Solve For { N $} : : : { \frac{3}{8} + N = \frac{7}{8} \}

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Introduction to Solving Linear Equations

Solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$ is a fundamental concept in mathematics, particularly in algebra. It involves isolating the variable n on one side of the equation, while keeping the other side intact. In this article, we will delve into the step-by-step process of solving for n in the given equation.

Understanding the Equation

The equation $\frac{3}{8} + n = \frac{7}{8}$ is a linear equation, where the variable n is added to the fraction $\frac{3}{8}$ to obtain the fraction $\frac{7}{8}$. To solve for n, we need to isolate the variable on one side of the equation.

Step 1: Subtract $\frac{3}{8}$ from Both Sides

To isolate the variable n, we need to subtract $\frac{3}{8}$ from both sides of the equation. This will allow us to move the constant term to the other side of the equation.

$\frac{3}{8} + n = \frac{7}{8}$

Subtracting $\frac{3}{8}$ from both sides:

$n = \frac{7}{8} - \frac{3}{8}$

Step 2: Simplify the Right-Hand Side

Now that we have subtracted $\frac{3}{8}$ from both sides, we can simplify the right-hand side of the equation.

$n = \frac{7}{8} - \frac{3}{8}$

To simplify, we can find a common denominator, which is 8 in this case. We can then subtract the numerators:

$n = \frac{7-3}{8}$

$n = \frac{4}{8}$

Step 3: Simplify the Fraction

The fraction $\frac{4}{8}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

$n = \frac{4}{8}$

Dividing both the numerator and the denominator by 4:

$n = \frac{1}{2}$

Conclusion

In conclusion, solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$ involves isolating the variable n on one side of the equation. By subtracting $\frac{3}{8}$ from both sides and simplifying the right-hand side, we can find the value of n, which is $\frac{1}{2}$.

Tips and Tricks

• When solving linear equations, it's essential to isolate the variable on one side of the equation.
• When subtracting fractions, find a common denominator and subtract the numerators.
• Simplify fractions by dividing both the numerator and the denominator by their greatest common divisor.

Real-World Applications

Solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$ has real-world applications in various fields, such as:

• Finance: When calculating interest rates or investment returns, solving for n can help determine the value of a variable.
• Science: In physics and engineering, solving for n can help determine the value of a variable in a mathematical model.
• Business: In business, solving for n can help determine the value of a variable in a financial model.

Final Thoughts

Solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$ is a fundamental concept in mathematics, particularly in algebra. By following the step-by-step process outlined in this article, you can solve for n and apply the concept to real-world applications. Remember to isolate the variable on one side of the equation, simplify fractions, and find a common denominator when subtracting fractions.

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Introduction

In our previous article, we explored the step-by-step process of solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$. In this article, we will address some of the most frequently asked questions related to solving for n in linear equations.

Q: What is the first step in solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$?

A: The first step in solving for n is to subtract $\frac{3}{8}$ from both sides of the equation. This will allow us to isolate the variable n on one side of the equation.

Q: Why do we need to find a common denominator when subtracting fractions?

A: When subtracting fractions, we need to find a common denominator to ensure that we are subtracting the same units. In this case, the common denominator is 8, which allows us to subtract the numerators and simplify the right-hand side of the equation.

Q: Can we simplify the fraction $\frac{4}{8}$ further?

A: Yes, we can simplify the fraction $\frac{4}{8}$ further by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This results in the simplified fraction $\frac{1}{2}$.

Q: What is the value of n in the equation $\frac{3}{8} + n = \frac{7}{8}$?

A: The value of n in the equation $\frac{3}{8} + n = \frac{7}{8}$ is $\frac{1}{2}$.

Q: How do we apply the concept of solving for n in real-world applications?

A: The concept of solving for n in linear equations has real-world applications in various fields, such as finance, science, and business. For example, in finance, solving for n can help determine the value of a variable in a financial model. In science, solving for n can help determine the value of a variable in a mathematical model.

Q: What are some common mistakes to avoid when solving for n in linear equations?

A: Some common mistakes to avoid when solving for n in linear equations include:

• Not isolating the variable n on one side of the equation
• Not finding a common denominator when subtracting fractions
• Not simplifying fractions by dividing both the numerator and the denominator by their greatest common divisor

Q: Can we use the concept of solving for n in linear equations to solve other types of equations?

A: Yes, the concept of solving for n in linear equations can be applied to other types of equations, such as quadratic equations and polynomial equations. However, the steps and techniques used may vary depending on the type of equation.

Q: How do we determine the value of n in an equation with multiple variables?

A: To determine the value of n in an equation with multiple variables, we need to isolate the variable n on one side of the equation and then solve for its value. This may involve using algebraic techniques, such as substitution and elimination, to solve for the value of n.

Conclusion

In conclusion, solving for n in the equation $\frac{3}{8} + n = \frac{7}{8}$ is a fundamental concept in mathematics, particularly in algebra. By following the step-by-step process outlined in this article, you can solve for n and apply the concept to real-world applications. Remember to isolate the variable n on one side of the equation, simplify fractions, and find a common denominator when subtracting fractions.

Final Thoughts

Solving for n in linear equations is a critical skill that has real-world applications in various fields. By mastering this concept, you can apply it to solve problems in finance, science, and business. Remember to avoid common mistakes, such as not isolating the variable n on one side of the equation, and to simplify fractions by dividing both the numerator and the denominator by their greatest common divisor.