Name ___________________________
Period__________
Date ___________
RN4
STUDENT PAGES
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
RN4.2
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
RN4.3
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
D
R
AF
T
RN4.1
RN4.4
Fraction and Decimal Games
• Identify equivalent fractions and decimals.
• Order fractions and decimals.
23
RN4.5
Vocabulary, Skill Builders, and Review
26
Rational Numbers Unit (Student Pages)
RN4 – SP
Rational Number Concepts
WORD BANK (RN4)
Word
Definition
Example or Picture
benchmark fraction
T
decimal
integer
R
mixed
number
AF
improper
fraction
D
negative
fraction
rational numbers
repeating
decimal
terminating decimal
Rational Numbers Unit (Student Packet)
RN4 – SP0
Rational Number Concepts
4.1 Terminating Decimals
TERMINATING DECIMALS
Ready (Summary)
Set (Goals)
• Use a variety of strategies to convert
between fractions and terminating
decimals.
• Demonstrate conversion fluency
between common fractions and
decimals.
• Compute with simple fractions.
T
We will learn various strategies to convert
between fractions and terminating
decimals.
Go (Warmup)
R
AF
Use the hundred grids to find the decimal equivalents for the following.
1
1
1.
= _______
2.
= _______
2
4
Write the decimal value for each.
one-half of a dollar
$________
D
3.
4.
one-fourth of a dollar $________
5.
1
= _____
10
6.
2
= _____
10
7.
7
= _____
10
8.
9
= _____
10
9.
1
= _____
100
10.
2
= _____
100
11.
17
= _____
100
12.
90
= _____
100
13. Which of the two values from problems 5-12 are equivalent?
Rational Numbers Unit (Student Packet)
RN4 – SP1
Rational Number Concepts
4.1 Terminating Decimals
ALL ABOUT FOURTHS
1. What is the relationship between
1
1
and ?
2
4
2. Here are two different methods to find the decimal equivalent for
Method 1
Method 2
1
with a denominator
4

1
that is a power of 10. 
 =
4
100

1
= 0.5 = 0. ___ ___
2
1
of
2
__________ is __________
AF
1
= ______________
4
Use the fact that
T
Rename the fraction
Therefore
1
4
Therefore
1
=___________
4
3. Complete the table.
Fraction
1
4
R
Decimal
0
4
4. Show how to use the decimal equivalent for
2
4
3
4
4
4
3
1
to find the decimal equivalent for
by
4
4
D
addition or multiplication.
5. Show how to use the decimal equivalent for
3
4
to find the decimal equivalent for
by
4
4
subtraction.
6. Is it true that
4
2
= ? Explain.
4
2
Rational Numbers Unit (Student Packet)
RN4 – SP2
Rational Number Concepts
4.1 Terminating Decimals
BENCHMARK FRACTIONS AND DECIMALS
A benchmark fraction refers to a fraction that is easily recognizable. Benchmark fractions are
commonly used in everyday experiences.
Write decimal equivalents for each of the following benchmark fractions.
1.
1
= _____
10
2
= _____
10
3
= _____
10
7
= _____
10
9
= _____
10
1
= _____
100
2
= _____
100
9
= _____
100
10
= _____
100
99
= _____
100
AF
2.
T
Describe an easy way to remember these kinds of fraction-decimal equivalents.
Describe an easy way to remember these kinds of fraction-decimal equivalents.
3.
1
= _____
2
1
= _____
4
2
= _____
4
3
= _____
4
R
Describe an easy way to remember these kinds of fraction decimal equivalents.
D
4. What is the relationship between
equivalent for
Use this relationship to find a decimal
1
.
5
5. What is the relationship between
equivalent for
1
1
and
?
5
10
1
1
and
?
8
4
Use this relationship to find a decimal
1
.
8
Rational Numbers Unit (Student Packet)
RN4 – SP3
Rational Number Concepts
4.1 Terminating Decimals
USING BENCHMARK FRACTIONS TO FIND DECIMALS
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.
3.
b.
2
5
c.
3
5
d.
4
5
a.
1
8
b.
3
8
c.
5
8
d.
7
8
a.
1
20
a.
1
25
b.
2
20
c.
3
20
d.
9
20
b.
2
25
c.
