Evaluate the Absolute Value: |-19¼| Step-by-Step

Q: Why does the absolute value of a negative number become positive?

Absolute value represents distance from zero on the number line. Since distance is always positive, $ \left|-19\frac{1}{4}\right| $ becomes $ 19\frac{1}{4} $.

Q: Can absolute value ever be negative?

Never! Absolute value always gives a non-negative result. The smallest possible absolute value is 0, which happens when $ |0| = 0 $.

Q: How do I handle mixed numbers in absolute value?

Treat the entire mixed number as one unit. Whether it's $ \left|-19\frac{1}{4}\right| $ or $ \left|19\frac{1}{4}\right| $, both equal $ 19\frac{1}{4} $.

Q: What's the easiest way to remember absolute value rules?

Think of absolute value as "making everything positive". The bars $ | | $ act like a positive filter - negative goes in, positive comes out!

Absolute Value with Mixed Numbers

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

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Understand the problem

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

Step-by-step solution

These signs in the exercises refer to the concept of "absolute value",

In absolute value we don't have "negative" or "positive", instead we measure the distance from point 0,

In other words, we always "cancel out" the negative signs.

In this exercise, we'll change the minus to a plus sign, and simply remain with 19 and a quarter.

And that's the solution!

Final Answer

$19\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value measures distance from zero on number line
Technique: Remove negative sign: $\left|-19\frac{1}{4}\right| = 19\frac{1}{4}$
Check: Result must always be positive or zero: $19\frac{1}{4} > 0$ ✓

Common Mistakes

Avoid these frequent errors

Thinking absolute value doesn't exist for negative numbers
Don't say "there is no absolute value" for negative numbers = completely wrong answer! Every real number has an absolute value. Always remember that absolute value makes negative numbers positive and keeps positive numbers unchanged.

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 the absolute value of a negative number become positive?

Absolute value represents distance from zero on the number line. Since distance is always positive, $\left|-19\frac{1}{4}\right|$ becomes $19\frac{1}{4}$ .

What happens to the absolute value of a positive number?

The absolute value of a positive number stays the same! For example, $\left|5\frac{1}{2}\right| = 5\frac{1}{2}$ because it's already positive.

Can absolute value ever be negative?

Never! Absolute value always gives a non-negative result. The smallest possible absolute value is 0, which happens when $|0| = 0$ .

How do I handle mixed numbers in absolute value?

Treat the entire mixed number as one unit. Whether it's $\left|-19\frac{1}{4}\right|$ or $\left|19\frac{1}{4}\right|$ , both equal $19\frac{1}{4}$ .

What's the easiest way to remember absolute value rules?

Think of absolute value as "making everything positive". The bars $| |$ act like a positive filter - negative goes in, positive comes out!

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