Name ___________________________
Period__________
Date ___________
RAT4
uc
e
STUDENT PAGES
od
RATIONAL NUMBERS
Student Pages for Packet 4: Rational Number Concepts
Terminating Decimals
 Use a variety of strategies to convert between fractions and
terminating decimals.
 Demonstrate conversion fluency between common fractions and
decimals.
 Compute with simple fractions.
1
RAT4.2
Repeating Decimals
 Explore patterns in repeating decimals.
 Use a variety of strategies to convert between fractions and
repeating decimals.
 Compare, order, and add common fractions and decimals.
7
RAT4.3
Ordering Rational Numbers on a Number Line
 Compare and order positive and negative fractions.
 Compare and order positive and negative decimals.
 Convert between fractions and decimals, and use these
representations for estimation.
 Distinguish between terminating and repeating decimals.
16
Fraction and Decimal Games
 Identify equivalent fractions and decimals.
 Order fractions and decimals.
23
pl
e:
D
o
N
ot
R
ep
r
RAT4.1
m
RAT4.4
Vocabulary, Skill Builders, and Review
26
Sa
RAT4.5
Rational Numbers Unit (Student Pages)
RAT4 – SP
Rational Number Concepts
WORD BANK (RAT4)
Definition
Example or Picture
uc
e
Word
od
benchmark fraction
ep
r
decimal
ot
R
improper
fraction
N
integer
pl
e:
D
negative
fraction
o
mixed
number
m
rational numbers
Sa
repeating
decimal
terminating decimal
Rational Numbers Unit (Student Packet)
RAT4 – SP0
Rational Number Concepts
4.1 Terminating Decimals
Ready (Summary)
Set (Goals)
We will learn various strategies to convert
between fractions and terminating
decimals.
uc
e
TERMINATING DECIMALS
Go (Warmup)
ep
r
od
 Use a variety of strategies to convert
between fractions and terminating
decimals.
 Demonstrate conversion fluency
between common fractions and
decimals.
 Compute with simple fractions.
pl
e:
D
o
N
ot
R
Use the hundred grids to find the decimal equivalents for the following.
1
1
1.
= _______
2.
= _______
2
4
Write the decimal value for each.
3.
5.
$________
4.
one-fourth of a dollar $________
1
= _____
10
6.
2
= _____
10
7.
7
= _____
10
8.
9
= _____
10
1
= _____
100
10.
2
= _____
100
11.
17
= _____
100
12.
90
= _____
100
m
9.
one-half of a dollar
Sa
13. Which of the two values from problems 5-12 are equivalent?
Rational Numbers Unit (Student Packet)
RAT4 – SP1
Rational Number Concepts
4.1 Terminating Decimals
1. What is the relationship between
1
1
and ?
2
4
2. Here are two different methods to find the decimal equivalent for
Method 2
1
= ______________
4
1
4
N
0
4
pl
e:
D
o
Decimal
4. Show how to use the decimal equivalent for
addition or multiplication.
5. Show how to use the decimal equivalent for
2
4
1
=___________
4
3
4
4
4
1
3
to find the decimal equivalent for
by
4
4
3
4
to find the decimal equivalent for
by
4
4
Sa
m
subtraction.
1
= 0.5 = 0. ___ ___
2
__________ is __________
Therefore
3. Complete the table.
Fraction
1
of
2
ot
R
Therefore
Use the fact that
ep
r
1
with a denominator
4

