Comparing Absolute Values: Are |-7| and |7| Opposite Numbers?

Absolute Value with Opposite Numbers

Are the numbers opposite?

7,7 \left|-7\right|,\left|7\right|

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Step-by-step written solution

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1

Understand the problem

Are the numbers opposite?

7,7 \left|-7\right|,\left|7\right|

2

Step-by-step solution

The opposite of a number is the number with the same magnitude but different sign. The absolute value of a number is always positive or zero. Let's examine the given numbers:

7 \left|-7\right| represents the absolute value of -7, which is 7.

7 \left|7\right| represents the absolute value of 7, which is also 7.

Since both absolute values are equal and positive, they represent the same number, not opposites. Therefore, they are not opposite numbers.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Absolute value always produces positive or zero results
  • Technique: Calculate each: |-7| = 7 and |7| = 7
  • Check: Since both equal 7, they are identical numbers, not opposites ✓

Common Mistakes

Avoid these frequent errors
  • Thinking absolute value preserves signs
    Don't assume |-7| stays negative = wrong comparison! Absolute value strips away the negative sign, always giving positive results. Always remember that |negative| = positive.

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?

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

How do I know if two numbers are opposites?

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Two numbers are opposites if they have the same distance from zero but different signs. For example: 7 and -7 are opposites, but 7 and 7 are identical.

Can absolute values ever be negative?

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Never! Absolute values are always positive or zero. Even 1000=1000 |-1000| = 1000 , which is positive.

Why aren't |-7| and |7| opposites?

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Because both equal positive 7! Since 7=7 |-7| = 7 and 7=7 |7| = 7 , they're the same number, not opposites.

What would be the opposite of |7|?

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The opposite of 7=7 |7| = 7 would be -7. Remember: opposites have the same magnitude but different signs.

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