Which Expression Means The Same As the Quotient Of 8 Less Than $x$ And 4?A. $(x + 4) - 8$ B. \$(x + 4) \div 8$[/tex\] C. $(8 - X) \div 4$ D. $(x - 8) + 4$ E. \$(x - 8) \div

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Introduction

In mathematics, the quotient of two numbers is the result of division. It is a fundamental concept in arithmetic and algebra. When we are given an expression that involves the quotient of two quantities, it is essential to understand the correct interpretation of the expression. In this article, we will explore the meaning of the expression "the quotient of 8 less than $x$ and 4" and determine which of the given options represents the same expression.

Breaking Down the Expression

The given expression is "the quotient of 8 less than $x$ and 4". To understand this expression, let's break it down into its components:

  • "8 less than $x$" means that we need to subtract 8 from $x$. This can be represented as $x - 8$.
  • The quotient of two numbers is the result of division. In this case, we need to divide the result of $x - 8$ by 4.

Analyzing the Options

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

A. $(x + 4) - 8$

This option adds 4 to $x$ and then subtracts 8. This is not the correct interpretation of the expression, as we need to subtract 8 from $x$ first.

B. $(x + 4) \div 8$

This option adds 4 to $x$ and then divides the result by 8. This is also not the correct interpretation of the expression, as we need to subtract 8 from $x$ first.

C. $(8 - x) \div 4$

This option subtracts $x$ from 8 and then divides the result by 4. This is the correct interpretation of the expression, as we need to subtract 8 from $x$ first and then divide the result by 4.

D. $(x - 8) + 4$

This option subtracts 8 from $x$ and then adds 4. This is not the correct interpretation of the expression, as we need to divide the result by 4.

E. $(x - 8) \div 4$

This option subtracts 8 from $x$ and then divides the result by 4. This is the correct interpretation of the expression, as we need to subtract 8 from $x$ first and then divide the result by 4.

Conclusion

In conclusion, the correct interpretation of the expression "the quotient of 8 less than $x$ and 4" is $(x - 8) \div 4$. This option correctly represents the quotient of 8 less than $x$ and 4.

Final Answer

The final answer is:

(x - 8) \div 4$<br/> **Quotient Expression Q&A** ========================== **Frequently Asked Questions** --------------------------- In the previous article, we explored the meaning of the expression "the quotient of 8 less than $x$ and 4" and determined which of the given options represents the same expression. In this article, we will answer some frequently asked questions related to the quotient expression. **Q: What is the quotient of two numbers?** -------------------------------------- A: The quotient of two numbers is the result of division. It is a fundamental concept in arithmetic and algebra. **Q: How do I interpret the expression "the quotient of 8 less than $x$ and 4"?** --------------------------------------------------------- A: To interpret the expression "the quotient of 8 less than $x$ and 4", you need to break it down into its components: * "8 less than $x$" means that you need to subtract 8 from $x$. This can be represented as $x - 8$. * The quotient of two numbers is the result of division. In this case, you need to divide the result of $x - 8$ by 4. **Q: What is the correct interpretation of the expression "the quotient of 8 less than $x$ and 4"?** --------------------------------------------------------- A: The correct interpretation of the expression "the quotient of 8 less than $x$ and 4" is $(x - 8) \div 4$. **Q: Why is option A incorrect?** --------------------------- A: Option A is incorrect because it adds 4 to $x$ and then subtracts 8. This is not the correct interpretation of the expression, as we need to subtract 8 from $x$ first. **Q: Why is option B incorrect?** --------------------------- A: Option B is incorrect because it adds 4 to $x$ and then divides the result by 8. This is also not the correct interpretation of the expression, as we need to subtract 8 from $x$ first. **Q: Why is option C correct?** ------------------------- A: Option C is correct because it subtracts $x$ from 8 and then divides the result by 4. This is the correct interpretation of the expression, as we need to subtract 8 from $x$ first and then divide the result by 4. **Q: What is the difference between the quotient and the product?** --------------------------------------------------------- A: The quotient and the product are two different mathematical operations. The quotient is the result of division, while the product is the result of multiplication. **Q: Can you provide an example of how to use the quotient expression in a real-world scenario?** ------------------------------------------------------------------------- A: Yes, here's an example: Suppose you have a box of cookies that contains 24 cookies. You want to divide the cookies equally among 4 people. To find out how many cookies each person will get, you can use the quotient expression: $\frac{24}{4} = 6

In this example, the quotient expression is used to divide the total number of cookies (24) by the number of people (4) to find out how many cookies each person will get (6).

Conclusion

In conclusion, the quotient expression is a fundamental concept in mathematics that is used to represent the result of division. By understanding the correct interpretation of the expression "the quotient of 8 less than $x$ and 4", you can apply it to real-world scenarios and solve problems with ease.

Final Answer

The final answer is:

(x−8)÷4(x - 8) \div 4