Lesson
12-5A
Equivalent Fractions and Decimals
Common Core
Domain
Number and Operations—Fractions
Cluster
Understand decimal notation
for fractions, and compare
decimal fractions.
Standards
4.NF.6 Use decimal notation for
fractions with denominators 10 or
100. Also 4.NF.5
Mathematical Practices
Make sense of problems and
persevere in solving them.
✔Reason abstractly and
quantitatively.
✔Construct viable arguments and
critique the reasoning of others.
Model with mathematics.
Use appropriate tools
strategically.
Attend to precision.
Look for and make use
of structure.
✔Look for and express regularity
in repeated reasoning.
Lesson Overview
Essential
Understanding
Objective
Students will
understand how
to use equivalent
fractions to write
fractions as
decimals.
Every fraction can be
represented by an infinite
number of equivalent
fractions, but each
fraction is represented by
the same decimal or an
equivalent form.
Materials
Decimal models
(Teaching Tool 24)
PROFESSIONAL
DEVELOPMENT
Math Background
Today calculators and computers are so
accessible that decimals have become preferred
over fractions for reporting and calculating.
However, students often find themselves using
fractions because they are writing ratios—the
number of parts considered to the number
of parts in all. Therefore, it is important that
students are able to pass back and forth
between fraction and decimal representations.
In the previous lesson, students wrote decimals
equivalent to fractions with powers of 10 as
denominators and vice versa. In this lesson,
students will write decimals equivalent to
1 Daily Common Core Review
Daily Common Core Review not
available for this lesson. Consider
using additional practice found in
the Student Edition as review.
46A Vocabulary
fractions with other denominators. Some
fractions can be simplified to fractions with
denominators that are factors of a power of
10. Once a fraction has been simplified, a
fraction equivalent to it can be written with a
denominator that is a power of 10. Finally, this
fraction can easily be written as a decimal.
Students will also encounter fractions that
have denominators that are multiples of 10
or 100, that can be changed to become
equivalent fractions with a power of 10 as
their denominators. Then these fractions can
be written as decimals.
2 Develop the Concept: Interactive
MATHEMATICAL
PRACTICES
Problem-Based Interactive Learning
10–15 min
Overview Students will use equivalent fractions to write fractions with
denominators other than 10 or 100 as decimals.
Focus How can you use equivalent fractions to change a fraction to a
decimal?
Materials Decimal models (Teaching Tool 24)
Set the Purpose You have learned to write fractions with denominators of
10 and 100 as decimals. Today, you will learn how to write more fractions
as decimals.
Connect What does it mean to write a fraction in simplest form? [The
numerator and denominator have no common factor other than 1.]
Pose the Problem Three fourths of the students in Mr. Brown’s
MATHEMATICAL
class have a younger brother or sister. How would you write ​ _34 ​ as a
PRACTICES
decimal? Give students time to work in pairs to solve this problem. Then
have them share their thinking.
Name
Teaching Tool
Martise
17
Communicate
When students
their thinking
share
with the class, they
communicate the
thought process
they used to write a
fraction as a decimal. Whole-Class Discussion Draw three large congruent squares on
the board. Use the second square to show tenths and the third square to
show a hundredths grid. How could you use the first square to show  _​34 ​? 
[Divide the square into 4 equal parts and shade 3 parts.] Divide the
square into fourths using a horizontal line and a vertical line. Shade 3 fourths. Point to the second square. Is it possible to shade some tenths
to show the same amount shaded as in the first square? [No] Point to the
third square. Is it possible to shade some hundredths to show the same
amount? [Yes] Shade ​ __34  ​ of the hundredths grid. What fraction tells how
75
75
many hundredths are shaded? [​ ___
   
​] Write ​ __34  ​ 5 ___
​ 100
   
​ on the board.
100
What decimal tells how many hundredths are shaded? [0.75] Write
75
___
​ 100
   
