Solve The Equation 4 N = 4 5 \frac{4}{n} = \frac{4}{5} N 4 ​ = 5 4 ​ .a. N = 5 N = 5 N = 5 B. N = 5 16 N = \frac{5}{16} N = 16 5 ​ C. N = 3 1 5 N = 3 \frac{1}{5} N = 3 5 1 ​ D. N = 50 N = 50 N = 50 Please Select The Best Answer From The Choices Provided: A B C D

Introduction

In mathematics, equations are a fundamental concept that helps us solve problems and understand various mathematical relationships. One of the most common types of equations is the proportionality equation, where two ratios are equal. In this article, we will focus on solving the equation $\frac{4}{n} = \frac{4}{5}$, which is a classic example of a proportionality equation.

Understanding the Equation

The given equation is $\frac{4}{n} = \frac{4}{5}$. To solve this equation, we need to find the value of $n$ that makes the equation true. The equation states that the ratio of 4 to $n$ is equal to the ratio of 4 to 5.

Step 1: Cross-Multiplication

To solve the equation, we can use the method of cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. In this case, we multiply 4 by 5 and $n$ by 4.

$\frac{4}{n} = \frac{4}{5}$

$4 \times 5 = 20$

$n \times 4 = 4n$

So, the equation becomes:

$\frac{20}{4n} = \frac{4}{5}$

Step 2: Simplifying the Equation

Now, we can simplify the equation by canceling out the common factors. In this case, we can cancel out the factor of 4 from the numerator and denominator.

$\frac{20}{4n} = \frac{4}{5}$

$\frac{5}{n} = \frac{4}{5}$

Step 3: Solving for $n$

Now, we can solve for $n$ by cross-multiplying again.

$\frac{5}{n} = \frac{4}{5}$

$5 \times 5 = 25$

$n \times 4 = 4n$

So, the equation becomes:

$\frac{25}{4n} = \frac{4}{5}$

Step 4: Finding the Value of $n$

Now, we can find the value of $n$ by dividing both sides of the equation by 4.

$\frac{25}{4n} = \frac{4}{5}$

$\frac{25}{4} = n \times \frac{4}{5}$

$n = \frac{25}{4} \times \frac{5}{4}$

$n = \frac{125}{16}$

Conclusion

In conclusion, the value of $n$ that satisfies the equation $\frac{4}{n} = \frac{4}{5}$ is $\frac{125}{16}$. This is the correct answer, and it can be verified by plugging the value of $n$ back into the original equation.

Answer

The correct answer is:

• B. $n = \frac{5}{16}$
  Solving the Equation: A Step-by-Step Guide =====================================================

Q&A: Frequently Asked Questions

Q: What is the equation $\frac{4}{n} = \frac{4}{5}$ trying to solve?

A: The equation $\frac{4}{n} = \frac{4}{5}$ is trying to find the value of $n$ that makes the equation true. In other words, it is trying to find the value of $n$ that makes the ratio of 4 to $n$ equal to the ratio of 4 to 5.

Q: Why do we need to cross-multiply in this equation?

A: We need to cross-multiply in this equation because it allows us to eliminate the fractions and make the equation easier to solve. By cross-multiplying, we can multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.

Q: What is the difference between the numerator and denominator in this equation?

A: In this equation, the numerator is 4 and the denominator is $n$. The numerator is the number on top of the fraction, while the denominator is the number on the bottom.

Q: Can we simplify the equation by canceling out common factors?

A: Yes, we can simplify the equation by canceling out common factors. In this case, we can cancel out the factor of 4 from the numerator and denominator.

Q: How do we solve for $n$ in this equation?

A: To solve for $n$ in this equation, we need to cross-multiply again and then divide both sides of the equation by 4.

Q: What is the value of $n$ that satisfies the equation $\frac{4}{n} = \frac{4}{5}$?

A: The value of $n$ that satisfies the equation $\frac{4}{n} = \frac{4}{5}$ is $\frac{125}{16}$.

Q: Can we verify the answer by plugging the value of $n$ back into the original equation?

A: Yes, we can verify the answer by plugging the value of $n$ back into the original equation. If the equation is true, then the value of $n$ is correct.

Q: What is the importance of solving equations like this one?

A: Solving equations like this one is important because it helps us understand the concept of proportionality and how to solve equations with fractions. It also helps us develop problem-solving skills and critical thinking.

Q: Can we apply this concept to real-life situations?

A: Yes, we can apply this concept to real-life situations. For example, if we are trying to find the cost of a product that is sold in a certain ratio, we can use this concept to solve for the cost.

Q: What are some common mistakes to avoid when solving equations like this one?

A: Some common mistakes to avoid when solving equations like this one include:

• Not cross-multiplying correctly
• Not canceling out common factors
• Not solving for $n$ correctly
• Not verifying the answer by plugging the value of $n$ back into the original equation

Conclusion

In conclusion, solving the equation $\frac{4}{n} = \frac{4}{5}$ requires a step-by-step approach, including cross-multiplication, simplifying the equation, and solving for $n$. By following these steps and avoiding common mistakes, we can find the value of $n$ that satisfies the equation.