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Amy Ferguson Moncure

7th Grade Math · Unit 2

Absolute Value

Find absolute values, compare them, and use them for distance.

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Key Ideas Easy Medium Hard
What to Remember

Distance from 0

The absolute value of a number is its distance from 0.

|−8| = 8 and |5| = 5.

The sign drops out

|−4| and |4| are equal.

Both numbers are 4 units from 0.

Order the distances

Replace each absolute value with its distance, then order those distances.

Equal distances stay equal.

Distance between two numbers

The distance between a and b is |a − b|.

|−3 − 5| = |−8| = 8.

Level 1

Easy

Find one absolute value, or compare two.

Example
Simplify. |−6|

Absolute value is the distance from 0.

|−6| = 6

Answer: 6

1
Simplify. |−12|
Show Answer

Absolute value is the distance from 0.

|−12| = 12

Answer: 12

2
Simplify. |0|
Show Answer

The distance from 0 to 0 is 0.

|0| = 0

Answer: 0

3
Simplify. |7|
Show Answer

7 is 7 units from 0.

|7| = 7

Answer: 7

4
Simplify. |−1|
Show Answer

Absolute value is the distance from 0.

|−1| = 1

Answer: 1

5
Compare. Write <, >, or =.
|−9|    ?    |6|
Show Answer

Absolute value is the distance from 0.

|−9| = 9

|6| = 6

|−9| > |6|

Answer: |−9| > |6|

6
Compare. Write <, >, or =.
|−4|    ?    |4|
Show Answer

Absolute value is the distance from 0.

|−4| = 4

|4| = 4

|−4| = |4|

Answer: |−4| = |4|

7
Compare. Write <, >, or =.
|−2|    ?    |5|
Show Answer

Absolute value is the distance from 0.

|−2| = 2

|5| = 5

|−2| < |5|

Answer: |−2| < |5|

8
Compare. Write <, >, or =.
|0|    ?    |−3|
Show Answer

Absolute value is the distance from 0.

|0| = 0

|−3| = 3

|0| < |−3|

Answer: |0| < |−3|

9
Compare. Write <, >, or =.
|−15|    ?    |8|
Show Answer

Absolute value is the distance from 0.

|−15| = 15

|8| = 8

|−15| > |8|

Answer: |−15| > |8|

10
Is |−20| greater than 20?
Show Answer

|−20| = 20

20 and 20 are equal, so the absolute value is not greater.

Answer: No. |−20| = 20

Level 2

Medium

Order four absolute values from least to greatest.

Example
Order the absolute values from least to greatest.
|−3|, |1|, |−1|, |4|

Absolute value is the distance from 0. Order those distances.

|−3| = 3

|1| = 1

|−1| = 1

|4| = 4

Least to greatest:

|−1| = |1| < |−3| < |4|

Answer: |−1| = |1| < |−3| < |4|

1
Order the absolute values from least to greatest.
|−5|, |2|, |−2|, |0|
Show Answer

Absolute value is the distance from 0. Order those distances.

|−5| = 5

|2| = 2

|−2| = 2

|0| = 0

Least to greatest:

|0| < |−2| = |2| < |−5|

Answer: |0| < |−2| = |2| < |−5|

2
Order the absolute values from least to greatest.
|−8|, |3|, |−1|, |8|
Show Answer

Absolute value is the distance from 0. Order those distances.

|−8| = 8

|3| = 3

|−1| = 1

|8| = 8

Least to greatest:

|−1| < |3| < |−8| = |8|

Answer: |−1| < |3| < |−8| = |8|

3
Order the absolute values from least to greatest.
|−4|, |−9|, |6|, |1|
Show Answer

Absolute value is the distance from 0. Order those distances.

|−4| = 4

|−9| = 9

|6| = 6

|1| = 1

Least to greatest:

|1| < |−4| < |6| < |−9|

Answer: |1| < |−4| < |6| < |−9|

4
Order the absolute values from least to greatest.
|7|, |−7|, |0|, |−3|
Show Answer

Absolute value is the distance from 0. Order those distances.

