Solve |9/3 - 4|: Absolute Value with Fractions

Q: Why can't I just make everything positive at the start?

The absolute value bars work like parentheses - you must complete everything inside them first. Taking absolute value of individual parts changes the meaning of the expression completely!

Q: What if I get a negative number inside the absolute value bars?

That's perfectly normal! The whole point of absolute value is to handle negative results. $ |{-1}| = 1 $ and $ |1| = 1 $ - both give positive answers.

Q: How do I remember the order of operations with absolute value?

Think of absolute value bars as super parentheses. Just like you solve (3-4) first, you solve everything inside |3-4| before taking the absolute value.

Q: Can the final answer ever be negative?

Never! Absolute value always gives a non-negative result. If you get a negative final answer, you made an error somewhere in your calculations.

Q: What's the difference between |-1| and -|1|?

$ |-1| = 1 $ (absolute value of negative one), but $ -|1| = -1 $ (negative of absolute value of one). The placement of the negative sign matters!

Absolute Value with Order of Operations

$\left|\frac{9}{3} - 4\right| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|\frac{9}{3} - 4\right| =$

Step-by-step solution

First, perform the division: $\frac{9}{3} = 3$ .

Then, subtract $4$ from $3$ :
$3 - 4 = -1$ .

The absolute value of $-1$ is $1$ , so the expression evaluates to $1$ . However, the absolute value takes the non-negative result, so we need to express: $|3 - 4| = 1$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Always simplify inside absolute value bars first
Technique: $\frac{9}{3} = 3$ , then $3 - 4 = -1$ , then $|-1| = 1$
Check: Final answer must be non-negative since absolute value means distance from zero ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value too early
Don't take absolute value of individual terms like |9/3| - |4| = 3 - 4 = -1! This ignores the correct order of operations. Always complete all operations inside the bars first: 9/3 - 4 = -1, then |-1| = 1.

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 can't I just make everything positive at the start?

The absolute value bars work like parentheses - you must complete everything inside them first. Taking absolute value of individual parts changes the meaning of the expression completely!

What if I get a negative number inside the absolute value bars?

That's perfectly normal! The whole point of absolute value is to handle negative results. $|{-1}| = 1$ and $|1| = 1$ - both give positive answers.

How do I remember the order of operations with absolute value?

Think of absolute value bars as super parentheses. Just like you solve (3-4) first, you solve everything inside |3-4| before taking the absolute value.

Can the final answer ever be negative?

Never! Absolute value always gives a non-negative result. If you get a negative final answer, you made an error somewhere in your calculations.

What's the difference between |-1| and -|1|?

$|-1| = 1$ (absolute value of negative one), but $-|1| = -1$ (negative of absolute value of one). The placement of the negative sign matters!

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