Comparing Absolute Values: Are |-5| and |5| Opposite Numbers?

Absolute Values with Opposite Number Identification

Are these numbers opposite?

∣−5∣,∣5∣ \left|-5\right|,\left|5\right|

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Are these numbers opposite?

∣−5∣,∣5∣ \left|-5\right|,\left|5\right|

2

Step-by-step solution

The opposite of a number is defined as the number with the same absolute value but different signs.

We have:

∣−5∣=5 \left|-5\right| = 5 and ∣5∣=5 \left|5\right| = 5 .

Both these absolute values are equal and positive, meaning they are the same number, not opposites. Therefore, the numbers are not opposite.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Absolute value always produces non-negative results regardless of input
  • Technique: Calculate ∣−5∣=5 |-5| = 5 and ∣5∣=5 |5| = 5 separately
  • Check: Compare results: both equal 5, so they're identical, not opposite ✓

Common Mistakes

Avoid these frequent errors
  • Confusing absolute values with their original numbers
    Don't think |-5| and |5| are opposites because -5 and 5 are opposites = wrong logic! Absolute value removes the sign, making both results positive 5. Always evaluate the absolute value first, then compare the results.

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 does absolute value actually do to a number?

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Absolute value gives you the distance from zero on a number line. It's always positive or zero, never negative. So ∣−5∣=5 |-5| = 5 and ∣5∣=5 |5| = 5 .

How can I remember what opposite numbers look like?

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Opposite numbers have the same absolute value but different signs. Examples: 3 and -3, or 7 and -7. They're equal distances from zero but on opposite sides!

Why aren't 5 and 5 considered opposites?

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Because they're exactly the same number! Opposites must have different signs. Since both ∣−5∣ |-5| and ∣5∣ |5| equal positive 5, they're identical.

What would be the opposite of |5|?

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Since ∣5∣=5 |5| = 5 , its opposite would be -5. Remember: find the absolute value first, then determine what number has the opposite sign!

Can absolute values ever be negative?

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Never! Absolute values represent distance, which is always positive or zero. If you get a negative result, you've made an error in your calculation.

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