Evaluate $3|-3|$.A. 6 B. -9 C. 9 D. -6

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Understanding Absolute Value

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is denoted by two vertical lines on either side of the number, such as |x|. The absolute value of a number is always non-negative, regardless of whether the number itself is positive or negative.

Evaluating the Expression

To evaluate the expression $3|-3|$, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the absolute value signs: |-3|.
  2. Multiply the result by 3.

Evaluating the Absolute Value

The absolute value of -3 is 3, because the distance of -3 from zero on the number line is 3 units.

Multiplying by 3

Now that we have the absolute value of -3, we can multiply it by 3:

3×3=93 \times 3 = 9

Conclusion

Therefore, the value of $3|-3|$ is 9.

Comparison with Answer Choices

Let's compare our result with the answer choices:

A. 6 - This is incorrect, because our result is 9, not 6. B. -9 - This is incorrect, because our result is 9, not -9. C. 9 - This is correct, because our result is indeed 9. D. -6 - This is incorrect, because our result is 9, not -6.

The final answer is C. 9.

Additional Examples

Here are a few more examples of evaluating expressions with absolute value:

  • 2∣−5∣=2×5=102|-5| = 2 \times 5 = 10

  • 4∣3∣=4×3=124|3| = 4 \times 3 = 12

  • −2∣−8∣=−2×8=−16-2|-8| = -2 \times 8 = -16

Tips and Tricks

When evaluating expressions with absolute value, remember to follow the order of operations (PEMDAS) and to always multiply the result by the coefficient outside the absolute value signs.

Common Mistakes

One common mistake when evaluating expressions with absolute value is to forget to multiply the result by the coefficient outside the absolute value signs. For example, in the expression $3|-3|$, some students might incorrectly write $|-3| \times 3 = -9$, because they forgot to multiply the result by 3.

Real-World Applications

Absolute value has many real-world applications, such as:

  • Measuring distances: Absolute value can be used to measure distances between two points on a number line.
  • Modeling real-world phenomena: Absolute value can be used to model real-world phenomena, such as the temperature difference between two locations.
  • Data analysis: Absolute value can be used to analyze data, such as the difference between two values.

Conclusion

In conclusion, evaluating expressions with absolute value requires following the order of operations (PEMDAS) and multiplying the result by the coefficient outside the absolute value signs. With practice and patience, you can become proficient in evaluating expressions with absolute value and apply it to real-world problems.

Frequently Asked Questions

Q: What is the definition of absolute value?

A: Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is denoted by two vertical lines on either side of the number, such as |x|. The absolute value of a number is always non-negative, regardless of whether the number itself is positive or negative.

Q: How do I evaluate an expression with absolute value?

A: To evaluate an expression with absolute value, follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the absolute value signs.
  2. Multiply the result by the coefficient outside the absolute value signs.

Q: What is the order of operations (PEMDAS)?

A: PEMDAS is a mnemonic device that helps you remember the order of operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between |-3| and -|-3|?

A: |-3| is the absolute value of -3, which is 3. On the other hand, -|-3| is the negative of the absolute value of -3, which is -3.

Q: Can I simplify expressions with absolute value?

A: Yes, you can simplify expressions with absolute value by following the order of operations (PEMDAS). For example, |-3| can be simplified to 3.

Q: How do I apply absolute value to real-world problems?

A: Absolute value can be applied to real-world problems in various ways, such as:

  • Measuring distances: Absolute value can be used to measure distances between two points on a number line.
  • Modeling real-world phenomena: Absolute value can be used to model real-world phenomena, such as the temperature difference between two locations.
  • Data analysis: Absolute value can be used to analyze data, such as the difference between two values.

Q: What are some common mistakes when evaluating expressions with absolute value?

A: Some common mistakes when evaluating expressions with absolute value include:

  • Forgetting to multiply the result by the coefficient outside the absolute value signs.
  • Not following the order of operations (PEMDAS).
  • Not simplifying expressions with absolute value.

Q: How can I practice evaluating expressions with absolute value?

A: You can practice evaluating expressions with absolute value by:

  • Working on sample problems and exercises.
  • Using online resources and practice tests.
  • Asking a teacher or tutor for help.

Additional Resources

  • Khan Academy: Absolute Value
  • Mathway: Absolute Value
  • Wolfram Alpha: Absolute Value

Conclusion

In conclusion, evaluating expressions with absolute value requires following the order of operations (PEMDAS) and multiplying the result by the coefficient outside the absolute value signs. With practice and patience, you can become proficient in evaluating expressions with absolute value and apply it to real-world problems.