Which List Correctly Orders $A, B$, And $C$ From Least To Greatest When $A=|7|, B=-6$, And $C=|-5|$?A. $A, B, C$ B. $B, C, A$ C. $C, B, A$ D. $A, C, B$

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Understanding the Problem

When dealing with numbers, it's essential to understand how to compare and order them from least to greatest. In this problem, we are given three numbers: A=∣7∣,B=−6A=|7|, B=-6, and C=∣−5∣C=|-5|. We need to determine the correct order of these numbers from least to greatest.

What are Absolute Values?

Before we proceed, let's understand what absolute values are. The absolute value of a number is its distance from zero on the number line. In other words, it's the number without its sign. For example, the absolute value of −3-3 is 33, and the absolute value of 44 is also 44.

Calculating Absolute Values

Now, let's calculate the absolute values of the given numbers:

  • A=∣7∣=7A=|7|=7
  • B=−6B=-6
  • C=∣−5∣=5C=|-5|=5

Comparing Numbers

Now that we have the absolute values of the numbers, we can compare them to determine the correct order from least to greatest.

  • B=−6B=-6 is the smallest number since it's negative and has the smallest absolute value.
  • C=5C=5 is the next smallest number since it has a larger absolute value than BB.
  • A=7A=7 is the largest number since it has the largest absolute value.

Conclusion

Based on the comparison of the numbers, the correct order from least to greatest is B,C,AB, C, A. Therefore, the correct answer is:

B. B,C,AB, C, A

Discussion

This problem requires a basic understanding of absolute values and how to compare numbers. It's essential to remember that absolute values are always non-negative, and comparing numbers involves looking at their absolute values.

Additional Tips

When dealing with absolute values, it's crucial to remember that the sign of the number is ignored. For example, ∣−3∣=3|-3|=3 and ∣3∣=3|3|=3. This means that when comparing numbers, we only need to look at their absolute values.

Common Mistakes

One common mistake when dealing with absolute values is to forget to ignore the sign of the number. For example, someone might compare −3-3 and 33 without taking into account their absolute values. This can lead to incorrect conclusions.

Real-World Applications

Understanding absolute values and how to compare numbers is essential in various real-world applications, such as:

  • Data analysis: When working with data, it's crucial to understand how to compare numbers and ignore their signs.
  • Finance: In finance, absolute values are used to calculate profits and losses.
  • Science: In science, absolute values are used to measure distances and quantities.

Conclusion

In conclusion, ordering numbers from least to greatest requires a basic understanding of absolute values and how to compare numbers. By ignoring the sign of the number and looking at its absolute value, we can determine the correct order from least to greatest. The correct answer is:

B. B,C,AB, C, A

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Q: What is the difference between absolute value and regular value?

A: The main difference between absolute value and regular value is that absolute value ignores the sign of the number. For example, the absolute value of −3-3 is 33, while the regular value of −3-3 is −3-3.

Q: How do I calculate the absolute value of a number?

A: To calculate the absolute value of a number, you simply ignore its sign. For example, the absolute value of −5-5 is 55, and the absolute value of 77 is 77.

Q: What is the correct order of the numbers A=∣7∣,B=−6A=|7|, B=-6, and C=∣−5∣C=|-5| from least to greatest?

A: The correct order of the numbers A=∣7∣,B=−6A=|7|, B=-6, and C=∣−5∣C=|-5| from least to greatest is B,C,AB, C, A. This is because B=−6B=-6 is the smallest number, C=∣−5∣=5C=|-5|=5 is the next smallest number, and A=∣7∣=7A=|7|=7 is the largest number.

Q: How do I compare numbers when dealing with absolute values?

A: When dealing with absolute values, you ignore the sign of the number and compare their absolute values. For example, to compare −3-3 and 33, you would compare their absolute values, which are both 33. Since they are equal, the numbers are equal.

Q: What are some common mistakes to avoid when dealing with absolute values?

A: Some common mistakes to avoid when dealing with absolute values include:

  • Forgetting to ignore the sign of the number
  • Comparing numbers without taking into account their absolute values
  • Not understanding the concept of absolute value

Q: How do I apply absolute values in real-world scenarios?

A: Absolute values are used in various real-world scenarios, including:

  • Data analysis: When working with data, it's crucial to understand how to compare numbers and ignore their signs.
  • Finance: In finance, absolute values are used to calculate profits and losses.
  • Science: In science, absolute values are used to measure distances and quantities.

Q: What are some real-world examples of using absolute values?

A: Some real-world examples of using absolute values include:

  • Calculating the distance between two points on a map
  • Measuring the temperature difference between two locations
  • Calculating the profit or loss of a business

Q: How do I practice ordering numbers from least to greatest using absolute values?

A: To practice ordering numbers from least to greatest using absolute values, you can try the following:

  • Create a list of numbers with different signs and absolute values
  • Compare the numbers and order them from least to greatest
  • Check your answers by using a calculator or a reference source

Q: What are some additional resources for learning about absolute values?

A: Some additional resources for learning about absolute values include:

  • Online tutorials and videos
  • Math textbooks and workbooks
  • Online math communities and forums

Q: How do I apply absolute values in different mathematical operations?

A: Absolute values can be applied in different mathematical operations, including:

  • Addition and subtraction
  • Multiplication and division
  • Exponents and roots

Q: What are some common applications of absolute values in mathematics?

A: Some common applications of absolute values in mathematics include:

  • Calculus: Absolute values are used to calculate derivatives and integrals.
  • Algebra: Absolute values are used to solve equations and inequalities.
  • Geometry: Absolute values are used to calculate distances and lengths.

Q: How do I use absolute values to solve real-world problems?

A: To use absolute values to solve real-world problems, you can try the following:

  • Identify the problem and the relevant information
  • Apply absolute values to the information
  • Use the results to solve the problem

Q: What are some common mistakes to avoid when using absolute values?

A: Some common mistakes to avoid when using absolute values include:

  • Forgetting to ignore the sign of the number
  • Comparing numbers without taking into account their absolute values
  • Not understanding the concept of absolute value