Which Description Can Be Written As The Expression $\frac{8}{21n}$?A. The Quotient Of Twenty-one Times A Number And Eight B. The Product Of Eight And Twenty-one Times A Number C. The Quotient Of Eight And Twenty-one Times A Number D. The

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Which Description Can Be Written as the Expression $\frac{8}{21n}$?

Understanding the Expression

The given expression is $\frac{8}{21n}$. To understand this expression, we need to break it down into its components. The numerator is 8, and the denominator is 21n. This means that the expression represents a quotient, where 8 is being divided by the product of 21 and n.

Analyzing the Options

Now, let's analyze each of the given options to determine which one can be written as the expression $\frac{8}{21n}$.

A. The Quotient of Twenty-One Times a Number and Eight

This option describes a quotient, where twenty-one times a number is being divided by 8. Mathematically, this can be represented as $\frac{21n}{8}$. This is the opposite of the given expression, where 8 is being divided by 21n.

B. The Product of Eight and Twenty-One Times a Number

This option describes a product, where 8 is being multiplied by 21 times a number. Mathematically, this can be represented as $8 \times 21n$. This is not the same as the given expression, where 8 is being divided by 21n.

C. The Quotient of Eight and Twenty-One Times a Number

This option describes a quotient, where 8 is being divided by 21 times a number. Mathematically, this can be represented as $\frac{8}{21n}$. This is the same as the given expression, where 8 is being divided by 21n.

D. The Product of Eight and Twenty-One

This option describes a product, where 8 is being multiplied by 21. Mathematically, this can be represented as $8 \times 21$. This is not the same as the given expression, where 8 is being divided by 21n.

Conclusion

Based on the analysis of each option, it is clear that only option C describes the expression $\frac{8}{21n}$. This option correctly represents a quotient, where 8 is being divided by 21 times a number.

Key Takeaways

  • The expression $\frac{8}{21n}$ represents a quotient, where 8 is being divided by 21n.
  • Option C is the only description that matches the given expression.
  • Understanding the components of an expression is crucial in determining its meaning.

Mathematical Representation

The expression $\frac{8}{21n}$ can be represented mathematically as:

821n=821×1n\frac{8}{21n} = \frac{8}{21} \times \frac{1}{n}

This representation shows that the expression is a quotient of two fractions, where the numerator is 8 and the denominator is 21n.

Real-World Applications

The expression $\frac{8}{21n}$ has real-world applications in various fields, such as:

  • Finance: The expression can be used to calculate interest rates or investment returns.
  • Science: The expression can be used to calculate concentrations or rates of chemical reactions.
  • Engineering: The expression can be used to calculate stresses or strains on materials.

Conclusion

In conclusion, the expression $\frac8}{21n}$ represents a quotient, where 8 is being divided by 21n. Option C is the only description that matches the given expression. Understanding the components of an expression is crucial in determining its meaning. The expression has real-world applications in various fields, and its mathematical representation can be used to calculate various quantities.
**Q&A Understanding the Expression $\frac{8{21n}$**

Frequently Asked Questions

We have received many questions about the expression $\frac{8}{21n}$ and its various applications. Below are some of the most frequently asked questions and their answers.

Q: What is the meaning of the expression $\frac{8}{21n}$?

A: The expression $\frac{8}{21n}$ represents a quotient, where 8 is being divided by 21n. This means that the expression is a fraction, where the numerator is 8 and the denominator is 21n.

Q: How do I simplify the expression $\frac{8}{21n}$?

A: To simplify the expression $\frac{8}{21n}$, you can cancel out any common factors between the numerator and the denominator. In this case, there are no common factors, so the expression cannot be simplified further.

Q: What is the value of the expression $\frac{8}{21n}$ when n = 1?

A: When n = 1, the expression $\frac{8}{21n}$ becomes $\frac{8}{21}$.

Q: Can I multiply the expression $\frac{8}{21n}$ by a number?

A: Yes, you can multiply the expression $\frac{8}{21n}$ by a number. For example, if you multiply the expression by 2, you get $\frac{16}{21n}$.

Q: Can I divide the expression $\frac{8}{21n}$ by a number?

A: Yes, you can divide the expression $\frac{8}{21n}$ by a number. For example, if you divide the expression by 2, you get $\frac{4}{21n}$.

Q: What is the inverse of the expression $\frac{8}{21n}$?

A: The inverse of the expression $\frac{8}{21n}$ is $\frac{21n}{8}$.

Q: Can I add or subtract the expression $\frac{8}{21n}$ to another expression?

A: Yes, you can add or subtract the expression $\frac{8}{21n}$ to another expression. However, you must ensure that the expressions have the same denominator.

Q: What is the domain of the expression $\frac{8}{21n}$?

A: The domain of the expression $\frac{8}{21n}$ is all real numbers except 0, since division by zero is undefined.

Q: Can I use the expression $\frac{8}{21n}$ in a real-world application?

A: Yes, the expression $\frac{8}{21n}$ has many real-world applications, such as calculating interest rates, investment returns, concentrations, and rates of chemical reactions.

Conclusion

In conclusion, the expression $\frac{8}{21n}$ is a quotient, where 8 is being divided by 21n. It has many real-world applications and can be used in various mathematical operations, such as multiplication, division, addition, and subtraction. We hope that this Q&A article has helped you understand the expression and its various applications.

Key Takeaways

  • The expression $\frac{8}{21n}$ represents a quotient, where 8 is being divided by 21n.
  • The expression can be simplified by canceling out common factors between the numerator and the denominator.
  • The expression can be multiplied or divided by a number.
  • The inverse of the expression is $\frac{21n}{8}$.
  • The domain of the expression is all real numbers except 0.
  • The expression has many real-world applications.