Download Absolute Value

Lesson
14
6.NS.7.c, 6.NS.7.d
Absolute Value
1 Getting the idea
The absolute value of a number is its distance from 0 on a number line.
3 units
5
4
3
2
1
3 units
0
1
2
3
4
5
The integers 23 and 3 are each 3 units from 0 on the number line. Numbers and their opposites have
the same absolute value. Absolute value is written using the symbols | |.
|3| 5 3
The absolute value of 3 is 3.
|23| 5 3
The absolute value of 23 is also 3.
The absolute values of 3 and 23 are equal because they are the same distance from 0 on the number
line.
Because distance is never negative, the absolute value of a number is never negative. The absolute
value of 0 is 0.
Example 1
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Duplicating any part of this book is prohibited by law. © 2015 Triumph Learning, LLC
Find |24|.
Strategy
Step 1 Graph the number and find its distance from 0 on a number line.
Graph the number on the number line.
Start at 0. Move 4 units left of 0 to graph a point at 24.
5
Step 2 4
3
2
1
0
1
2
3
4
5
4
5
Find the distance from the number to 0.
The distance from 24 to 0 on the number line is 4 units.
4 units
5
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4
3
2
1
0
1
2
3
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Step 3 Write the absolute value.
|24| 5 4 The absolute value of 24 is 4.
Solution
|24| 5 4
Example 2
Kari has an online account to buy music that she can download to her tablet. After Kari purchases some
music, her account balance is 2$18. Use absolute value to express her account balance as a debt.
Strategy
Step 1 Use absolute value.
Understand the situation.
An account with a negative balance represents a debt, or money owed. The
amount of a debt is equal to the absolute value of a negative account balance.
An account with a balance of $0 represents no debt.
An account with a positive balance represents a credit.
Step 2 Use a number line to find the absolute value of the account balance.
Graph 218 on the number line.
18 units
25
20
15
10
5
0
5
10
15
20
25
The point for 218 is 18 units from 0 on the number line.
|2$18| 5 $18
Express the account balance as a debt.
Since debt is equal to the absolute value of a negative account balance, the debt is
$18. This means Kari needs to pay $18 to eliminate her debt.
Solution
Kari’s account balance represents a debt of $18.
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Step 3 128 Domain 2: The Number System
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Example 3
The temperature at 7:00 a.m. was 25°F. The temperature at 4:00 p.m. was 8°F. Use absolute value to
express each temperature as the number of degrees above or below zero.
Strategy
Step 1 Use absolute value to describe temperature.
Understand the situation.
A positive number represents a temperature above zero. A negative number
represents a temperature below zero. The number of degrees above or below
zero represents a quantity, so you need to use absolute value.
Step 2 Use a number line to find the absolute value of each temperature.
Graph 25 and 8 on a vertical number line.
The distance from 25 to 0 is 5 units.
|25°F| 5 5°F
The distance from 8 to 0 is 8 units.
|8°F| 5 8°F
10
8
6
4
8 units
2
0
2
5 units
4
6
8
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Duplicating any part of this book is prohibited by law. © 2015 Triumph Learning, LLC
10
Step 3 Express each temperature as the number of degrees above or below zero.
Express positive temperatures as “degrees above zero.” Express negative
temperatures as “degrees below zero.”
The temperature 25°F represents a temperature of 5 degrees below zero.
The temperature 8°F represents a temperature of 8 degrees above zero.
Solution
At 7:00 a.m. the temperature was 5°F below zero, and at 4:00 p.m. it was 8°F
above zero.
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Example 4
Malena has a store account to make purchases. Her account balance was 2$1,023.15. After making a
new purchase, her balance is now 2$1,256.80. Compare Malena’s account balance before and after
the purchase. Then compare her debt before and after the purchase.
Strategy
Compare the two numbers. Then compare the absolute values of the numbers.
Step 1 Compare the account balance after the purchase to the account balance before the
purchase.
Compare 2$1,256.80 and 2$1,023.15.
2$1,256.80 , 2$1,023.15
After making a purchase, Malena’s account balance is less than the account
balance before the purchase.
Step 2 Find the debt before and after the purchase.
Remember that debt is the absolute value of a negative account balance.
Debt before purchase:
|2$1,023.15| 5 $1,023.15
Debt after purchase:
|2$1,256.80| 5 $1,256.80
Step 3 Compare the debt after the purchase to the debt before the purchase.