​ 5 0.75 on the board.
Suppose you did not have models to use. How could you have written ​ _34 ​ as
an equivalent fraction with a denominator of 100? [Multiply 3 and 4 by
25 to get 75 and 100.] Could you have written _​ 34  ​as an equivalent fraction
with a denominator of 10? Explain. [No; You can’t multiply 4 by a whole
number to get 10.]
3
_
​ 4  ​
 ​​
75
75 ___
___
3
_
  ​    ​ = 0.75
 = ​    ​  
4
100
100
TT 17
SF_TT_04_08
Copyright © Pearson
Education, Inc., or
its affiliates. All Rights
Reserved. 4
2/15/11 1:08 PM
M_TET17.indd
MTH12_ANC4_TR
17
Small-Group Interaction Work with your partner. Write __
​ 52  ​ as a
decimal. [0.4]
36
36
12
Write ___
​ 300
  ​ as a decimal. Show your thinking. [​ ___  ​  5 ___
​ 100
   
​5 0.12]
300
eTools Fractions
www.pearsonsuccessnet.com
46B
3 Develop the Concept: Visual
Equivalent Fractions
and Decimals
How can you use equivalent fractions
to change a fraction to a decimal?
A pan of cornbread was divided into 12 equal
6
​ 12
  ​ of the
pieces, and 6 out of 12 pieces or __
cornbread remains. Write a fraction equivalent
6
​ 12
  ​ , and then change the fraction to a decimal.
to __
6 _
In simplest form __
​ 12
  ​ is ​ 1 ​.  Find an equivalent
2
fraction with a denominator of 10.
What are equivalent
fractions? [Fractions
that represent the
same amount]
How can you write
equivalent fractions?
[Multiply or divide
the numerator and
denominator by the
same number.]
2 times what number equals 10?
35
5
_​ 1 ​  5 __
​ 10
  ​ 
2
35
_​ 1  ​5 __
​ 5  ​ 
2 10
__
​ 5  ​ is five tenths, or 0.5.
10
So, 0.5 of the cornbread remains.
Lesson
12-5A
1
Set the Purpose Call students’ attention to the Visual Learning
Bridge at the top of the page. In this lesson, you will learn how to
use equivalent fractions to write fractions as decimals.
Common
Core
4.NF.6 Use decimal
notation for fractions with
denominators 10 or 100.
Also 4.NF.5
Other Examples
3
as a decimal.
Write ___
Write 0.8 as a fraction in simplest form.
3 __
In simplest form ___
is 1.
12 4
8
0.8 is eight tenths, or ___
.
10
12
Find an equivalent fraction with a
denominator of 100.
8
Simplify the fraction ___
.
10
8 and 10 are multiples of what
number?
4 times what number equals 100?
3 25
Explain It
Reason Quantitatively Point out to students that, when a
problem contains a fraction and a decimal, it is helpful to change
one number so that it is in the same form as the other. How could
you change _​ 12  ​to a decimal with the same number of decimal places
as 0.12? [Find a fraction equivalent to ​ __12  ​ with a denominator of 100.]
How could you change 0.12 to a fraction? [Write it as a fraction with
a denominator of 100.]
How can you use equivalent fractions
to change a fraction to a decimal?
A pan of cornbread was divided into 12 equal
6
of the
pieces, and 6 out of 12 pieces or ___
12
cornbread remains. Write a fraction equivalent
6
, and then change the fraction to a decimal.
to ___
12
Other Examples
Look at the first example. What question could you ask yourself
3
to decide if you first need to change __
​ 12
  ​ to simplest form? [Can I
multiply 12 by a number to get 10 or 100?] What is the answer to
your question? [No] Could you find a fraction equivalent to  _​14  ​that
has a denominator of 10? Explain. [No; There is no whole number
I can multiply the denominator 4 by to get a denominator of 10.]
Equivalent Fractions
and Decimals
42
25
1 5 ___
__
4
8 5 __
___
3 25
42
4
100
5
10
25
___
is twenty-five hundredths, or 0.25.
100
3
So, ___
5 0.25.
12
4.
0.8 is eight tenths, or __
5
4.
So, 0.8 5 __
5
Explain It
1. Reason Why is the fraction __12 not written as 0.12?
See margin.
2 as an
2. What steps would you take to rename __
4
equivalent fraction with a denominator of 100?
See margin.
46
1. S ample answer: 0.12 5 ____
​ 12  ​ and __
​ 1 ​5 ___
​ 5  ​ 5 ____
​ 50  ​. 
100
2
10
100
____
​ 12   
​is not equivalent to ____
​ 50  ​. 
MTH12_SE04_CCTK_TPC12_L05A.indd 46
100
100
2. Sample answer: First I would find what number to multiply 4
by to get 100 in the denominator. That number is 25. Then I
would multiply the numerator and denominator by 25:
25 3 2 5 50 and 25 3 4 5 100. So __
​ 2 ​5 ____
​ 50   
​.
4
46 100
7/12/11 MT
3:1
Write _
​ 34 ​ as a decimal.
6
How do you simplify __
​ 12
  ​ to _
​ 12  ​?
[Divide both 6 and 12 by 6.]
How do you know that ​ _12   ​ is in
simplest form? [The only whole
number that you can divide 1 and
2 by is 1.]
Multiply to find an equivalent fraction
with a denominator of 100.
4 times what number equals 100?
3 25
_
​ 3 ​5 ___
​  75  ​ 
4
_​ 3 ​ 5 ___
​ 75  ​ 
4 100
100
3 25
75
​ ___
  ​ is seventy-five hundredths, or 0.75.
100
6 __
In simplest form ___
is 1 . Find an equivalent
12 2
fraction with a denominator of 10.
2 times what number equals 10?
3
Write __
as a decimal.
4
35
4 times what number equals 100?
3 25
5
1 5 ___
__
2
5
1 5 ___
__
2
Multiply to find an equivalent fraction
with a denominator of 100.
10
3
75
__
5 ____
4
35
3 ___
75
__
5
2 10
5
___
is five tenths, or 0.5.
10
4
100
100
100
MATHEMATICAL
Guided Practice
PRACTICES
Do you know HOW?
Do you UNDERSTAND?
For 1 through 6, write each fraction
as a decimal.
7. Write a fraction and an equivalent
decimal to show the part of the
cornbread that has been eaten.
___
6or0.5
12
8. Writing to Explain When you
write a fraction as a decimal, why
do you need to rename the fraction
as an equivalent fraction with a
denominator of 10 or 100?
n
1. __35 5 __
10  6
50
2. __245 __
 100
 
