Compare Absolute Values Quiz/Game
The absolute value of a number, denoted by $|x|$, is its distance from zero on the number line. Distance is always non-negative (zero or positive). Therefore, the result of calculating an absolute value is never negative. Scroll down the page for a more detailed explanation.
 
This game focuses on comparing integers and absolute value expressions. It generates problems like |-5| _ -|5| and asks you to select the correct comparison operator (<, >, =).
 

Absolute Value Arena

Score: 0 Question: 0

Compare the values using
<, >, or =

Start Game

Compare

< = >

Next Problem ➜

 

How to Play the Compare Absolute Values Game

1. Start: Each Quiz consists of 10 questions. Choose your mode: Speed, Distance, Time, or Mixed Problems.
   
2. Look at the Problem: Work out the problem. (Speed, distance, or time)
   
3. Select Your Answer: Select the correct answer.
   
4. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green.
   
5. Get a New Problem: Click “Next Challenge” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
6. Finish Game When you have completed 10 questions, your final score will be displayed.
7. Play Again Click “Play Again” to restart the game.
    
   

Comparing Absolute Values
Comparing absolute value expressions using <, >, or = requires a fundamental understanding of what the absolute value symbol (||) represents.

Defining Absolute Value
The absolute value of a number, denoted by |x|, is its distance from zero on the number line.
Key Rule: Distance is always non-negative (zero or positive). Therefore, the result of calculating an absolute value is never negative.
|x| ≥ 0

Examples:
|5| = 5 (5 is 5 units from zero)
|-5| = 5 (-5 is 5 units from zero)
|0| = 0

Step-by-Step Comparison Process
To compare two expressions involving absolute values, you must first resolve the expressions into simple numerical values.
Step 1: Simplify Each Side Numerically
Always calculate the final numerical value of the expression on the left and the expression on the right.
Crucial Point: Follow the order of operations: The absolute value (distance calculation) is performed before any external operations (like a negative sign outside the bars).
Step 2: Compare the Resulting Numbers
Once both sides are reduced to simple integers, use the standard comparison operators ($<, >, =$) to determine the relationship.

Examples
Here are examples based on the types of problems you provided:
Example 1: Comparing Two Absolute Values
Compare: |-9| __ |9|
Evaluate both sides: 9 __ 9
Answer: |-9| = |9|

Example 2: Comparing an Absolute Value to an Integer
Compare: 16 __ |-16|
Evaluate both sides 16 __ 16
Answer: 16 = |-16|

Example 3: Absolute Value with an External Negative Sign
Compare: -|10| __ |-10|
Evaluate both sides: -10 __ 10
Answer: -|10| < |-10|

Example 4: Comparing Two Negative Absolute Values
Compare: |-4| __ |-5|
Evaluate both sides: 4 __ 5
Answer: |-4| < |-5| (because 4 is less than 5)

This video gives a clear, step-by-step approach to learn how to compare absolute values.

• Show Video

 

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