Table of Contents
Fractions, Decimals, and Percents (A.1.3.4.4).......................... 4
Ordering Numbers (A.1.3.2.2)..................................................... 8
Solving Problems (A.3.3.3.1)..................................................... 12
Order of Operations (A.3.3.2.3)................................................ 16
Evaluating Expressions (D.1.3.2.2).......................................... 20
Writing Expressions (D.2.3.1.2)................................................ 24
Solving Equations (D.2.3.2.1). .................................................. 28
Input-Output Tables (D.1.3.2.1)................................................. 32
Polygons (C.1.3.1.1).................................................................... 36
Changes in Perimeter (B.1.3.3.3).............................................. 40
Changes in Area (B.1.3.3.3)...................................................... 44
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Volume (B.1.3.1.1)....................................................................... 48
Interpreting Data (E.3.3.1.1)...................................................... 52
Mean (E.1.3.2.2). ........................................................................ 56
Probability (E.2.3.2.1)................................................................ 60
Acknowledgments................................................................ 64
A.1.3.4.4
FL
At the beginning of each lesson, you will see a box with the shape of
Florida and a Grade-Level Expectation code in it. This code tells you
what is being covered in the lesson.
3
1BRFL06MM_FM.indd 3
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A.1.3.4.4
FL
Fractions, Decimals,
and Percents
Sometimes when you solve a math problem,
you have to convert fractions, decimals, and
percents into different forms.
Fractions, decimals, and percents are all different
ways of expressing part of a whole.
For example, if you had 10 pieces of candy and 2 of
Miami-Dade International
Airport offers direct flights to
121 destinations. About 6%
of those destinations are in
Florida.
them were red, you could show the amount of red
2
candy pieces with a fraction (​ 10
 ​ of the candy pieces

are red), a decimal (0.2 of the candy pieces are red),
or a percent (20% of the candy pieces are red).
Each expression represents the same amount.
Write 0.35 as a fraction in simplest form.
Identify the place value of the last digit in the
decimal number. The last digit, 5, is in the
hundredths place. So, 0.35 is read as
“thirty-five hundredths.”
Write the fraction that shows “thirty-five
hundredths.”
35
  ​ 
0.35 5 ​ 100

Write the fraction in simplest form.
Divide the numerator and denominator by 5.
35 4 5
7
​ 100
  
​ 
5 ​ 20
  ​ 
4
5
 
7
0.35 5 ​ 20
  ​ 

Build A Bridge 1
Express the decimal as a
fraction in simplest form.
0.75
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Example 1
4
6M_Fraction Decimal Percen.indd 4
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Fractions with denominators of 10, 100, or 1,000 can be written as a decimal
6
using place value. For example, ​ 100
   ​,  read as “six hundredths,” is written in decimal

form as 0.06.
For fractions with other denominators, first try writing an equivalent fraction with
100 as the denominator. Then, write the numerator as a decimal by moving the
decimal point two places to the left. If that option does not work, divide the
numerator by the denominator. Continue to divide until the remainder is 0 or there
is a repeating decimal.
Example 2
Write ​ 18
 ​ as a decimal.
25

Try writing an equivalent fraction with a
denominator of 100.
18 • 4
72
​ 18
 ​ 5 ​
 
​ 
5 ​ 100
  ​ 
25
25
•4



Build A Bridge 2
Write the fraction as a
decimal.
​ 19
 ​ 
20

The equivalent fraction is read as “seventy-two
hundredths.” Write the decimal that shows
“seventy-two hundredths.”
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72
​ 100
  ​ 5 0.72

​ 18
 ​ 5 0.72
25

A percent is a ratio that compares a number to 100. Write the ratio as an equivalent
fraction with 100 as the denominator, or write the ratio as a decimal and multiply by
100 to find the percent.
Example 3
Emma answered 17 out of 20 questions correctly
on a science quiz. Write her score as a percent.
Write an equivalent fraction with 100 as the
denominator.
Build A Bridge 3
Natasha hiked 6 miles on
a 10-mile trail. Write the
distance of the trail she
hiked as a percent.
17 • 5
85
​ 17
 ​ 5 ​
 
​ 
5 ​ 100
  ​ 5 0.85
20
20
•
5
  
The numerator is the percent.
85
​ 100
  ​ 5 0.85 5 85%

Emma scored 85% on the science quiz.
5
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Guided PractiCE
1 What does a fraction express?
2 How do you convert a fraction with a denominator of 100 to a decimal?
3 If you have 10 pieces of candy and 4 are yellow, what percent of the candy
pieces are yellow? How do you know?
For Numbers 4–6, write each decimal as a fraction in simplest form.
4 0.4
5 0.55
6 0.68
For Numbers 7–9, write each fraction as a decimal.
16
8​ 25
 ​ 

9​ 58 ​ 

For Numbers 10–12, write each fraction or decimal as a percent.
10 0.7
11​ 18 ​ 

12 0.88
3
13 At Parker Middle School, ​ 10
  ​ of the sixth graders participate in an after-school

3
sports program. What percent is equivalent to ​ 10
  ​?
  
14 Nine out of 20 T-shirts are navy. Which set of numbers shows this ratio?
9
A​ 20
  ​,  0.45, 45%

9
B​ 20
  ​,  0.48, 48%

9
C​ 20
  ​,  0.55, 55%

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7​ 45 ​ 

6
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Practice
For Numbers 1–3, write each decimal as a fraction in simplest form.
1 0.62
2 0.15
3 0.2
For Numbers 4–6, write each fraction as a percent.
9
4​ 100
   ​ 

6
5​ 25
  ​ 

6​ 32
  ​
32

The table shows the kinds of music in Ariel’s CD collection. Use the table to
answer Numbers 7–9.
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Genre
Part of
Collection
Rock
20%
Country
0.375
Pop
7
40
Blues
1
4
7 Write the part of the collection that is country as a percent. 8 Write the part of the collection that is pop as a decimal. 9 Which has a greater percent in the collection—pop or blues? 10 Riley has a 25-page photo album. He has pictures on 19 pages. What percent
of Riley’s photo album has pictures?
11 Cameron is reading the departures board at Miami-Dade International Airport.
He notices that 24 of the next 50 flights are flying to the West Coast. Which set
of numbers matches this ratio?
24
  ​, 0.5, 50%
A​ 50

12
B​ 25
 ​,  0.48, 48%

44
C​ 100
  ​,  0.44, 44%

7
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