What Is The Value Of \[$-5 + |-18|\$\]?A. 13 B. 23 C. \[$-13\$\] D. \[$-23\$\]

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What is the Value of −5+∣−18∣-5 + |-18|?

Understanding Absolute Value and Order of Operations

In mathematics, absolute value is a fundamental concept that deals with the magnitude of a number without considering its sign. It is denoted by two vertical lines on either side of the number, such as ∣x∣|x|. When evaluating expressions involving absolute value, it's essential to follow the order of operations, which dictates that absolute value should be evaluated before any other operations.

Evaluating the Absolute Value of -18

In the given expression, ∣−18∣|-18|, we need to find the absolute value of -18. Since absolute value represents the magnitude of a number, we ignore the negative sign and consider only the absolute value of 18. Therefore, ∣−18∣=18|-18| = 18.

Evaluating the Expression −5+18-5 + 18

Now that we have evaluated the absolute value of -18, we can proceed to evaluate the entire expression. The expression −5+∣−18∣-5 + |-18| becomes −5+18-5 + 18. Following the order of operations, we add 5 and 18, which results in 1313.

Conclusion

Therefore, the value of −5+∣−18∣-5 + |-18| is 1313. This is the correct answer among the given options.

Key Takeaways

  • Absolute value represents the magnitude of a number without considering its sign.
  • When evaluating expressions involving absolute value, follow the order of operations.
  • Ignore the negative sign when evaluating the absolute value of a negative number.
  • Add or subtract the absolute value from the other number in the expression.

Common Mistakes to Avoid

  • Failing to follow the order of operations when evaluating expressions involving absolute value.
  • Ignoring the absolute value when evaluating the expression.
  • Not considering the magnitude of the number when evaluating absolute value.

Real-World Applications

  • Absolute value is used in various real-world applications, such as finance, physics, and engineering.
  • It is used to represent the magnitude of a quantity, such as distance, speed, or temperature.
  • Absolute value is also used in data analysis and statistics to represent the magnitude of a data point.

Practice Problems

  • Evaluate the expression −3+∣−12∣-3 + |-12|.
  • Evaluate the expression 4+∣−15∣4 + |-15|.
  • Evaluate the expression −2+∣−9∣-2 + |-9|.

Solutions

  • −3+∣−12∣=−3+12=9-3 + |-12| = -3 + 12 = 9
  • 4+∣−15∣=4+15=194 + |-15| = 4 + 15 = 19
  • −2+∣−9∣=−2+9=7-2 + |-9| = -2 + 9 = 7

Conclusion

In conclusion, the value of −5+∣−18∣-5 + |-18| is 1313. This is a fundamental concept in mathematics that deals with absolute value and order of operations. By following the order of operations and ignoring the negative sign when evaluating absolute value, we can accurately evaluate expressions involving absolute value.
Frequently Asked Questions (FAQs) About Absolute Value

Q: What is absolute value? A: Absolute value is a mathematical concept that represents the magnitude of a number without considering its sign. It is denoted by two vertical lines on either side of the number, such as ∣x∣|x|.

Q: How do I evaluate absolute value? A: To evaluate absolute value, ignore the negative sign and consider only the absolute value of the number. For example, ∣−18∣=18|-18| = 18.

Q: What is the order of operations when evaluating expressions involving absolute value? A: The order of operations when evaluating expressions involving absolute value is as follows:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any absolute value expressions.
  4. Evaluate any multiplication and division operations from left to right.
  5. Evaluate any addition and subtraction operations from left to right.

Q: Can I use absolute value to represent negative numbers? A: Yes, absolute value can be used to represent negative numbers. For example, ∣−5∣=5|-5| = 5.

Q: Can I use absolute value to represent fractions? A: Yes, absolute value can be used to represent fractions. For example, ∣34∣=34|\frac{3}{4}| = \frac{3}{4}.

Q: Can I use absolute value to represent decimals? A: Yes, absolute value can be used to represent decimals. For example, ∣3.5∣=3.5|3.5| = 3.5.

Q: How do I evaluate expressions involving absolute value and fractions? A: To evaluate expressions involving absolute value and fractions, follow the order of operations and ignore the negative sign when evaluating absolute value. For example, ∣−34∣=34|\frac{-3}{4}| = \frac{3}{4}.

Q: How do I evaluate expressions involving absolute value and decimals? A: To evaluate expressions involving absolute value and decimals, follow the order of operations and ignore the negative sign when evaluating absolute value. For example, ∣3.5∣=3.5|3.5| = 3.5.

Q: Can I use absolute value to represent complex numbers? A: Yes, absolute value can be used to represent complex numbers. For example, ∣3+4i∣=32+42=5|3 + 4i| = \sqrt{3^2 + 4^2} = 5.

Q: How do I evaluate expressions involving absolute value and complex numbers? A: To evaluate expressions involving absolute value and complex numbers, follow the order of operations and ignore the negative sign when evaluating absolute value. For example, ∣3+4i∣=32+42=5|3 + 4i| = \sqrt{3^2 + 4^2} = 5.

Q: What are some real-world applications of absolute value? A: Absolute value has many real-world applications, including:

  • Finance: Absolute value is used to represent the magnitude of a financial quantity, such as the value of a stock or a bond.
  • Physics: Absolute value is used to represent the magnitude of a physical quantity, such as distance, speed, or temperature.
  • Engineering: Absolute value is used to represent the magnitude of a physical quantity, such as the magnitude of a force or a torque.
  • Data analysis: Absolute value is used to represent the magnitude of a data point, such as the magnitude of a error or a deviation.

Q: What are some common mistakes to avoid when evaluating expressions involving absolute value? A: Some common mistakes to avoid when evaluating expressions involving absolute value include:

  • Failing to follow the order of operations.
  • Ignoring the absolute value when evaluating the expression.
  • Not considering the magnitude of the number when evaluating absolute value.

Q: How can I practice evaluating expressions involving absolute value? A: You can practice evaluating expressions involving absolute value by working through examples and exercises, such as:

  • Evaluating expressions involving absolute value and integers.
  • Evaluating expressions involving absolute value and fractions.
  • Evaluating expressions involving absolute value and decimals.
  • Evaluating expressions involving absolute value and complex numbers.

Conclusion

In conclusion, absolute value is a fundamental concept in mathematics that represents the magnitude of a number without considering its sign. By following the order of operations and ignoring the negative sign when evaluating absolute value, we can accurately evaluate expressions involving absolute value.