1
that is a power of 10. 
 =
4
100

Rename the fraction
od
Method 1
1
4
uc
e
ALL ABOUT FOURTHS
6. Is it true that
4
2
= ? Explain.
4
2
Rational Numbers Unit (Student Packet)
RAT4 – SP2
Rational Number Concepts
4.1 Terminating Decimals
BENCHMARK FRACTIONS AND DECIMALS
Write decimal equivalents for each of the following benchmark fractions.
2
= _____
10
3
= _____
10
7
= _____
10
9
= _____
10
od
1
= _____
10
1.
uc
e
A benchmark fraction refers to a fraction that is easily recognizable. Benchmark fractions are
commonly used in everyday experiences.
2
= _____
100
9
= _____
100
10
= _____
100
99
= _____
100
ot
R
1
= _____
100
2.
ep
r
Describe an easy way to remember these kinds of fraction-decimal equivalents.
Describe an easy way to remember these kinds of fraction-decimal equivalents.
1
= _____
4
2
= _____
4
N
1
= _____
2
3.
3
= _____
4
pl
e:
D
o
Describe an easy way to remember these kinds of fraction decimal equivalents.
4. What is the relationship between
m
equivalent for
1
.
5
Sa
5. What is the relationship between
equivalent for
1
.
8
Rational Numbers Unit (Student Packet)
1
1
and
?
5
10
1
1
and
?
8
4
Use this relationship to find a decimal
Use this relationship to find a decimal
RAT4 – SP3
Rational Number Concepts
4.1 Terminating Decimals
USING BENCHMARK FRACTIONS TO FIND DECIMALS
3
5
a.
1
8
b.
3
8
c.
5
8
a.
1
20
b.
2
20
a.
1
25
b.
a.
1
50
b.
4
5
d.
7
8
c.
3
20
d.
9
20
2
25
c.
5
25
d.
14
25
2
50
c.
15
50
d.
43
50
m
5.
d.
od
c.
ep
r
2
5
pl
e:
D
4.
b.
ot
R
3.
1
5
N
2.
a.
o
1.
uc
e
Use your knowledge about basic arithmetic and benchmark fractions to change the following
fractions to decimals (no approximations). Do not use the long division algorithm or a
calculator. You may do the problems in any order.
Sa
6. Why are all of the decimals above called “terminating decimals?”
Rational Numbers Unit (Student Packet)
RAT4 – SP4
Rational Number Concepts
4.1 Terminating Decimals
MORE BENCHMARK FRACTIONS AND DECIMALS
Describe the relationship between each pair of fractions.
1
1
and
25
50
1
1
and
25
100
3.
od
2.
uc
e
1
1
and
50
100
1.
4.
Fact 2:
5
= 0.5
10
5
20
twentieths are half of tenths
o
Fact 2:
pl
e:
D
5.
5
= 1
5
5
1
4


5
5
5
N
Show work here:
Fact 1:
= ________
ot
R
Fact 1:
ep
r
Use the given facts to find the decimal equivalents for each fraction.
fraction
4
5
decimal
= ________
fraction
decimal
Show work here:
Fact 1:
m
6.
Fact 2:
1
= 0.5
2
1
1
is one-tenth of
20
2
1
20
= ________
fraction
decimal
Sa
Show work here:
Rational Numbers Unit (Student Packet)
RAT4 – SP5
Rational Number Concepts
4.1 Terminating Decimals
USING DIVISION TO FIND TERMINATING DECIMALS
a
poses the division problem of dividing a by b. Therefore, we can change a
b
fraction to a decimal using a division procedure.
uc
e
The fraction
3
into a decimal using a division procedure.
8
Method 1: Traditional Algorithm
Method 2: Chunking Algorithm
375
8 3000
24
60
56
40
40
0
3000  8  375
 Since 3000 is 1000 times larger than
3.000, we must divide the result by
1000.
375
 0.375
1000
N
ot
R
2400 300
600
560 +70
40
40
+5
0 375
Think:
 We want to divide 3.000 by 8.
 With chunking, we will divide 3000 by
8 to make the division easier.
ep
r
.375
8 3.000
od
Example: Change
2.
pl
e:
D
7
8
3
20
3.
11
25
Sa
m
1.
o
Use division to convert each fraction to a decimal.
Rational Numbers Unit (Student Packet)
RAT4 – SP6
Rational Number Concepts
4.2 Repeating Decimals
uc
e
REPEATING DECIMALS
Set (Goals)
We will change thirds, sixths, and ninths to
decimals and explore patterns in repeating
decimals. We will continue to convert
between fractions and decimals. We will
continue to compare, order, and add
simple fractions and decimals.
 Explore patterns in repeating decimals.
 Use a variety of strategies to convert
between fractions and repeating
decimals.
 Compare, order, and add common
fractions and decimals.
ot
R
Go (Warmup)
ep
r
od
Ready (Summary)
Change the following fractions to decimals using any method.
1
2
2.
5.
17
100
6.
1
4
3.
1
8
4.
1
10
11
25
8.
4
5
o
N
1.
23
50
pl
e:
D
7.
m
9. List all of the decimal values above in order from least to greatest.
Sa
______