5
25
d.
14
25
2
50
c.
15
50
d.
43
50
D
R
4.
1
5
5.
a.
1
50
T
2.
a.
AF
1.
b.
6. Why are all of the decimals above called “terminating decimals?”
Rational Numbers Unit (Student Packet)
RN4 – SP4
Rational Number Concepts
4.1 Terminating Decimals
MORE BENCHMARK FRACTIONS AND DECIMALS
Describe the relationship between each pair of fractions.
1.
1
1
and
50
100
2.
1
1
and
25
50
1
1
and
25
100
3.
4.
Fact 2:
5
= 0.5
10
5
20
= ________
AF
Fact 1:
T
Use the given facts to find the decimal equivalents for each fraction.
twentieths are half of tenths
fraction
decimal
Show work here:
Fact 1:
R
Fact 2:
5.
5
= 1
5
4
1
5
=
−
5
5
5
4
5
= ________
fraction
decimal
D
Show work here:
Fact 1:
Fact 2:
6.
1
= 0.5
2
1
1
is one-tenth of
20
2
1
20
= ________
fraction
decimal
Show work here:
Rational Numbers Unit (Student Packet)
RN4 – 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.
The fraction
3
into a decimal using a division procedure.
8
Method 1: Traditional Algorithm
Method 2: Chunking Algorithm
Example: Change
2400 300
600
560 +70
40
40
+5
0 375
• Since 3000 is 1000 times larger than
3.000, we must divide the result by
1000.
AF
24
60
56
40
40
0
375
8 3000
T
.375
8 3.000
Think:
• We want to divide 3.000 by 8.
• With chunking, we will divide 3000 by
8 to make the division easier.
7
8
2.
3
20
3.
11
25
D
1.
R
Use division to convert each fraction to a decimal.
Rational Numbers Unit (Student Packet)
RN4 – SP6
Rational Number Concepts
4.2 Repeating Decimals
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.
T
Ready (Summary)
AF
Go (Warmup)
Change the following fractions to decimals using any method.
1
2
5.
17
100
1
4
2.
R
1.
23
50
1
8
4.
1
10
7.
11
25
8.
4
5
D
6.
3.
9. List all of the decimal values above in order from least to greatest.
<
______
<
______
<
______
Rational Numbers Unit (Student Packet)
<
<
______
______
<
<
______
______
______
RN4 – SP7
Rational Number Concepts
4.2 Repeating Decimals
INVESTIGATING ONE-THIRD
Each of these squares represents one square unit.
2.
AF
T
1.
This square is divided into tenths. Shade
one-third of it. This illustrates that
1
= _____ tenths + _____ of a tenth.
3
3.
4.
D
R
This square represents one whole. Shade
one-third of it. This illustrates that
1
= _____ of a whole.
3
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)
RN4 – 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.
5. The previous page illustrates that
6. Use a division algorithm to find decimal equivalents for
A.
B.
C.
3 1. 0 0
This division shows that
1
=
3
This division shows that
1
=
3
AF
This division shows that
1
=
3
3 1. 0 0 0
T
3 1. 0
1
.
3
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.
R
Problem 6 illustrates that
7. Show some different decimal representations of
1
using a series of dots.
3
D
1
= 0.33... = 0.333... = ________ = ________
3
8. Show some different decimal representations of
1
using a repeat bar.
3
1
= 0.3 = 0.33 = ___________ = ___________
3
9. Sometimes
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)
RN4 – SP9
Rational Number Concepts
4.2 Repeating Decimals
THIRDS AND NINTHS
Use the given facts to find the decimal equivalents for each fraction.
Fact 1:
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:
T
2
9
decimal
= ________
R
fraction
1
= 0. ______
9
4
2
Fact 2:
is __________
9
9
Fact 1:
4
9
decimal
= ________
fraction
decimal
D
4.
= ________
fraction
1
= 0. ______
9
2
1
is __________
Fact 2:
9
9
Fact 1:
3.
1
9
decimal
AF
2.
= ________
5. Continue the pattern for ninths. Find these decimal equivalents.
3
=
9
5
=
9
Rational Numbers Unit (Student Packet)
6
=
9
7
=
9
8
=
9
RN4 – SP10
Rational Number Concepts
4.2 Repeating Decimals
SIXTHS
1. Use a division algorithm to find decimal equivalents for
A.
