Which Of The Following Best Describes The English Expression the Product Of Nine And A Number Minus Five?A. $9(x-5$\] B. $\frac{9}{x-5}$ C. $\frac{9}{x}-5$ D. $9x-5$

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Introduction

In mathematics, expressions are used to represent complex ideas and relationships between variables. Understanding these expressions is crucial for solving problems and making informed decisions. In this article, we will analyze the English expression "the product of nine and a number minus five" and determine which of the given options best describes it.

Breaking Down the Expression

The English expression "the product of nine and a number minus five" can be broken down into three key components:

  1. The product of nine and a number: This means that we are multiplying nine by a variable, which we can represent as x. The product of two numbers is obtained by multiplying them together.
  2. Minus five: This means that we are subtracting five from the result of the product.

Analyzing the Options

Now that we have broken down the expression, let's analyze the given options:

Option A: 9(x−5)9(x-5)

This option represents the product of nine and a number minus five. The parentheses indicate that we are subtracting five from the result of the product. This option is a strong candidate for the correct answer.

Option B: 9x−5\frac{9}{x-5}

This option represents the quotient of nine and a number minus five. The division symbol indicates that we are dividing nine by the result of the product. This option does not match the English expression.

Option C: 9x−5\frac{9}{x}-5

This option represents the quotient of nine and a number minus five. The division symbol indicates that we are dividing nine by the number, and then subtracting five from the result. This option does not match the English expression.

Option D: 9x−59x-5

This option represents the product of nine and a number minus five. However, the order of operations is incorrect. The product of nine and the number should be calculated first, and then five should be subtracted from the result.

Conclusion

Based on our analysis, the correct answer is Option A: 9(x−5)9(x-5). This option accurately represents the English expression "the product of nine and a number minus five". The parentheses indicate that we are subtracting five from the result of the product, which matches the English expression.

Understanding the Importance of Order of Operations

The order of operations is a fundamental concept in mathematics that determines the order in which operations are performed when there are multiple operations in an expression. In the English expression "the product of nine and a number minus five", the order of operations is crucial in determining the correct answer.

Real-World Applications

Understanding the English expression "the product of nine and a number minus five" has real-world applications in various fields, such as:

  • Business: In business, understanding the product of two numbers and subtracting a certain amount is crucial in calculating profits, losses, and expenses.
  • Science: In science, understanding the product of two numbers and subtracting a certain amount is crucial in calculating rates, ratios, and proportions.
  • Engineering: In engineering, understanding the product of two numbers and subtracting a certain amount is crucial in calculating stresses, strains, and loads.

Conclusion

In conclusion, the English expression "the product of nine and a number minus five" can be represented by the option 9(x−5)9(x-5). Understanding this expression is crucial in various fields, and it has real-world applications. By analyzing the expression and understanding the order of operations, we can determine the correct answer and make informed decisions.

Final Thoughts

Q: What is the product of nine and a number minus five?

A: The product of nine and a number minus five is a mathematical expression that represents the result of multiplying nine by a variable (x) and then subtracting five from the result.

Q: How do I represent the product of nine and a number minus five mathematically?

A: You can represent the product of nine and a number minus five mathematically using the expression 9(x−5)9(x-5).

Q: What is the order of operations in the expression 9(x−5)9(x-5)?

A: The order of operations in the expression 9(x−5)9(x-5) is as follows:

  1. Evaluate the expression inside the parentheses: x−5x-5
  2. Multiply nine by the result: 9(x−5)9(x-5)
  3. Subtract five from the result: 9(x−5)−59(x-5)-5

Q: How do I apply the order of operations in real-world scenarios?

A: In real-world scenarios, you can apply the order of operations by following these steps:

  1. Identify the mathematical expression: Identify the mathematical expression that needs to be evaluated.
  2. Evaluate the expression inside the parentheses: Evaluate any expressions inside parentheses first.
  3. Multiply and divide from left to right: Multiply and divide numbers from left to right.
  4. Add and subtract from left to right: Add and subtract numbers from left to right.

Q: What are some real-world applications of the product of nine and a number minus five?

A: Some real-world applications of the product of nine and a number minus five include:

  • Business: Calculating profits, losses, and expenses
  • Science: Calculating rates, ratios, and proportions
  • Engineering: Calculating stresses, strains, and loads

Q: How do I simplify complex mathematical expressions?

A: You can simplify complex mathematical expressions by following these steps:

  1. Identify the mathematical expression: Identify the mathematical expression that needs to be simplified.
  2. Evaluate any expressions inside parentheses: Evaluate any expressions inside parentheses first.
  3. Multiply and divide from left to right: Multiply and divide numbers from left to right.
  4. Add and subtract from left to right: Add and subtract numbers from left to right.

Q: What are some common mistakes to avoid when working with mathematical expressions?

A: Some common mistakes to avoid when working with mathematical expressions include:

  • Incorrect order of operations: Failing to follow the correct order of operations can lead to incorrect results.
  • Incorrect evaluation of expressions inside parentheses: Failing to evaluate expressions inside parentheses correctly can lead to incorrect results.
  • Incorrect multiplication and division: Failing to multiply and divide numbers correctly can lead to incorrect results.

Conclusion

In conclusion, understanding the English expression "the product of nine and a number minus five" is crucial in various fields, including business, science, and engineering. By following the correct order of operations and simplifying complex mathematical expressions, you can make informed decisions and achieve accurate results.