______

______
Rational Numbers Unit (Student Packet)

______

______

______

______

______
RAT4 – SP7
Rational Number Concepts
4.2 Repeating Decimals
INVESTIGATING ONE-THIRD
2.
ot
R
ep
r
od
1.
uc
e
Each of these squares represents one square unit.
This square is divided into tenths. Shade
one-third of it. This illustrates that
1
= _____ tenths + _____ of a tenth.
3
3.
4.
m
pl
e:
D
o
N
This square represents one whole. Shade
one-third of it. This illustrates that
1
= _____ of a whole.
3
Sa
This square is divided into ____________.
Shade one-third of it. This illustrates that
1
= _____ tenths + _____ hundredths
3
+ ______ of a hundredth
This square is divided into ____________.
Shade one-third of it. This illustrates that
1
= _____ tenths + _____ hundredths
3
+ ______ thousandths
+ ______ of a thousandth.
Rational Numbers Unit (Student Packet)
RAT4 – SP8
Rational Number Concepts
4.2 Repeating Decimals
INVESTIGATING ONE-THIRD (continued)
1
cannot be written as a fraction with a denominator of
3
10, 100, or 1,000. Explain why this is true.
6. Use a division algorithm to find decimal equivalents for
1
.
3
B.
C.
3 1. 0 0
3 1. 0 0 0
ep
r
3 1. 0
od
A.
uc
e
5. The previous page illustrates that
This division shows that
1
=
3
ot
R
This division shows that
1
=
3
This division shows that
1
=
3
pl
e:
D
o
N
1
, when converted to a decimal by division, results in a repeating
3
decimal. That is, the decimal part is a pattern of digits that repeats infinitely from some point
on. To show the repeating pattern, use a series of dots (…) or a repeat bar.
Problem 6 illustrates that
7. Show some different decimal representations of
1
using a series of dots.
3
1
= 0.33... = 0.333... = ________ = ________
3
Sa
m
8. Show some different decimal representations of
9. Sometimes
1
using a repeat bar.
3
1
= 0.3 = 0.33 = ___________ = ___________
3
1
1
1
is written as 0.33 . What do you think the
in the decimal means?
3
3
3
Rational Numbers Unit (Student Packet)
RAT4 – SP9
Rational Number Concepts
4.2 Repeating Decimals
THIRDS AND NINTHS
1.
Fact 2:
1
= .333...
3
2
1
is twice
3
3
2
3
fraction
1
= .333...
3
1
1
Fact 2:
is ________ of
9
3
Fact 1:
1
= 0. ______
9
2
1
Fact 2:
is __________
9
9
Fact 1:
o
decimal
= ________
fraction
4
9
pl
e:
D
4.
= ________
ep
r
2
9
1
= 0. ______
9
4
2
Fact 2:
is __________
9
9
Fact 1:
decimal
fraction
N
3.
1
9
ot
R
2.
= ________
od
Fact 1:
uc
e
Use the given facts to find the decimal equivalents for each fraction.
decimal
= ________
fraction
decimal
m
5. Continue the pattern for ninths. Find these decimal equivalents.
Sa
3
=
9
5
=
9
Rational Numbers Unit (Student Packet)
6
=
9
7
=
9
8
=
9
RAT4 – SP10
Rational Number Concepts
4.2 Repeating Decimals
1. Use a division algorithm to find decimal equivalents for
A.
1
.
6
B.
C.
6 1. 0 0 0
6 1. 0 0 0 0
ep
r
od
6 1. 0 0
uc
e
SIXTHS
This division shows that
1
=
6
ot
R
This division shows that
1
=
6
This division shows that
1
=
6
1
, when converted to a decimal by division, results in a terminating or a
6
repeating decimal? Explain.
N
2. Does it appear that
1
using a series of dots.
6
o
3. Show some different decimal representations
pl
e:
D
1
= 0.16... = 0.1666... = ________ = ________
6
4. Show some different decimal representations
1
using repeat bar.
6
1
= 0.16 = 0.166 = ___________ = ___________
6
Sa
m
5. Why do you think it is necessary to show more than two decimal places for
6. Challenge: Sometimes
1
?
6
2
2
1
is written as 0.16 . What do you think the
means?
3
3
6
Rational Numbers Unit (Student Packet)
RAT4 – SP11
Rational Number Concepts
4.2 Repeating Decimals
COMPARING FRACTIONS AND DECIMALS
1
=
3
1
=
6
od
he is wrong.
1
1
= 0.1666… = 0.16 , then
= 0.1444… = 0.14 . Explain why
6
4
ep
r
1. Dilbert thinks that since
1
=
9
2.
3.
_____
4.
1
3
7
9
6.
1
9
_____ 0.3
0.3 _____
0.3 _____ 0.3
11.
1
3
_____ 0.2
3
9
10.
1
3
_____ 0.3
12.
1
6
_____
0.3 _____ 0.333
3
9
9.
pl
e:
D
8.
1
3
7.
o
1
3
_____
N
5.
ot
R
Use the symbols <, =, or > to compare.
1
9
uc
e
Copy the decimal equivalents for the following fractions from the previous pages.
_____ 0.333
13.
0.16 _____
2
12
0.2
2
9
_____
Sa
m
14.Order the following from least to greatest. (Hint: two numbers have the same value, so it
does not matter which of these is listed first.)
1
6
_______
2
3
0.222
_______
_______
Rational Numbers Unit (Student Packet)
2
9
_______
0.2
_______
0.16
_______
RAT4 – SP12
Rational Number Concepts
4.2 Repeating Decimals
PRACTICE WITH FRACTIONS AND DECIMALS
1
=
3
1
=
6
uc
e
Copy the decimal equivalents for the following fractions from the previous pages.
1
=
9
Change the fractions into decimals.
2
6
6.
7
9
3.
3
6
8
9
od
5.
6
9
4.
ep
r
2.
4
6
7.
5
6
8.
ot
R
5
9
N
1.
Use the symbols <, =, or > to compare.
10.
1
6
_____
pl
e:
D
1
3
o
9.
12.
11.
3
7
_____
3
8
13.
0.56 ____
2
6
_____
3
9
14.
5
9
5
5
_____
8
9
0.42 _____ 0.4
m
15. Order the following from least to greatest. (Hint: Two numbers have the same value, so it
does not matter which of these is listed first.)
Sa
1
3
_______
4
9
0.333
_______
Rational Numbers Unit (Student Packet)
_______
2
9
_______
0.3
_______
0.3
_______
RAT4 – SP13
Rational Number Concepts
4.2 Repeating Decimals
ADDING RATIONAL NUMBERS
1.
1 1

