(Washington)
7.79 miles
ᎏ
7ᎏ
100
Flathead Tunnel
(Montana)
7.78 miles
ᎏ, or 7ᎏᎏ
7ᎏ
100
50
miles
Moffat Tunnel
(Colorado)
6.21 miles
21
ᎏ
6ᎏ
1 00
miles
Hoosac Tunnel
(Massachusetts)
4.7 miles
78
BART Transbay Tubes
(San Francisco, CA)
miles
39
7
10
4 ᎏᎏ
6
3 ᎏᎏ,
10
3.6 miles
or
miles
3
3 ᎏᎏ
5 miles
Source: The Top 10 of Everything 2005
2.
The longest one-word name of any place in America is
Chargoggagoggmanchauggagoggchaubunagungamaugg.
Materials 䊐 number cards 0–9 (4 of each)
䊐 1 Place-Value Mat (Decimals)
(Math Masters, p. 493)
Players
2 or more
Skill
Place value for decimals
Object of the game To make the largest 3-digit decimal
numbers.
Directions
1. This game is played the same as Number Top-It (7-Digit
Numbers). The only difference is that players use a placevalue mat for decimals.
2. Players take turns turning over the top card from the deck
and placing it on any of their empty boxes. Each player
takes 3 turns, and places 3 cards on his or her row of the
game mat.
3. Players play 5 rounds for a game. Shuffle the deck between
each round. The player with the smallest total number of
points at the end of the 5 rounds wins the game.
Phil and Claire played Number Top-It using the
place-value mat for decimals. Here is the result.
This name for a lake near Webster, Massachusetts, is 45 letters long. It is a
Native American name that means “You fish on your side, I’ll fish on mine, and
no one fishes in the middle.” Use this word to answer the problems below.
c.
3.
What fraction of the word is made up of the letter a?
What fraction of the word is made up of the letter c?
15
ᎏᎏ,
45
9
ᎏᎏ,
45
3
ᎏᎏ,
45
or
or
or
–
1
ᎏᎏ ⫽ 0.3
3
1
ᎏᎏ ⫽ 0.2
5
–
1
ᎏᎏ ⫽ 0.06
15
In the space above, write the decimal equivalents for the fractions in Problem 2.
Place-Value Mat (Decimals)
Phil
Ones
.
0
.
3
.
6
Tenths
Hundredths Thousandths
5
Claire
0
8
4
6
b.
What fraction of the word is made up of the letter g?
3
a.
(3-Place Decimals)
2
4
56
2
STUDY LINK
Student Page
Time
5
Date
8
Name
Claire’s number is larger than Phil’s number. So Claire
scores 1 point for this round, and Phil scores 2 points.
Practice
4.
10冄7
苶,1
苶4
苶6
苶→
714 R6
5.
10冄苶苶
8苶4
苶→
Math Masters, p. 139
8 R4
6.
10冄苶6
苶7
苶5
苶→
67 R5
Student Reference Book, p. 327
Lesson 5 6
323
Teaching Master
Name
Date
LESSON
Time
3 Differentiation Options
Fractions and Decimals
56
䉬
Write the fraction name and decimal name for the shaded portion of each square.
Use your transparent 100-grid to check your answer. For Problem 9, color the
grid to show a fraction and then write the fraction and decimal name for the
shaded portion of the square.
1.
3.
2.
READINESS
Playing Number Top-It
3
10
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⫽ 0.
7
20
3
—
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4.
⫽ 0.
5.
40
100
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⫽ 0.
—
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7.
⫽ 0.
8
100
⫽ 0.
4
—
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⫽ 0.
1
9.
28.5
100
08
⫽ 0.
—
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⫽ 0.
285
15–30 Min
(3-Place Decimals)
(Student Reference Book, p. 327)
10
100
6
8.
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6.
6
10
4
2
5
35
PARTNER
ACTIVITY
To provide experience with decimal place value and ordering
decimals, have students play Number Top-It (3-Place Decimals).
See Student Reference Book, page 327 for directions. After playing
the game, have students choose two decimals from their record
sheet and write them using number names.
Answers vary.
—
—
—
—
—
—
—
—
—
—
—
—
—
—
⫽ 0.
Math Masters, p. 140
ENRICHMENT
Writing Fraction and
PARTNER
ACTIVITY
15–30 Min
Decimal Equivalents for a
Shaded 100-Grid
(Math Masters, pp. 140 and 141)
To apply students’ understanding of fractions and
decimals, have them complete Math Masters, page 140.
Distribute the transparent 100-grids. Students write the
fraction and decimal names for the shaded portions of squares
and use a transparent 100-grid to check their answers. Students
then shade a copy of Math Masters, page 141 to create their own
designs and estimate the fraction and decimal names for the
shaded portions. Have students copy their favorite design from
Problem 9 and display their designs in the Fractions, Decimals,
and Percents Museum.
Teaching Master
Name
LESSON
56
䉬
Date
Time
100-Grids
EXTRA PRACTICE
5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with comparing fractions,
decimals, and percentages, see 5-Minute Math, page 93.
Math Masters, p. 141
324
Unit 5
Fractions, Decimals, and Percents