1
3. __
5 0.2
3
4. ___
12 0.25
2
5. __
8 0.25
3
6. __
5 0.6
0.6
n
0.50
n
9. __255 __
10  4
n
n
8
4 5 __
7 5 ___
n
10. __
45 5 __
11. __
13. ___
100
  12. __28 5 ___
5 n  10
10  8
100  25
100  7
3
14. __
12
6
15. ___
10
0.25
0.8
0.8
4
16. ___
10
0.6
0.4
0.25
35
18. ___
100
17. __
15 0.2or0.20
0.35
19. __48, 0.5
20. __15, 0.15
65
21. ___
, 0.65
100
2 , 0.35
22. __
4
4 , 0.08
23. __
8
6
24. ___
, 0.6
12
4 , 0.5
25. __
8
8
26. ___
, 0.08
100
3 , 0.25
27. ___
12
3
28. __
, 0.03
10
4 , 0.8
29. __
5
30. __12, 0.05
Yes
No
Yes
No
No
No
Exercise 3
Error Intervention
If students multiply only the numerator or denominator of the fraction
by 2,
then review with them how to find equivalent fractions. Remember,
you must multiply the numerator and the denominator by the same
number to write a fraction that has the same value.
​ 48  ​
Reteaching Work together with students to write __
​ 35  ​and __
as decimals.
Yes
Independent Practice
For Exercises 19–30, remind students that when deciding if numbers
are equivalent, it is helpful to have both numbers written in the
same form. Encourage students to write the fractions as decimals.
However, keep in mind that some students may choose to write the
decimals as fractions.
0.07
In 19 through 30, tell whether each pair shows equivalent numbers.
PRACTICES
Remind students that when changing a fraction to a decimal, they
should first ask themselves if they can multiply the denominator of the
fraction to get 10 or 100. If not, encourage them to try simplifying
the fraction.
3
In 9 through 18, write each fraction as a decimal.
0.4
MATHEMATICAL
Seemargin.
Independent Practice
Guided Practice
3 25
75
___
is seventy-five hundredths, or 0.75.
So, 0.5 of the cornbread remains.
Could you use the same steps to change _​ 34 ​ 
6
to a decimal as you used to change __
​ 12
  ​ to a
3
decimal? Explain. [No; ​ _4  ​is in simplest form
already. Also, the denominator 4 can be
multiplied by 25 to get the denominator 100.]
6
Could you use the same steps to change ​ __
   ​
12
3
to a decimal as you used to change _​ 4  ​to a
decimal? Explain. [No; There is no whole
number I can multiply the denominator 12 by
to get the denominator 10 or 100.]
No
Yes
Yes
Yes
No
Lesson 12-5A
47
8.Sample answer: So that the denominator of the fraction is
equivalent to the place value of the decimal.
TH12_SE04_CCTK_TPC12_L05A.indd
14 AM
47
7/12/11 3:14 AM
47
3 Develop the Concept
Problem Solving
MATHEMATICAL
Students use underlying processes and mathematical tools for
Exercises 31–40. Remind students to check for reasonableness when
solving each problem.
Exercise 31
Language of Math: Everyday Vocabulary The term batting
average may be new to students. A batting average tells the number
of hits a player usually gets out of a certain number of times at bat.
24
The fraction ___
​ 100
   