2 4
ep
r
ot
R
1 3

4 8
1 2

3 3
pl
e:
D
4.
2
3

5 10
N
3.
2 1

 _______
4 4
o
2.
0. 5
+0. 2 5
0.5 + 0.25
od

Change each fraction expression to a
decimal expression and add
uc
e
Add each fraction expression
1 1

3 6
m
5.
Sa
6. Which problems above were easier to add as fractions? Explain.
7. Which problems above were easier to add as decimals? Explain.
Rational Numbers Unit (Student Packet)
RAT4 – SP14
Rational Number Concepts
4.2 Repeating Decimals
BELIEVE IT OR NOT
2.
3
=1 can also be written as 0._______.
3
Fact 1:
1
= 0.16666...
6
Fact 2:
1
2
=
= 0.33333...
3
6
decimal
Therefore, 0.______ = 1
3
6
= ________
fraction
decimal
3 1
1
 can also be written as 0.______. Therefore, 0._______ =
6 2
2
pl
e:
D
o
This shows that
fraction
od
This shows that
= ________
ep
r
Fact 2:
3
3
N
1.
1
= .333...
3
3
1
is three times
3
3
ot
R
Fact 1:
uc
e
Use the given facts to find the decimal equivalents for each fraction.
Fact 1: 1 = 0.999….
Fact 2:
5
1
= 1
6
6
m
3.
1
= 0.30  0.030  0.0030...
3
1
1
Fact 2:
is one-half of
6
3
Sa
Fact 1:
4.
Rational Numbers Unit (Student Packet)
5
6
= ________
fraction
1
6
decimal
= ________
fraction
decimal
RAT4 – SP15
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
uc
e
ORDERING RATIONAL NUMBERS
ON A NUMBER LINE
Ready (Summary)
Set (Goals)
We will practice ordering rational numbers,
including positive and negative fractions
and decimals, on a number line.
Compare and order positive and
negative fractions.
Compare and order positive and
negative decimals.
Convert between fractions and
decimals, and use these
representations for estimation.
Distinguish between terminating and
repeating decimals.

