Translate The Phrase Into A Numerical Expression: Fifty Minus Two Plus The Quantity Three Divided By Six.A. \[$(3 / 6) + 2 - 50\$\]B. \[$50 - 2 + 3 + 6\$\]C. \[$50 - 2 + (3 \div 6)\$\]D. \[$50 / 2 + 3 / 6\$\]

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Understanding the Problem

In this article, we will explore the concept of translating a phrase into a numerical expression. We will use the given phrase "Fifty minus two plus the quantity three divided by six" as an example to demonstrate how to solve numerical expressions.

Breaking Down the Phrase

To translate the phrase into a numerical expression, we need to break it down into its individual components. The phrase can be broken down into the following parts:

  • Fifty
  • Minus
  • Two
  • Plus
  • The quantity
  • Three
  • Divided by
  • Six

Order of Operations

When translating a phrase into a numerical expression, it is essential to follow the order of operations (PEMDAS):

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

Analyzing the Options

Let's analyze each option to determine which one correctly translates the phrase into a numerical expression:

Option A: {(3 / 6) + 2 - 50$}$

This option follows the order of operations, but it does not correctly translate the phrase. The phrase "Fifty minus two plus the quantity three divided by six" implies that the quantity three divided by six should be added to fifty, not subtracted.

Option B: ${50 - 2 + 3 + 6\$}

This option does not follow the order of operations. The phrase "Fifty minus two plus the quantity three divided by six" implies that the quantity three divided by six should be added to fifty, not simply added to the result of fifty minus two.

Option C: ${50 - 2 + (3 \div 6)\$}

This option correctly translates the phrase into a numerical expression. The quantity three divided by six is evaluated first, and then added to fifty minus two.

Option D: ${50 / 2 + 3 / 6\$}

This option does not correctly translate the phrase into a numerical expression. The phrase "Fifty minus two plus the quantity three divided by six" implies that the quantity three divided by six should be added to fifty minus two, not simply added to the result of fifty divided by two.

Conclusion

In conclusion, the correct answer is Option C: ${50 - 2 + (3 \div 6)\$}. This option correctly translates the phrase into a numerical expression by following the order of operations and accurately representing the phrase.

Tips and Tricks

When translating a phrase into a numerical expression, it is essential to follow the order of operations and accurately represent the phrase. Here are some tips and tricks to help you solve numerical expressions:

  • Read the phrase carefully and break it down into its individual components.
  • Identify the order of operations and evaluate expressions accordingly.
  • Use parentheses to clarify the order of operations.
  • Avoid making assumptions or simplifying the phrase without accurately representing it.

Practice Problems

Here are some practice problems to help you practice translating phrases into numerical expressions:

  • Translate the phrase "Twenty-five minus the quantity four divided by two plus three" into a numerical expression.
  • Translate the phrase "Fifty minus two plus the quantity six divided by three" into a numerical expression.
  • Translate the phrase "Thirty minus the quantity two divided by four plus five" into a numerical expression.

Answer Key

Here are the answers to the practice problems:

  • Option C: [$25 - (4 \div 2) + 3$
  • Option C: [$50 - 2 + (6 \div 3)$
  • Option C: [$30 - (2 \div 4) + 5$

Conclusion

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

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

Q: How do I translate a phrase into a numerical expression?

A: To translate a phrase into a numerical expression, follow these steps:

  1. Read the phrase carefully and break it down into its individual components.
  2. Identify the order of operations and evaluate expressions accordingly.
  3. Use parentheses to clarify the order of operations.
  4. Avoid making assumptions or simplifying the phrase without accurately representing it.

Q: What is the difference between a numerical expression and an algebraic expression?

A: A numerical expression is an expression that contains only numbers and mathematical operations, whereas an algebraic expression is an expression that contains variables and mathematical operations. For example, the expression "2 + 3" is a numerical expression, while the expression "2x + 3" is an algebraic expression.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, follow the order of operations:

  1. Evaluate any expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the importance of following the order of operations?

A: Following the order of operations is crucial in mathematics because it ensures that expressions are evaluated consistently and accurately. Without following the order of operations, expressions may be evaluated incorrectly, leading to incorrect results.

Q: Can you provide examples of phrases that can be translated into numerical expressions?

A: Here are some examples of phrases that can be translated into numerical expressions:

  • "Twenty-five minus the quantity four divided by two plus three"
  • "Fifty minus two plus the quantity six divided by three"
  • "Thirty minus the quantity two divided by four plus five"

Q: How do I practice translating phrases into numerical expressions?

A: To practice translating phrases into numerical expressions, try the following:

  • Read and analyze phrases that contain mathematical operations.
  • Break down the phrase into its individual components.
  • Identify the order of operations and evaluate expressions accordingly.
  • Use parentheses to clarify the order of operations.
  • Avoid making assumptions or simplifying the phrase without accurately representing it.

Q: What are some common mistakes to avoid when translating phrases into numerical expressions?

A: Some common mistakes to avoid when translating phrases into numerical expressions include:

  • Not following the order of operations.
  • Not using parentheses to clarify the order of operations.
  • Making assumptions or simplifying the phrase without accurately representing it.
  • Not evaluating expressions with multiple operations correctly.

Conclusion

In conclusion, translating phrases into numerical expressions requires careful attention to the order of operations and accurate representation of the phrase. By following the tips and tricks outlined in this article, you can improve your skills in solving numerical expressions and accurately translate phrases into numerical expressions.