Comparing Absolute Values: Are -|-56| and |+56| Opposite Numbers?

Q: What's the difference between |-56| and -|-56|?

$ |-56| = 56 $ (positive), but $ -|-56| = -56 $ (negative). The negative sign outside the absolute value bars changes the final result to negative!

Q: How do I know if two numbers are opposites?

Two numbers are opposites if they add up to zero. For example, -56 + 56 = 0, so they are opposites. They're also the same distance from zero but on opposite sides of the number line.

Q: Does |+56| equal |56|?

Yes! The plus sign inside absolute value bars doesn't change anything. $ |+56| = |56| = 56 $. Absolute value always gives the positive distance from zero.

Q: Why is the absolute value always positive?

Absolute value represents distance, and distance is never negative! Whether you go 56 steps left or right from zero, you've still traveled 56 units.

Absolute Value Operations with Negative Signs

Are the numbers opposite?

$-\left|-56\right|,\left|+56\right|$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Are the numbers opposite?

$-\left|-56\right|,\left|+56\right|$

Step-by-step solution

The opposite of a number is what you add to a number to get zero. The opposite of a positive number is a negative number. And the opposite of a negative number is a positive number.

For instance, the opposite of the number $56$ is $-56$ .

In this question, we are dealing with $-\left|-56\right|$ and $\left|+56\right|$ .

The absolute value of a number is the distance from zero, which is always positive. Hence, $\left|+56\right| = 56$ and $\left|-56\right| = 56$ .

Therefore, $-\left|-56\right| = -56$ and $+\left|56\right| = 56$ .

Thus, $-56$ and $56$ are opposites, and the answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value always gives positive distance from zero
Technique: Evaluate inside first: $|-56| = 56$ , then apply negative sign
Check: Opposite numbers sum to zero: -56 + 56 = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing absolute value with negative signs
Don't think $-|-56|$ equals +56! The negative sign is outside the absolute value bars. Always evaluate the absolute value first to get 56, then apply the negative sign to get -56.

Practice Quiz

Test your knowledge with interactive questions

$\left|-19\frac{1}{4}\right|=$

FAQ

Everything you need to know about this question

What's the difference between |-56| and -|-56|?

$|-56| = 56$ (positive), but $-|-56| = -56$ (negative). The negative sign outside the absolute value bars changes the final result to negative!

How do I know if two numbers are opposites?

Two numbers are opposites if they add up to zero. For example, -56 + 56 = 0, so they are opposites. They're also the same distance from zero but on opposite sides of the number line.

Does |+56| equal |56|?

Yes! The plus sign inside absolute value bars doesn't change anything. $|+56| = |56| = 56$ . Absolute value always gives the positive distance from zero.

Why is the absolute value always positive?

Absolute value represents distance, and distance is never negative! Whether you go 56 steps left or right from zero, you've still traveled 56 units.

Can zero have an opposite number?

Yes! The opposite of zero is zero itself, because 0 + 0 = 0. Zero is special because it's the only number that equals its own opposite.

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