od

ep
r

ot
R

Go (Warmup)

Draw a circle around each number that represents a terminating decimal and a square
around each number that represents a repeating decimal.
Then use  ,  , or = to make each statement true.
1.
_____
1
6
Think
2.
8.
2
1
6
= 0.5
(terminating → circle)
= 0.1666… = 0.16
_____
0.3
3.
1
3
_____
0.33
3
9
_____
3
8
5.
7
8
_____
14
16
3
5
_____
0.35
7.
0.4
_____
2
5
_____
0.7
9.
-9
Sa
6.
1
0.3
m
4.
pl
e:
D
o
1
2
N

0.7
Rational Numbers Unit (Student Packet)
_____
(repeating → square)
-12
RAT4 – SP16
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NEGATIVE FRACTIONS
uc
e
Use the number line below:
1. Write in the fractions for each marking that are greater than 0. These are positive fractions.
2. Write in the fractions for each marking that are less than 0. These are negative fractions.
-1
ep
r
od
3. Write the decimal equivalent under each fraction on the number line.
0
1
1
1
3
-1
-
1
3
2
3
-
2
3
pl
e:
D
o
N
0
ot
R
4. Estimate the location of each number on the number line below. Then write the decimal
equivalents below each fraction.
5. Estimate the location of each number on the number line below. Then write the decimal
equivalents below each fraction.
1
-1
2
5
-
1
5
2
10
-
4
5
-
6
10
Sa
m
0
Rational Numbers Unit (Student Packet)
RAT4 – SP17
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NEGATIVE MIXED NUMBERS
Read as:
1 and
1
2
-1 and -
1
2
1
3
=
2
2
pl
e:
D
1
 1
-1 –  
 2
-2
o
0
-1
1
2
 1
(-1) +  - 
 2
ot
R
N
As a difference:
1
2
“negative one and
one-half”
 1
(1) +  
 2
As a sum:
As an improper
fraction
-1
“one and one-half”
The combination
of:
Graph:
1
2
od
1
Example:
A negative mixed number is the
combination of a negative integer
and a negative fraction.
uc
e
A positive mixed number is the
combination of a positive integer
and a positive fraction.
ep
r
Definition:
-
1
2
-1
=
 1
- 1 
 2
0
= -
3
2
Fill in the blanks.
Mixed number
As a sum
______ and ______
______ + ______
1
3
______ and ______
______ + ______
______ – ______
2
5
______ and ______
______ + ______
______ – ______
1
3
m
1. 2
The combination of
Sa
2. -2
3. -3
Rational Numbers Unit (Student Packet)
As a difference
RAT4 – SP18
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NEGATIVE MIXED NUMBERS (continued)
1
3
6. -3
2
5
ep
r
5. -2
od
1
3
ot
R
4. 2
uc
e
Write the improper fraction for the mixed number. Write down the integers that the fraction is
located between. Then estimate the location of each number on a graph.
Round to
Round to
Mixed
Improper
the nearest the nearest
Sketch of
number
fraction
larger
smaller
graph
integer
integer
7. Write the following numbers in order from least to greatest.
5
8
2
3
1
2
3
-2
N
-1
1
10
-1
3
4
-2
1
4
pl
e:
D
o
________ < ________ < ________ < ________ < ________ < ________
8. Here is a list of numbers:
2
3
1
1
2
-
3
4
-1
1
3
-2
1
4
The greatest is _________. The least is _________.

Make markings for some relevant integer values on the number line below.
m

Estimate the location of each number on the number line below.