$1,256.80 . $1,023.15
Solution
After making a purchase, Malena’s account balance is less than the account
balance before the purchase and her debt is greater than her debt before the purchase.
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After making a purchase, Malena’s debt is greater than her debt before
the purchase.
130 Domain 2: The Number System
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2 COACHED EXAMPLE
A diver photographed several animals during an underwater dive. The table below shows the
elevations below sea level of the diver when the photographs were taken. Use absolute value to
order the animals from least depth to greatest depth.
Animal
Elevation (in feet)
Dolphin
224
Shrimp
230
Angelfish
215
Understand the situation.
Elevation describes a position in relation to sea level, so it can be positive or negative.
Depth describes the distance below sea level, so it cannot be
To find the depth of each animal, find the
.
of each elevation.
Find the depth of each animal.
feet
Depth of dolphin: |224| 5
Depth of shrimp: |230| 5
feet
feet
Depth of angelfish: |215| 5
Order the depths from least to greatest.
feet,
feet,
feet
Order the animals from shallowest to deepest.
,
,
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Duplicating any part of this book is prohibited by law. © 2015 Triumph Learning, LLC
The order of the animals from the least depth to the greatest depth is
,
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,
.
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3 LESSON PRACTICE
1
Graph and label the following numbers on the number line.
• 22​ __21 ​ and |2​ __21 ​| 
• 23.8 and |23.8|
5
2
4
3
2
1
0
2
3
4
5
Circle the numbers that make the statements true.
23
3
1
29
|25| , 24 |210| . |213|
27
|215|
Use the words from the box to complete each statement.
As the value of a positive number increases, the absolute value of the
.
number
As the value of a positive number decreases, the absolute value of the .
As the value of a negative number increases, the absolute value of the
number
.
As the value of a negative number decreases, the absolute value of the
number
4
.
Determine which of the following statements are true. Circle all that apply.
A. 27 , 7
B. |27| , |7|
C. |27| . 7
D. 27 , |7|
E. 27 5 |7|
F. |27| 5 7
G. |27| 5 |7|
increases
decreases
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number
132 Domain 2: The Number System
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5
Paul’s account balance is less than 2$50.
Part A
What is a possible balance for Paul’s account? Explain your answer.
Part B
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Duplicating any part of this book is prohibited by law. © 2015 Triumph Learning, LLC
Does Paul’s account balance represent a debt greater than or less than $50? Use the possible
balance from Part A to justify your answer.
6
Order the absolute values of 32, 2173, and 2139 from least to greatest. Use words, numbers,
or models to justify your answer.
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7
For each number in the table, find an equivalent value from the numbers in the box. There may
be zero, one, or two equivalent values for each number.
214
Number
Equivalent Expressions
Expression 1
|14|
Expression 2
|214|
|15|
|215|
15
16
|16|
|216|
217
|17|
|217|
8
Look at each set of numbers. Are the numbers in order from least to greatest? Select Yes or No.
A. |29|, 24, 2
○ Yes ○ No
B. 211, |28|, 15
○ Yes ○ No
C. |23|, |210|, |14| ○ Yes ○ No
9
○ Yes ○ No
The balance in Pedro’s account is 2$24.50. The balance in John’s account is 2$33.75.
Select True or False for each statement.
A. The balance in Pedro’s account is greater than ○ True ○ False
the balance in John’s account.
B. Pedro’s debt is greater than John’s debt.
○ True ○ False
C. John owes more than Pedro.
○ True ○ False
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D. |21|, |26|, |5|
134 Domain 2: The Number System
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10
Use the number line shown below.
A
10
B
8
6
4
C
2
0
2
D
4
6
8
10
Which point represents the number with the greatest absolute value? point
Which point represents the number with the least absolute value? point
11
The table below shows the elevations at which several items were found at an archaeological
dig site.
Object
Bracelet
Coins
Clay pot
Elevation (in meters)
22.3
22.9
21.8
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Duplicating any part of this book is prohibited by law. © 2015 Triumph Learning, LLC
Explain how to find the depth of the objects in the table. Then find the depth of each object.
12
Elise says that if a number has a greater value than another number, then the number also has a
greater absolute value. Is she correct? If not, provide a counterexample.
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