​tells you that Roger usually gets 24 hits out of 100
times at bat. However, sometimes he may get more or less. Point out
that batting averages are usually written as a decimal to the nearest
thousandth without the 0 to the left of the decimal point. Therefore,
the batting average 0.24 or 0.240 would usually be written .240.
Exercise 38
Use Bar Diagrams What hidden question do you need to answer
before you can solve this problem? [How many days are in 1 week?] How does the bar diagram show the answer to this question? [The
bar is divided into 7 parts, and each part represents one day.]
Exercise 39
Check for Reasonableness Encourage students to check the
answer they choose for reasonableness. Visualize ​ _45 ​ of a shape
shaded. About how much of the shape is shaded: a little less than
half, a little more than half, or almost the whole shape? [Almost
the whole shape] Is the value of the decimal you chose close to
1 whole? [Yes]
Early Finishers Have students write and solve a comparison
problem similar to Exercise 33 that is about a class of 25 fourth
graders.
Have students explain how they can use equivalent
8
fractions to change a fraction to a decimal, using ___
​ 100
   ​ and __
​ 48 ​ as
examples.
MATHEMATICAL
Problem Solving
PRACTICES
31. Roger got 24 hits out of 100 times
at bat. What is his batting average
as a fraction in simplest form? Then
write an equivalent decimal. ___
​6​​;​​0.24
25
32. Critique Reasoning The model
below represents 1 whole. Maura says
that the shaded part of the model
70
5 0.07. Is Maura
shows that ___
100
correct? Explain why or why not.
See​margin.
PRACTICES
BattingAverage5
Numberofhits
Numberoftimesatbat
33. A band has 20 instruments. Tyler
says that __25 of the instruments are
string instruments and 0.5 of the
instruments are wind instruments.
Does the band have the same
number of wind instruments and
string instruments? Explain.
See​margin.
34. Gina wrote a 4-digit number. She
used each of the digits 1, 3, 5, and
7 once. How many different 4-digit
numbers can Gina write?
35. Writing to Explain Which is greater,
3
__
or 0.75? Explain your answer.
4
__
​3​is​equivalent​to​​____
​75​​,​​and​​____
​75​​​5​0.75.​
4
100
100
36. Reason The cell phone was
invented in Sweden in 1979. How
many years ago was the cell phone
invented?
37. Write a fraction in simplest form and
an equivalent decimal to show what
part of a dollar 5 cents represents.
(Hint: 1 dollar 5 100 cents.)
___
​1​​;​​0.05​
20
24​numbers
Answer​for​2011:​32​years
For 38, use the diagram at the right.
0.75​5 0.75.​The​numbers​are​equal.
?newspapersinall
38. Kwan has 37 customers on his paper route.
He delivers newspapers every day. How many
newspapers does he deliver in one week?
37
259​newspapers
39. Reasonableness Betty’s score on
4.
a 5-point quiz was 4 out of 5, or __
5
What is __45 written as a decimal?
37
37
37
37
37
Newspapersdelivered
eachday
40. Nine of the 12 students in the school
play are fourth graders. Which
decimal represents the part of the
students that are fourth graders?
A
0.4
B
0.45
A
0.25
C
0.6
B
0.6
D
0.8
C
0.75
D
0.9
Journal
37
48
32. Maura is not correct; Sample answer: The grid shows
____
​ 70   
​or 0.7. To show 0.07, only 7 small squares should be
100
shaded.
MTH12_SE04_CCTK_TPC12_L05A.indd 48
2 ​written as a decimal is 0.4.
33. N
o; Sample answer: ​ __
5
0.4  0.5, so the band has fewer string instruments than
wind instruments.
48 7/12/11 MT
3:1
Solve each equation for z.
1. z 1 22 5 24
2. z 2 19 5 24
3. z 3 4 5 32
4. z 4 9 5 4
5. 15 1 z 5 24
6. z 2 22 5 22
7. 6 3 z 5 6
8. z 4 5 5 1
9. 3 3 z 5 18
z52
z543
z536
z58
z59
z51
z544
z55
Exercises 1–9
Reteaching Students may have difficulty remembering to work
backward to solve the problem. Have them write out the problem
in word form and how to solve the problem in word form. Use
Exercise 8 as an example. Students should say z divided by
5 equals 1 and ask what divided by 5 equals 1. Remind them
to work backward from there. Ask students what they need to
do to both sides of the equation to isolate z.
z56
Round each decimal to the nearest tenth.
10. 9.64
9.6
11. 1.05
12. 3.52
1.1
13. 16.67
3.5
14. 87.24
16.7
87.2