Write the decimal equivalents below each fraction.
Sa

Rational Numbers Unit (Student Packet)
RAT4 – SP19
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NUMBER LINE A
3
4
-
6
5
-0.8
-0.08
-1.1
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2. Write an inequality statement to show the order of the numbers.
9
-1
10
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-
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1. Estimate the location of each number on the number line.
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_______  _______  _______  _______  _______  _______
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3. What integers and/or benchmark fractions did you locate on your number line?
3
6
and on the number line.
4
5
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4. Explain how you located -
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5. Explain how you located -0.8 and -0.08 on the number line.
Rational Numbers Unit (Student Packet)
RAT4 – SP20
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NUMBER LINE B
2
3
-
5
3
-0.5
-
5
11
-0.53
-0.123
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2. Write an inequality statement to show the order of the numbers.
od
1
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1. Estimate the location of each number on the number line.
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_______  _______  _______  _______  _______  _______
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3. What integers and/or benchmark fractions did you locate on your number line?
-0.5 and -
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4. Explain how you located
2
3
and -
5
3
on the number line.
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5. Explain how you located 1
5
on the number line.
11
Rational Numbers Unit (Student Packet)
RAT4 – SP21
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NUMBER LINE C
4
5
7
3
-0.4
-0.302
-1.25
3
2
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2. Write an inequality statement to show the order of the numbers.
-
od
2
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1. Estimate the location of each number on the number line.
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_______  _______  _______  _______  _______  _______
N
3. What integers and/or benchmark fractions did you locate on your number line?
and
3
2
and
7
on the number line.
3
o
4
5
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4. Explain how you located 2
-1.25 on the number line.
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5. Explain how you located -
Rational Numbers Unit (Student Packet)
RAT4 – SP22
Rational Number Concepts
4.4 Fraction and Decimal Games
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FRACTION AND DECIMAL GAMES
Ready (Summary)
Set (Goals)
We will practice finding fraction and
decimal equivalences and ordering
fractions and decimals through fraction
games.
Go (Warmup)
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 Identify equivalent fractions and
decimals.
 Order fractions and decimals.
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Write <, =, or > in each blank to make each statement true.
1.
2.
1
2
-3 _____ -3
3
3
5
3
______
8
8
4.
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3.
0.333 _______ 0.3
5.
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5
2
_____
8
3
6.
1
101
_____
2
200
m
7.
-2
13
1
_____ -3
4
2
8.
7
1
_____
8
8
9.
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0.333 _____
1
3
10.
-1.5 _____ -1
Rational Numbers Unit (Student Packet)
3
5
0.1 _______ 0.011
RAT4 – SP23
Rational Number Concepts
4.4 Fraction and Decimal Games
ORDER IT!
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Need:
 2 or more players
 32 or more Fraction Cards or Decimal Cards
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
Shuffle all the cards and place the cards face down in a pile.
To begin, put 5 cards face-up, in the order they are drawn.
The first player draws a card from the pile and places it on top of one of the existing face
up cards. If all of the cards are now in order from least to greatest, then the player wins.
If not, then play continues until all five cards are in order from least to greatest.
The next player draws a card from the pile and places it on top of one of the existing
face-up cards. If all the cards are now in order from least to greatest, then the player
wins. If not, then play continues until all five cards are in order from least to greatest.
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


