Compare Absolute Values: Are |-3| and |3| Opposite Numbers?

Q: What exactly does absolute value mean?

Absolute value measures the distance from zero on a number line, always giving a positive result. Think of it as removing the negative sign if there is one.

Q: When are two numbers considered opposites?

Two numbers are opposites when they are the same distance from zero but in opposite directions. For example, 5 and -5 are opposites, but 3 and 3 are identical!

Q: Why do both |-3| and |3| equal 3?

Absolute value always gives the positive distance from zero. Since -3 is 3 units from zero and 3 is also 3 units from zero, both absolute values equal 3.

Q: How do I remember this concept?

Remember: Absolute value = distance from zero. Distance is always positive! So $ |-3| $ and $ |3| $ both measure 3 units, making them equal, not opposite.

Absolute Value Properties with Opposite Number Identification

Are the numbers opposite?

$\left|-3\right|,\left|3\right|$

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Understand the problem

Are the numbers opposite?

$\left|-3\right|,\left|3\right|$

Step-by-step solution

To determine if the numbers are opposites, consider the following:

Step 1: Calculate the absolute values:
- $\left|-3\right| = 3$
- $\left|3\right| = 3$
Step 2: Evaluate whether these numbers are opposites.

For two numbers to be opposites in a mathematical context, they must be equidistant from zero on the number line but in opposite directions. Since both calculations give us $3$ and $3$ , they are the same numbers, not opposites.

Therefore, the answer to the question is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Absolute Value Rule: Both positive and negative numbers have positive absolute values
Technique: Calculate $|-3| = 3$ and $|3| = 3$ , then compare results
Check: Opposite numbers must be equidistant from zero in different directions ✓

Common Mistakes

Avoid these frequent errors

Confusing absolute values with the original numbers
Don't think |-3| and |3| are opposites because -3 and 3 are opposites = wrong comparison! You're comparing the absolute values (both equal 3), not the original numbers. Always evaluate the absolute values first, then determine if those results are opposites.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

$\left|18\right|=$

FAQ

Everything you need to know about this question

What exactly does absolute value mean?

Absolute value measures the distance from zero on a number line, always giving a positive result. Think of it as removing the negative sign if there is one.

When are two numbers considered opposites?

Two numbers are opposites when they are the same distance from zero but in opposite directions. For example, 5 and -5 are opposites, but 3 and 3 are identical!

Why do both |-3| and |3| equal 3?

Absolute value always gives the positive distance from zero. Since -3 is 3 units from zero and 3 is also 3 units from zero, both absolute values equal 3.

Can absolute values ever be opposites?

Only if one of the absolute values equals zero! Since absolute values are always positive or zero, the only way two absolute values can be opposites is if they are 0 and 0 (which are the same).

How do I remember this concept?

Remember: Absolute value = distance from zero. Distance is always positive! So $|-3|$ and $|3|$ both measure 3 units, making them equal, not opposite.

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