Absolute Value Mastery

Step-by-Step Review: Distance and Order

NAME:

DATE:

The Absolute Value Rule

Absolute value \( |x| \) represents the distance of a number from zero on the number line. Because distance is never negative, absolute value is always positive or zero.

We Do

#1: Understanding Distance

What is the absolute value of \(-12.9\)? Explain what this value tells you about its position relative to zero.

Step 1: Identify

What is the number inside the bars?

Step 2: Distance

How far is this number from 0?

Step 3: Solve

Write final \( |-12.9| = \)

Explanation:

We Do

#2: Calculation Mastery

Calculate each absolute value. Key Rule: Distance is always positive!

A

\( |18| \)

B

\( |-2.1| \)

C

\( |-\frac{5}{8}| \)

D

\( |0| \)

3

Plot and label the following on the number line: Point A at \(-5\) and Point B at \( |-5| \).

-8

-6

-4

-2

0

2

4

6

8

4

Compare using \( < \), \( > \), or \( = \):

\( |-10| \)

\( 7 \)

\( -4.5 \)

\( |-3| \)

\( |9.2| \)

\( |-9.2| \)

\( -8 \)

\( |-1| \)

5

Which temperature is closer to the freezing point (\(0^\circ\text{C}\)): \(-7^\circ\text{C}\) or \(3^\circ\text{C}\)? Use absolute value to justify your answer.

6

The elevation of a city is \(10\) feet from sea level. Name the two possible elevations that the city could have.

Elevation 1:

Elevation 2:

7

Write a number that has an absolute value greater than \( |-2.6| \) but is itself a negative number.

MY NUMBER:

8

If \( |x| = 15 \), what are the possible values for \(x\)?

\( x = \)

OR

9

Pre-Check: Fractional Decimals

Convert each rational number to a decimal to make comparing easier.

Fraction	Decimal Equivalent
\( \frac{16}{5} \)
\( \frac{1}{4} \)
\( -\frac{3}{4} \)
\( -\frac{3}{8} \)

10

The Ultimate Challenge

Place these numbers in order from least to greatest. Use your work from Question 9 to help!

\( \frac{16}{5} \) \( -3 \) \( 6 \) \( 3.1 \) \( -2.5 \) \( \frac{1}{4} \) \( -\frac{3}{4} \) \( -\frac{3}{8} \)

Final Order (Least to Greatest)

____ < ____ < ____ < ____ < ____ < ____ < ____ < ____

Absolute Value Mastery

Absolute Value Review Packet Student

Absolute Value Review Packet Key

Absolute Value Mastery Student Packet

Absolute Value Review Key Final

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