1
.
6
B.
6 1. 0 0 0
6 1. 0 0 0 0
T
6 1. 0 0
C.
This division shows that
1
=
6
This division shows that
1
=
6
AF
This division shows that
1
=
6
1
, when converted to a decimal by division, results in a terminating or a
6
repeating decimal? Explain.
2. Does it appear that
R
3. Show some different decimal representations
1
using a series of dots.
6
1
= 0.16... = 0.1666... = ________ = ________
6
D
4. Show some different decimal representations
1
using repeat bar.
6
1
= 0.16 = 0.166 = ___________ = ___________
6
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)
RN4 – SP11
Rational Number Concepts
4.2 Repeating Decimals
COMPARING FRACTIONS AND DECIMALS
Copy the decimal equivalents for the following fractions from the previous pages.
1
=
3
1
=
6
1. Dilbert thinks that since
1
=
9
1
1
= 0.1666… = 0.16 , then
= 0.1444… = 0.14 . Explain why
6
4
AF
Use the symbols <, =, or > to compare.
T
he is wrong.
3.
2.
1
9
_____
7
9
4.
1
3
_____
1
9
1
3
6.
5.
_____ 0.3
8.
0.3 _____
0.3 _____ 0.333
3
9
10.
9.
1
3
0.3 _____ 0.3
D
11.
1
6
_____ 0.3
12.
_____ 0.2
3
9
7.
R
1
3
_____
0.16 _____
1
3
_____ 0.333
0.2
_____
13.
2
12
2
9
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
_______
RN4 – SP12
Rational Number Concepts
4.2 Repeating Decimals
PRACTICE WITH FRACTIONS AND DECIMALS
Copy the decimal equivalents for the following fractions from the previous pages.
1
=
3
1
=
6
1
=
9
Change the fractions into decimals.
2.
5.
2
6
6.
6
9
7
9
3.
8
9
4.
T
5
9
3
6
4
6
7.
AF
1.
5
6
8.
Use the symbols <, =, or > to compare.
10.
R
9.
1
3
1
6
_____
3
7
11.
_____
3
8
13.
5
9
D
12.
0.56 ____
2
6
_____
3
9
14.
5
5
_____
8
9
0.42 _____ 0.4
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.)
1
3
4
9
_______
0.333
_______
Rational Numbers Unit (Student Packet)
_______
2
9
_______
0.3
_______
0.3
_______
RN4 – SP13
Rational Number Concepts
4.2 Repeating Decimals
ADDING RATIONAL NUMBERS
Add each fraction expression
1.
1 1
+
2 4
=
Change each fraction expression to a
decimal expression and add
0.5 + 0.25
0. 5
+0. 2 5
2 1
+
= _______
4 4
2.
1 3
+
4 8
4.
D
5.
R
1 2
+
3 3
AF
3.
T
3
2
+
5 10
1 1
+
3 6
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)
RN4 – SP14
Rational Number Concepts
4.2 Repeating Decimals
BELIEVE IT OR NOT
Use the given facts to find the decimal equivalents for each fraction.
Fact 2:
This shows that
2.
1
= 0.16666...
6
Fact 2:
1
2
=
= 0.33333...
3
6
R
5
1
= 1−
6
6
D
Fact 2:
1
= 0.30 + 0.030 + 0.0030...
3
1
1
Fact 2:
is one-half of
6
3
Fact 1:
4.
decimal
Therefore, 0.______ = 1
3
6
= ________
fraction
decimal
3 1
1
= can also be written as 0.______. Therefore, 0._______ =
6 2
2
Fact 1: 1 = 0.999….
3.
= ________
fraction
3
=1 can also be written as 0._______.
3
Fact 1:
This shows that
3
3
AF
1.
1
= .333...
3
3
1
is three times
3
3
T
Fact 1:
Rational Numbers Unit (Student Packet)
5
6
= ________
fraction
1
6
decimal
= ________
fraction
decimal
RN4 – SP15
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
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.
•
T
•
AF
•
Go (Warmup)
•
1.
1
2
_____
1
1
6
0.3
_____
2
1
Think
0.3
D
2.