Find the sum. Estimate to check if the answer is reasonable.
15. 9 1 3,529 1 27 1 621
4,186
16. 17,868 1 913 1 2,781
21,562
18. 2 1 129 1 56 1 374
17. 475 1 25 1 5,350 1 25,275
31,125
561
Reason Find each value of w that is not correct.
Write it correctly, and explain the error.
19. 20 1 w 5 68
w 5 88
Seemargin.
20. w 2 12 5 50
w 5 62
Correct
21. w 4 2 5 9
w 5 11
22. w 3 6 5 42
w58
Seemargin.
w57;Divided
incorrectly.
Number Sense
Construct Arguments Write whether each
statement is true or false. Explain your answer.
23. The expression 101 2 25 equals 76.
True;101225510022511or7511576.
24. The product of 4 and 682 is closer to 2,400 than 2,800.
False;43682isabout4370052,800.
25. The sum of 251 and 173 is less than 400.
False;Thesumof251and173isabout25011705420,and420.400.
26. The quotient of 0 divided by 1 is 1.
True;Usingmentalmath,53405200,535525,and2001255225.
28. The difference of 844 and 172 is greater than 600.
True;Thedifferenceisgreaterthan80022005600.
Lesson 12-5A
Exercises 19–22
Reason Quantitatively Discuss with students common errors they
can make when solving equations. Remind students to look closely at
the operation in each equation and decide if the given value for the
variable is correct.
Number Sense
False;Thequotientof0dividedbyanynonzeronumberisalways0.
27. The product of 5 and 45 is 25 more than 200.
Exercises 10–14
Students can extend previous knowledge about rounding numbers to
the tens and hundreds place when working on these exercises. What
place value do you use when rounding a number to the hundreds
place? [Tens] What place value will you use when rounding a
decimal to the tenths place? [Hundredths]
49
Exercise 27
Point out that this exercise is different from the others because it
requires the use of two operations. Remind students that the word
is separates the two quantities they are checking for equality. What
expression represents the quantity to the left of is? [5 3 45] What
expression represents the quantity to the right of is? [200 1 25]
19. w 5 88 is incorrect. The correct solution is w 5 48; Found
the sum of 68 and 20 instead of the difference.
21. w 5 11 is incorrect. The correct solution is w 5 18; Found
the sum of 9 and 2 instead of the product.
TH12_SE04_CCTK_TPC12_L05A.indd
49
13 AM
7/12/11 3:13 AM
49
4 Close/Assess and Differentiate
Close
Essential Understanding Every fraction can be represented by an infinite
number of equivalent fractions, but each fraction is represented by the same
decimal or an equivalent form. In this lesson, you learned how to use equivalent
fractions to change a fraction to a decimal.
ASSESSMENT
Quick Check Master
Quick Check
Name
Exercises 1–4 are worth 1 point each.
Use the rubric to score Exercise 5.
12-5A
3 as a decimal?
1. Which shows __
12
2.Which shows a pair of equivalent
numbers?
A 0.025
16 ; 0.8
A __
20
B 0.25
Exercise 5
25 ; 0.4
B ___
100
C 0.312
D 0.35
9 as a decimal?
3. Which shows __
20
C
6 ; 0.68
__
D
0.75
8
3;
__
5
Writing to Explain Students should explain why they must first
simplify __
​ 36 ​ to __
​ 12  ​and then write an equivalent fraction with a denominator
that is equivalent to a decimal place value.
4.Which shows a pair of equivalent
numbers?
A 0.92
4 ; 0.45
__
5
3 ; 0.3
B ___
100
A
B 0.55
C 0.45
15 ; 0.8
C __
20
D 0.092
3
D ___
; 0.06
Model Thinking Aloud Help students verbalize what they are
thinking. Say, To change a fraction to a decimal, I need a fraction with a
denominator of 10 or 100. I notice that the denominator of _​ 63 ​ is 6.
50
5.WritingtoExplain When writing __36 as a decimal, why do you
5?
first need to rename the fraction as __1 and then as __
2
10
Seestudentsamplestotheright.
Q 12•5A
Student Samples
3-point answer The student correctly explains
why he or she must first simplify __
​ 36 ​ and then writes
an equivalent fraction with a denominator that is
equivalent to a decimal place value.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
MTH12_ANC4_TRM_Q12-05a.indd 31
Formative
Assessment
Use the Quick Check to assess
students’ understanding.
6 by
_3
I can’t multiply
or of ​ 6  ​is 6.
at
in
m
no
st I
de
fir
he
So
T
100.
r to get 10, or
1
be
m
_
nu
le
ho
w
 