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The object of this game is to get five numbers in a row, in order, from least value to greatest
value. Once a card is placed on the table face up, it may not be moved to another location.
However, a new card may be placed on top of it.
In order to win, the player must convince the opponent with a reasonable argument that the
cards are in order.
__________
__________
__________
__________
o
__________
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1. Play two rounds of the Order It! Record one of the ordered card sequences here.
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2. Explain why the numbers are in order.
Rational Numbers Unit (Student Packet)
RAT4 – SP24
Rational Number Concepts
4.4 Fraction and Decimal Games
MEMORY AND CHALLENGE GAMES
1. Recall the Fraction Memory Game (see RAT Lesson 1.3), where you matched equivalent
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fraction number cards to their picture cards. Create a new memory game that matches
fraction number cards to their decimal equivalent cards. Play the game with a classmate.
Record two sets of cards you matched here.
Fraction
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Explain why the numbers are equivalent.
Decimal
Decimal
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Fraction
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Explain why the numbers are equivalent.
2. Recall the Fraction Challenge Game (see RAT Lesson 1.3) where you divided a deck of
N
cards, and then you and your opponent each placed a card from your stack face up. The
player with the fraction of higher value wins. Create a new Challenge Game using fraction
and decimal cards. Play the game with a classmate. Record two sets of cards where you
won here.
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Who won? ____________ Explain.
m
me
Who won? ____________ Explain.
my opponent
Sa
me
my opponent
Rational Numbers Unit (Student Packet)
RAT4 – SP25
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
FOCUS ON VOCABULARY (RAT4)
P
N
T
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M
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F
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A
V
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M
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A
M
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A
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F
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K
A
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F
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F
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P
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A
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F
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G
L
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G
A
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R
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R
O
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O
E
Word Bank
fraction
mixed number
terminating decimal
P
R
C
G
T
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R
I
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M
A
N
E
K
N
P
I
N
improper fraction
negative fraction
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benchmark fraction
integer
repeating decimal
R
E
N
A
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M
G
R
R
B
C
A
K
R
V
A
N
A
od
T
I
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A
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T
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C
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I
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K
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V
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P
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T
O
G
N
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F
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N
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O
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X
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o
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B
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A
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T
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A
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G
I
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R
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T
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F
D
M
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E
G
T
M
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Find the words in the word search puzzle. Then, choose five words and write their definitions
or give examples.
Rational Numbers Unit (Student Packet)
RAT4 – SP26
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 1
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Write each number in expanded form.
1. 15.85 _____________________________________________________________
2. 0.024 _____________________________________________________________
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Write the sum in standard form and in words.
3. 0.4 + 0.03 + 0.001 ___________________________________________________
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Order the numbers from least to greatest.
4.
0.06
0.615
0.6
0.66
0.061
5.
0.11
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________ < ________ < ________ < ________ < ________
0.001
0.1
0.0112
0.01
________ < ________ < ________ < ________ < ________
192.45 – 0.19
7.
5.9 + 13.001
8.
47.85 – 4.37
11.
3.7 – 0.55
9.
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6.
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Compute.
0.113 – 0.02
10.
0.45 + 1.37
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Complete.
12
=
= 0. ____ = ____ %
20
100
13.
1
=
2
= 0. ____ = ____ %
3
=
4
15.
3
=
10
= 0. ____ = ____ %
Sa
12.
14.
= 0. ____ = ____ %
Rational Numbers Unit (Student Packet)
RAT4 – SP27
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 2
Use a splitting, replicating or a grouping diagram to show that these fractions are equivalent.
5
10
=
6
12
3.
1
5
=
3
15
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od
2.
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4
1
=
16
4
1.
Write each mixed number as an improper fraction and write each improper fraction as a
mixed number.
4
1
5
6.
38
6
9.
13
14
________
4
4
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5.
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15
4
4.
5
3
25
________
4
5
8.
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7.
o
Use <, >, or = to make each statement true.
17
25
________
2
3
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10. Estimate the location of each number on the number line.
1
1
8
Rational Numbers Unit (Student Packet)
1
8
3
7
3
6
1
1
4
RAT4 – SP28
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 3
1. Write decimal equivalents for each of the following benchmark fractions.
2
8
3. Use the relationship between
below.
1
50
b.
4
4
c.
3
8
d.
5
8
1
1
and
to find the decimal equivalents for fractions
50
100
3
50
c.
23
50
d.
48
50
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a.
d.
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b.
N
1
8
3
4
1
1
and
to find the decimal equivalents for fractions below.
8
4
2. Use the relationship between
a.
c.
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2
4
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b.
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1
4
a.
4. Use the given facts to find the decimal equivalents for the
8
1
8
Fact 2:
8 1 7
 