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.
R
•
= 0.5
(terminating → circle)
= 0.1666… = 0.16
6
3.
1
3
_____
0.33
4.
3
9
_____
3
8
5.
7
8
_____
14
16
6.
3
5
_____
0.35
7.
0.4
_____
2
5
8.
0.7
_____
0.7
9.
-9
Rational Numbers Unit (Student Packet)
_____
(repeating → square)
-12
RN4 – SP16
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NEGATIVE FRACTIONS
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.
0
1
AF
-1
T
3. Write the decimal equivalent under each fraction on the number line.
4. Estimate the location of each number on the number line below. Then write the decimal
equivalents below each fraction.
1
1
3
-1
-
1
3
2
3
-
2
3
R
0
D
5. Estimate the location of each number on the number line below. Then write the decimal
equivalents below each fraction.
0
1
-1
Rational Numbers Unit (Student Packet)
2
5
-
1
5
2
10
-
4
5
-
6
10
RN4 – SP17
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NEGATIVE MIXED NUMBERS
A positive mixed number is the
combination of a positive integer
and a positive fraction.
1
Example:
Read as:
Graph:
-1
1 and
1
2
“negative one and
one-half”
1
2
-1 and -
 1
(1) +  
 2
1
2
 1
(-1) +  - 
 2
AF
As a difference:
1
2
“one and one-half”
The combination
of:
As a sum:
A negative mixed number is the
combination of a negative integer
and a negative fraction.
T
Definition:
 1
-1 –  
 2
1
2
-2
R
0
As an improper
fraction
1
1
3
=
2
2
-1
-
1
2
=
-1
 1
- 1 
 2
0
= -
3
2
D
Fill in the blanks.
Mixed number
The combination of
As a sum
1
3
______ and ______
______ + ______
2. -2
1
3
______ and ______
______ + ______
______ – ______
3. -3
2
5
______ and ______
______ + ______
______ – ______
1. 2
Rational Numbers Unit (Student Packet)
As a difference
RN4 – SP18
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NEGATIVE MIXED NUMBERS (continued)
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
larger
smaller
graph
number
fraction
integer
integer
5. -2
1
3
6. -3
2
5
T
1
3
AF
4. 2
7. Write the following numbers in order from least to greatest.
5
8
-1
2
3
1
2
3
-2
1
10
-1
3
4
-2
1
4
R
________ < ________ < ________ < ________ < ________ < ________
2
3
1
1
2
-
3
4
-1
1
3
-2
1
4
D
8. Here is a list of numbers:
•
The greatest is _________. The least is _________.
•
Make markings for some relevant integer values on the number line below.
•
Estimate the location of each number on the number line below.
•
Write the decimal equivalents below each fraction.
Rational Numbers Unit (Student Packet)
RN4 – SP19
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NUMBER LINE A
1. Estimate the location of each number on the number line.
-
3
4
-
6
5
-0.8
-0.08
-1.1
-1
9
10
T
2. Write an inequality statement to show the order of the numbers.
AF
_______ < _______ < _______ < _______ < _______ < _______
3. What integers and/or benchmark fractions did you locate on your number line?
3
6
and on the number line.
4
5
D
R
4. Explain how you located -
5. Explain how you located -0.8 and -0.08 on the number line.
Rational Numbers Unit (Student Packet)
RN4 – SP20
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NUMBER LINE B
1. Estimate the location of each number on the number line.
1
2
3
-
5
3
-0.5
-
5
11
-0.53
-0.123
T
2. Write an inequality statement to show the order of the numbers.
AF
_______ < _______ < _______ < _______ < _______ < _______
3. What integers and/or benchmark fractions did you locate on your number line?
5
on the number line.
11
R
-0.5 and -
D
4. Explain how you located
5. Explain how you located 1
2
3
Rational Numbers Unit (Student Packet)
and -
5
3
on the number line.
RN4 – SP21
Rational Number Concepts
4.3 Ordering Rational Numbers on a Number Line
NUMBER LINE C
1. Estimate the location of each number on the number line.
2
4
5
7
3
-0.4
-0.302
-1.25
-
3
2
T
2. Write an inequality statement to show the order of the numbers.
AF
_______ < _______ < _______ < _______ < _______ < _______
3. What integers and/or benchmark fractions did you locate on your number line?
and
7
on the number line.