.
​
 
any
3
rm. That’s ​ 2
​ _   ​in simplest fo
or
need to write 6
and denomin5at
the numerator
__  ​. The
​ 
I can multiply
n
tio
lent frac 5 10
1
_
get the equiva
__
the
of ​ 2 ​ by 5 to
n write ​ 10  ​ as
tenths, so I ca
s
ow
sh
n
tio
frac
decimal 0.5.
7/14/11 8:37 PM
2-point answer The student correctly shows
changing __
​ 36 ​ to a decimal but does not explain why
the steps are necessary.
÷ 3 × 5
​ 6_3 ​ = ​ 2_1 ​ = ​ __5   ​= 0.5
10
÷3 ×5
1-point answer The student demonstrates
little or no understanding of how to change a
fraction to a decimal.
5
__
1
3
_
​ _6  ​= ​ 2 ​ = ​ 10  ​ 
Prescription for Differentiated Instruction
Use student work on the Quick Check to prescribe differentiated instruction.
49A Points
Prescription
0–4
Intervention
5–6
On-Level
7
Advanced
Differentiated Instruction
Intervention
On-Level
Advanced
Par tner
Par tner
Talk
Equivalent Fractions and
Decimals
Sh
70
0 100
•Remind students that one way
to write an equivalent fraction
is to multiply the numerator and
denominator by the same number.
•You can write a fraction with a
denominator of 10 as a decimal.
What denominators can be
multiplied by a number to get
an equivalent fraction with a
denominator of 10? [2, 5] Make
a list as students name the
denominators. Work together to
5
change ​ __12  ​ to ​ __
   
​ to 0.5.
10
Get Started
or
0
0.90
1
0.5
2
0.75
3
0.3
4
0.15
5
0.6
6
0.8
7
0.25
8
0.2
9
0.4
2
3
10
20
4
3
5
5
2
5
6
3
4
7
7 100
9
1
4
One Whole
One Whole
0.4
0.05
0.8
0.07
0.6
3
4
6
20
1
4
3
5
4
5
0.5
0.25
0.7
0.9
0.75
1
5
9
10
3
20
2
5
1
2
Take turns. Say any fraction that has 10 in the denominator.
Your partner explains how to show that fraction on the grid and
says an equivalent decimal in hundredths.
If you have
more time
Center Activity H 12-5A
• Repeat for hundredths. Have students
name a few denominators for
hundredths.
k.
are
wor
your t
hinking while you
Pick a number tile to find a decimal. Say that decimal.
Explain how to show that decimal on the whole grid with 100 parts.
Explain how to find an equivalent fraction.
Cover the equivalent fraction with your number tile.
Display each 0–9 tile exactly once. If you have a partner, take turns.
1
1 20
4
5
90
8 100
Sh
k.
are
wor
your t
hinking while you
Pick a number tile to find a fraction. Say the fraction.
Explain how to show that fraction on the whole grid with 100 parts.
Explain how to find the equivalent decimal.
Cover the equivalent decimal with your number tile.
Display each 0–9 tile exactly once. If you have a partner, take turns.
Get Started
or
10–15 min Talk
If you have
more time
Try again. This time say the equivalent fraction in the grid
and another equivalent fraction for each decimal.
Center Activity HH 12-5A
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:
Partner Talk Listen for names of equivalent decimals. For example, a student
might say, “Two tenths is equivalent to twenty hundredths because there are ten hundredths
in every tenth.”
Leveled Homework
Reteaching Master
Practice Master
Reteaching
Name
Name
12-5A
Equivalent Fractions
and Decimals
6
1
___
= __
12
2
2
×5
10
100  
25
0.25
 
