Calculate the Absolute Value: Finding |-4¾|

Q: Why does absolute value always give a positive answer?

Absolute value measures distance from zero on the number line. Since distance is never negative, absolute value is always positive or zero. Think of it as asking "how far?" not "which direction?"

Q: Can absolute value equal zero?

Yes! $ |0| = 0 $ because zero is exactly zero units away from itself on the number line. This is the only case where absolute value equals zero.

Absolute Value with Mixed Numbers

$\left|-4\frac{3}{4}\right|=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|-4\frac{3}{4}\right|=$

Step-by-step solution

The absolute value of a number is the positive form of that number, representing its distance from zero on the number line.

Step 1: Identify the number whose absolute value is needed: $-4\frac{3}{4}$

Step 2: Remove the negative sign from the number: $4\frac{3}{4}$

Thus, the absolute value of $-4\frac{3}{4}$ is $4\frac{3}{4}$ .

Final Answer

$4\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value represents the distance from zero on the number line
Technique: Remove the negative sign: $|-4\frac{3}{4}| = 4\frac{3}{4}$
Check: Verify that $4\frac{3}{4}$ is positive and equals the distance from zero ✓

Common Mistakes

Avoid these frequent errors

Keeping the negative sign inside absolute value bars
Don't think that $|-4\frac{3}{4}| = -4\frac{3}{4}$ ! Absolute value always produces a non-negative result because it measures distance, which cannot be negative. Always remove the negative sign and make the number 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

Why does absolute value always give a positive answer?

Absolute value measures distance from zero on the number line. Since distance is never negative, absolute value is always positive or zero. Think of it as asking "how far?" not "which direction?"

What happens if the number is already positive?

If the number inside the absolute value bars is already positive, it stays the same! For example, $|3\frac{1}{2}| = 3\frac{1}{2}$ . Absolute value only changes negative numbers.

Can absolute value equal zero?

Yes! $|0| = 0$ because zero is exactly zero units away from itself on the number line. This is the only case where absolute value equals zero.

How do I work with mixed numbers in absolute value?

Treat the mixed number as one complete value. The negative sign applies to the entire mixed number, not just the whole number part. So $|-4\frac{3}{4}|$ means the absolute value of negative four and three-fourths.

Is there a shortcut for finding absolute value?

Yes! Simply ask: "Is this number positive or negative?" If it's negative, remove the negative sign. If it's positive or zero, keep it the same. That's it!

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