3
3
2
and
-1.25 on the number line.
R
4
5
D
4. Explain how you located 2
5. Explain how you located -
Rational Numbers Unit (Student Packet)
RN4 – SP22
Rational Number Concepts
4.4 Fraction and Decimal Games
FRACTION AND DECIMAL GAMES
Ready (Summary)
Set (Goals)
• Identify equivalent fractions and
decimals.
• Order fractions and decimals.
T
We will practice finding fraction and
decimal equivalences and ordering
fractions and decimals through fraction
games.
Go (Warmup)
AF
Write <, =, or > in each blank to make each statement true.
1.
2.
1
2
-3 _____ -3
3
3
3
5
______
8
8
3.
4.
5
2
_____
8
3
R
5.
0.333 _______ 0.3
6.
D
101
1
_____
200
2
7.
-2
-
8.
7
1
_____
8
8
9.
13
1
_____ -3
4
2
0.333 _____
1
3
10.
-1.5 _____ -1
3
5
Rational Numbers Unit (Student Packet)
0.1 _______ 0.011
RN4 – SP23
Rational Number Concepts
4.4 Fraction and Decimal Games
ORDER IT!
Need:
• 2 or more players
• 32 or more Fraction Cards or Decimal Cards
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.
T
•
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.
AF
•
•
•
In order to win, the player must convince the opponent with a reasonable argument that the
cards are in order.
1. Play two rounds of the Order It! Record one of the ordered card sequences here.
__________
__________
__________
__________
R
__________
D
2. Explain why the numbers are in order.
Rational Numbers Unit (Student Packet)
RN4 – 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
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.
Explain why the numbers are equivalent.
Fraction
Decimal
Decimal
AF
Fraction
T
Explain why the numbers are equivalent.
2. Recall the Fraction Challenge Game (see RAT Lesson 1.3) where you divided a deck of
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.
R
Who won? ____________ Explain.
my opponent
D
me
me
Who won? ____________ Explain.
my opponent
Rational Numbers Unit (Student Packet)
RN4 – SP25
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
FOCUS ON VOCABULARY (RN4)
Find the words in the word search puzzle. Then, choose five words and write their definitions
or give examples.
V
C
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F
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K
B
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D
benchmark fraction
integer
repeating decimal
Rational Numbers Unit (Student Packet)
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Word Bank
fraction
mixed number
terminating decimal
improper fraction
negative fraction
RN4 – SP26
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 1
Write each number in expanded form.
1. 15.85 _____________________________________________________________
2. 0.024 _____________________________________________________________
Write the sum in standard form and in words.
Order the numbers from least to greatest.
4.
0.06
0.615
0.6
T
3. 0.4 + 0.03 + 0.001 ___________________________________________________
0.66
0.061
5.
0.11
AF
________ < ________ < ________ < ________ < ________
0.001
0.1
0.0112
0.01
________ < ________ < ________ < ________ < ________
Compute.
192.45 – 0.19
9.
0.113 – 0.02
7.
5.9 + 13.001
R
6.
0.45 + 1.37
47.85 – 4.37
11.
3.7 – 0.55
D
10.
8.
Complete.
12.
12
=
= 0. ____ = ____ %
20
100
13.
1 =
2
= 0. ____ = ____ %
14.
3
=
4
15.
3
=
10
= 0. ____ = ____ %
= 0. ____ = ____ %
Rational Numbers Unit (Student Packet)
RN4 – 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.
4
1
=
16
4
2.
5
10
=
6
12
3.
1
5
=
3
15
T
1.
Write each mixed number as an improper fraction and write each improper fraction as a
mixed number.
15
4
5.
4
1
5
6.
38
6
9.
13
14
________
4
4
AF
4.
5
3
25
________
4
5
8.
17
25
________
2
3
D
7.
R
Use <, >, or = to make each statement true.
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
RN4 – 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.
b.
2
4
2. Use the relationship between
1
8
b.
d.
below.
1
50
c.
3
8
d.
3
50
c.
23
50
D
4. Use the given facts to find the decimal equivalents for the
Fact 1:
8
=1
8
Fact 2:
8 1 7
− =
8 8 8
7
8
fraction
=
5
8
1
1
and
to find the decimal equivalents for fractions
100
50
R
b.