9
2. ___
5 ____  
20
45
100  
2 ;  0.5
6. __
5
15
10
5; 2
0.2
 
   
0.8
50
        
      
0.08
25
100
32
5
0.32
12. Which decimal is equivalent
to ___
 5   ?
20
4
7. ___
25
     
      
0.16
13
8. ___
      
20
     
0.65  
    
9
9. ___
50
  0.18
Tell whether each pair shows equivalent numbers.
No
      
Yes  
          
No
            
R 12•5A
MTH12_ANC4_TRM_R12-05a.indd 32
0.95 0.46
A 0.20
C 0.35
B 0.25
D 0.52
4 ;   0.25
8. ___
16
3 ; 0.75
__
0.6
16
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MTH12_ANC4_TRM_P12-05a.indd 33
5
4.
3.
11. Kevin has 20 words to learn for
his spelling test on Friday. He
has learned 6 of the words.
So, he has learned ___
 6   of the
20
6
in simplest form,
words. Write ___
20
and find an equivalent decimal.
1 ; 0.25
__
1 ; 0.25
__
4
4
3 ; 0.3
___
6.
5.
10
13. Gina wrote that __
 45  is greater
than 0.75. Is Gina correct?
Explain why or why not.
1 ; 0.5
__
3 ; 0.6
__
2
4 ∙ 0.8 and
Yes; __
5
0.8 > 0.75.
P 12•5a
2 ; 0.4
__
4
11  ;  0.22
9. ___
Yes
2.
1.
50
5
Shade some parts of each shape below. Write a fraction in simplest
form and a decimal to represent the shaded part of the shape.
7.
4 as __
1.
Sample answer: I renamed ___
4
16
Next, I multiplied the numerator and
25
25
1
__
____
____
denominator by 25: ∙
.
∙ 0.25,
4
100 100
4 ∙ 0.25.
so ___
Yes
9
14. Nine out of 15, or ___
, of the people at the skating rink brought their own
15
9
.
skates. Write an equivalent decimal for ___
15
Write a fraction in simplest form and a decimal for the shaded
part of each shape.
23
5. ___
14. Look at Exercise 8. Explain how you decided whether the
numbers are equivalent.
10
3
7 ; 0.35
2 ; 0.25      11. ___
10. __
; 0.4      12. __
; 0.35      13. ___
5
5
25
20
    
No
2 ∙ 0.4
Yes; __
Write each fraction as a decimal.
4             6. ___
4
5. __
5
20
10. A rock band has 5 members,
2  of the members play
and  __
5
string instruments. Also, 0.4
of the members sing. Does the
band have the same number
of string instrument players as
singers? Explain.
8
4. ___
5 ____ 
20
0.44
7 ;   0.07
7. ___
No
12
3
1    ___ 
3. ___
5  
5 ___
0.45
0.75
25
In 6 through 9, tell whether each pair shows equivalent numbers.
In 1 through 4, find the missing numbers. Then write each
fraction as a decimal.
4
19
4. ___
11
3. ___
12
0.2
Step 2 Rename the fraction Step 3 Write the decimal.
using a denominator of 10, ___
5
is five tenths.
100, or 1,000.
10
5
___
= 0.5
×5
Think: What
10
5
1
__ = ___
number times
6
So, ___
= 0.5
2 equals 10?
1
1. __
5 ____ 
9
2. ___
1
1. __
5
12
12-5A
Visualize Fractions and
Decimals
In 1 through 5, write each fraction as a decimal.
6
Write ___
as a decimal.
Enrichment
Name
12-5a
Equivalent Fractions
and Decimals
A fraction and a decimal can both be used to represent the same value.
Step 1 Write the
fraction in simplest form.
Enrichment Master
Practice
8.
Answers may vary.
Check students’
Answers may vary.
Check students’ work. work.
E 12•5A
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49B