|7| = 7

|−7| = 7

|0| = 0

|−3| = 3

Least to greatest:

|0| < |−3| < |−7| = |7|

Answer: |0| < |−3| < |−7| = |7|

5
Order the absolute values from least to greatest.
|−12|, |10|, |−10|, |4|
Show Answer

Absolute value is the distance from 0. Order those distances.

|−12| = 12

|10| = 10

|−10| = 10

|4| = 4

Least to greatest:

|4| < |−10| = |10| < |−12|

Answer: |4| < |−10| = |10| < |−12|

6
Order the absolute values from least to greatest.
|−6|, |6|, |−2|, |9|
Show Answer

Absolute value is the distance from 0. Order those distances.

|−6| = 6

|6| = 6

|−2| = 2

|9| = 9

Least to greatest:

|−2| < |−6| = |6| < |9|

Answer: |−2| < |−6| = |6| < |9|

7
Order the absolute values from least to greatest.
|1|, |−1|, |−8|, |5|
Show Answer

Absolute value is the distance from 0. Order those distances.

|1| = 1

|−1| = 1

|−8| = 8

|5| = 5

Least to greatest:

|−1| = |1| < |5| < |−8|

Answer: |−1| = |1| < |5| < |−8|

8
Order the absolute values from least to greatest.
|−11|, |2|, |−3|, |11|
Show Answer

Absolute value is the distance from 0. Order those distances.

|−11| = 11

|2| = 2

|−3| = 3

|11| = 11

Least to greatest:

|2| < |−3| < |−11| = |11|

Answer: |2| < |−3| < |−11| = |11|

9
Order the absolute values from least to greatest.
|0|, |−4|, |4|, |−1|
Show Answer

Absolute value is the distance from 0. Order those distances.

|0| = 0

|−4| = 4

|4| = 4

|−1| = 1

Least to greatest:

|0| < |−1| < |−4| = |4|

Answer: |0| < |−1| < |−4| = |4|

10
Order the absolute values from least to greatest.
|15|, |−9|, |−15|, |3|
Show Answer

Absolute value is the distance from 0. Order those distances.

|15| = 15

|−9| = 9

|−15| = 15

|3| = 3

Least to greatest:

|3| < |−9| < |−15| = |15|

Answer: |3| < |−9| < |−15| = |15|

Level 3

Hard

The distance between two numbers, including a short situation.

Example
Find the distance between −1 and 6.

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−1 − 6|

= |−7|

= 7

Answer: 7

1
Find the distance between −3 and 5.
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−3 − 5|

= |−8|

= 8

Answer: 8

2
Find the distance between 2 and −6.
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |2 − (−6)|

= |8|

= 8

Answer: 8

3
Find the distance between −7 and −2.
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−7 − (−2)|

= |−5|

= 5

Answer: 5

4
Find the distance between 0 and −9.
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |0 − (−9)|

= |9|

= 9

Answer: 9

5
Find the distance between −4 and 4.
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−4 − 4|

= |−8|

= 8

Answer: 8

6
A whale is at −18 meters and a seal is at −5 meters. How far apart are they?
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−18 − (−5)|

= |−13|

= 13

The distance is 13 meters.

Answer: 13 meters

7
Town A is at mile −6 and town B is at mile 11 on the same road. What is the distance between them?
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−6 − 11|

= |−17|

= 17

The distance is 17 miles.

Answer: 17 miles

8
The temperature changes from −2°F to 8°F. How many degrees apart are those temperatures?
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−2 − 8|

= |−10|

= 10

The distance is 10 degrees.

Answer: 10 degrees

9
A bird is at 4 meters and a fish is at −7 meters. What is the distance between them?
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |4 − (−7)|

= |11|

= 11

The distance is 11 meters.

Answer: 11 meters

10
Find the distance between −20 and −8.
Show Answer

The distance between two numbers is the absolute value of their difference.

Distance = |a − b|

= |−20 − (−8)|

= |−12|

= 12

Answer: 12

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