4
4
1
1
and
to find the decimal equivalents for fractions below.
8
4
2
8
3. Use the relationship between
a.
3
4
AF
a.
c.
T
1
4
a.
d.
48
50
7
.
8
Show work here:
________
decimal
Rational Numbers Unit (Student Packet)
RN4 – 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.
2
_________ 0.5
4
10.
-13 _________ -5
11.
-1 _________ -100
12.
T
1.
AF
-7 _________ 7
13. Write these numbers from least to greatest.
-1
1
4
1
1
4
-2
1
8
-1
3
4
-2
1
10
R
__________ < __________ < __________ < __________ < __________
D
14. Estimate the location of each number on the number line.
-
2
3
-
7
3
-1
9
10
-1.1
-0.5
-0.05
15. Write an inequality statement to show the order of the numbers.
_______ < _______ < _______ < _______ < _______ < _______
Rational Numbers Unit (Student Packet)
RN4 – SP30
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
SKILL BUILDER 5
1. Estimate the location of each number on the number line.
2
8
3
1
5
-0.405
-2.25
-
4
3
-0.8
AF
T
2. Explain how you located -0.405 and -0.8.
Use the symbols <, >, or = to compare.
3.
4.
1
1
1
_____ 0.3
_____
9
3
6
6.
1
_____ 0.1666
6
7.
1
9
8.
2
1
_____
18
9
R
0.11_____
9.
5.
10.
1
6
3
9
11.
1
_____ 0.12
9
2
1
_____
3
6
D
0.16 _____
0.333 _____
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)
RN4 – SP31
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
TEST PREPARATION (RN4)
Show your work on a separate sheet of paper and choose the best answer.
1. What is the decimal equivalent for
A.
0.125
B.
3
?
8
C.
0.375
0.38
D.
1
4
D.
1
8
D.

0.625
2. What is the fraction equivalent for 0.125?
B.
1
3
T
1
2
C.
3. Choose the symbol that makes the statement
A.
2
_____ 0.66 true.
3
AF
A.
<
B.
>
C.
=
4. Place the numbers listed below in order from least to greatest.
-
-2
C.
-2
2
3
-
7
3
-2.66
2
7
2
, -2.66 , - , - , -0.06
3
3 3
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
D
A.
2
3
R
-0.06
-2.66 , -
5. Which number does F represent on the number line?
F
G
H
0
A.
7
16
B.
Rational Numbers Unit (Student Packet)
7
8
C.
-
7
8
D.
-
7
16
RN4 – SP32
Rational Number Concepts
4.5 Vocabulary, Skill Builder, and Review
KNOWLEDGE CHECK (RN4)
Show your work on a separate sheet of paper and write your answers on this page.
4.1
Terminating Fractions
1.
What is the decimal equivalent for
8 1 7
− =
8 8 8
What is the fraction equivalent for 0.18?
4.2
Repeating Decimals
3.
Order the following from least to greatest.
AF
2.
T
HINT:
7
?
8
1
3
0.61
2
3
0.33
0.3
0.6
Which is greater,
2
or 0.60? Explain.
3
D
4.
R
________ < ________ < ________ < ________ < ________ < ________
4.3
5.
Ordering Rational Numbers on a Number Line
Estimate the location of each number on the number line.
-0.5
Rational Numbers Unit (Student Packet)
-0.05
-
5
11
-
5
4
1
1
4
-1.30
RN4 – SP33
Rational Number Concepts
Home-School Connection (RN4)
Here are some questions to review with your young mathematician.
1. Find the decimal equivalent for
1
= 0.3 = 0.33 = 0.333 . Is he correct? Explain.
3
3. Which is greater, -2.32 or -2.3? Explain.
T
2. Jorge says that
13
.
25
AF
Parent (or Guardian) signature ____________________________
Selected California Mathematics Content Standards
NS 5.1.2
NS 5.2.1
R
NS 6.1.1
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.
NS 7.1.3
NS7.1.5
D
FIRST PRINTING
Rational Numbers Unit (Student Packet)
DO NOT DUPLICATE © 2010
RN4 – SP34