Calculate the Absolute Value: Evaluating |-7½|

Q: What exactly does absolute value mean?

Absolute value measures how far a number is from zero on the number line. It's always positive because distance is always positive!

Q: Can absolute value ever be negative?

Never! Absolute value represents distance, and distance is always zero or positive. Even $ |-1000| = 1000 $.

Q: How do I work with mixed numbers in absolute value?

Treat the mixed number as one unit. $ -7\frac{1}{2} $ is a single negative number, so $ |-7\frac{1}{2}| = 7\frac{1}{2} $.

Absolute Value with Mixed Numbers

$\left|-7\frac{1}{2}\right|=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|-7\frac{1}{2}\right|=$

Step-by-step solution

The absolute value of a number is always its positive value. It represents the distance of the number from zero on the number line, regardless of direction. The absolute value of any negative number is its opposite positive number.

Step 1: Identify the number to find the absolute value of: $-7\frac{1}{2}$

Step 2: Change the negative sign to positive: $7\frac{1}{2}$

Hence, the absolute value of $-7\frac{1}{2}$ is $7\frac{1}{2}$ .

Final Answer

$7\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value is always the positive distance from zero
Technique: Remove negative sign: $|-7\frac{1}{2}| = 7\frac{1}{2}$
Check: Result is positive and equals original number's distance from zero ✓

Common Mistakes

Avoid these frequent errors

Thinking absolute value doesn't apply to negative numbers
Don't say 'there is no absolute value' for negative numbers = missing the whole concept! Every real number has an absolute value. Always convert negative numbers to their positive equivalent inside absolute value bars.

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?

Absolute value measures how far a number is from zero on the number line. It's always positive because distance is always positive!

Why does a negative number become positive in absolute value?

Think of it as distance! If you walk 7½ steps to the left of zero, you're still 7½ steps away from zero. The direction doesn't matter for distance.

Can absolute value ever be negative?

Never! Absolute value represents distance, and distance is always zero or positive. Even $|-1000| = 1000$ .

How do I work with mixed numbers in absolute value?

Treat the mixed number as one unit. $-7\frac{1}{2}$ is a single negative number, so $|-7\frac{1}{2}| = 7\frac{1}{2}$ .

What if the number inside is already positive?

If it's already positive, absolute value doesn't change it! For example, $|5\frac{1}{3}| = 5\frac{1}{3}$ .

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