8 8 8
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Fact 1:
7
8
fraction
=
7
.
8
Show work here:
________
decimal
Rational Numbers Unit (Student Packet)
RAT4 – SP29
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 4
Use the symbols <, >, or = to compare.
1
_________ 0.333
3
2.
1
1
_________
4
3
3.
2
_________ 0.6
3
4.
3
3
_________
4
3
5.
0.66 _________ 0.6
6.
4
_________ 0.45
5
7.
0.56 _________ 0.5
8.
1
_________ 0.1
8
9.
10.
-13 _________ -5
11.
-1 _________ -100
12.
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1.
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2
_________ 0.5
4
-7 _________ 7
13. Write these numbers from least to greatest.
1
4
1
1
4
-2
1
8
-1
N
-1
3
4
-2
1
10
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__________ < __________ < __________ < __________ < __________
14. Estimate the location of each number on the number line.
2
3
-
7
3
-1
9
10
-1.1
-0.5
-0.05
m
-
Sa
15. Write an inequality statement to show the order of the numbers.
_______ < _______ < _______ < _______ < _______ < _______
Rational Numbers Unit (Student Packet)
RAT4 – SP30
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 5
1
5
8
3
-0.405
-2.25
-
4
3
-0.8
od
2
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1. Estimate the location of each number on the number line.
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2. Explain how you located -0.405 and -0.8.
Use the symbols <, >, or = to compare.
3.
4.
1
1
1
_____ 0.3
_____
3
6
9
9.
N
1
9
10.
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0.11_____
7.
0.16 _____
1
6
1
_____ 0.1666
6
8.
2
1
_____
18
9
0.333 _____
o
6.
5.
11.
1
2
_____
6
3
3
9
1
_____ 0.12
9
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12. Order these numbers from least to greatest.
0.44
4
9
2
3
0.4
0.6
1
6
________ < ________ < ________ < ________ < ________ < ________
Rational Numbers Unit (Student Packet)
RAT4 – SP31
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
TEST PREPARATION (RAT4)
3
?
8
0.125
B.
0.375
C.
0.38
C.
1
4
D.
1
2
1
3
B.
A.
<
B.
D.
>
1
8
2
_____ 0.66 true.
3
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3. Choose the symbol that makes the statement
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2. What is the fraction equivalent for 0.125?
A.
0.625
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1. What is the decimal equivalent for
A.
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Show your work on a separate sheet of paper and choose the best answer.
C.
=
D.
N
4. Place the numbers listed below in order from least to greatest.
-
2
3
-2
o
-0.06
2
3
-
7
3
-2.66
B.
-2.66 , -
7
2
2
, -2 , -0.06 , 3
3
3
7
2
, -2.66 , - , -0.06
3
3
D.
-0.06 , -
2 7
2
, - , -2.66 , -2
3
3
3
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2
7
2
, -2.66 , - , - , -0.06
3
3
3
A.
-2
C.
-2.66 , -
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5. Which number does F represent on the number line?
A.
7
16
F
G
H
0
B.
Rational Numbers Unit (Student Packet)
7
8
C.
-
7
8
D.
-
7
16
RAT4 – SP32
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
KNOWLEDGE CHECK (RAT4)
1.
What is the decimal equivalent for
HINT:
8 1 7
 
8 8 8
7
?
8
What is the fraction equivalent for 0.18?
4.2
Repeating Decimals
3.
Order the following from least to greatest.
0.61
2
3
0.33
N
1
3
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2.
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Terminating Fractions
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4.1
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Show your work on a separate sheet of paper and write your answers on this page.
0.3
0.6
4.3
2
or 0.60? Explain.
3
Ordering Rational Numbers on a Number Line
Estimate the location of each number on the number line.
-0.5
-0.05
-
5
11
-
5
4
1
1
4
-1.30
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5.
Which is greater,
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4.
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________ < ________ < ________ < ________ < ________ < ________
Rational Numbers Unit (Student Packet)
RAT4 – SP33
Rational Number Concepts
Home-School Connection (RAT4)
1. Find the decimal equivalent for
13
.
25
3. Which is greater, -2.32 or -2.3? Explain.
od
1
= 0.3 = 0.33 = 0.333 . Is he correct? Explain.
3
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r
2. Jorge says that
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Here are some questions to review with your young mathematician.
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Parent (or Guardian) signature ____________________________
Selected California Mathematics Content Standards
NS 6.1.1
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NS 7.1.3
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NS 5.2.1
Interpret percents as part of a hundred; find decimal and percent equivalents for common
fractions and explain why they represent the same value; compute a given percent of a whole
number.
Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive
integers from negative integers; and verify the reasonableness of results.
Compare and order positive and negative fractions, decimals, and mixed numbers and place
them on a number line.
Convert fractions to decimals and percents and use these representations in estimations,
computations, and applications.
Know that every rational number is either a terminating or a repeating decimal and be able to
convert terminating decimals into reduced fractions.
o
NS 5.1.2
NS7.1.5
DO NOT DUPLICATE © 2010
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FIRST PRINTING
Rational Numbers Unit (Student Packet)
RAT4 – SP34