Solve For \[$ B \$\] In The Equation:$\[ \frac{3}{2} + B = \frac{7}{4} \\]Find \[$ B = \$\]

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving for the variable $b$ in the equation $\frac{3}{2} + b = \frac{7}{4}$. This equation involves fractions, and we will use algebraic techniques to isolate the variable $b$.

Understanding the Equation

The given equation is $\frac{3}{2} + b = \frac{7}{4}$. To solve for $b$, we need to isolate the variable on one side of the equation. The equation involves fractions, and we will use the concept of equivalent ratios to simplify the equation.

Step 1: Simplify the Equation

To simplify the equation, we can start by finding the least common multiple (LCM) of the denominators, which are 2 and 4. The LCM of 2 and 4 is 4. We can multiply both sides of the equation by 4 to eliminate the fractions.

$\frac{3}{2} + b = \frac{7}{4}$

Multiplying both sides by 4:

$4 \times \frac{3}{2} + 4b = 4 \times \frac{7}{4}$

Simplifying the equation:

$6 + 4b = 7$

Step 2: Isolate the Variable

Now that we have simplified the equation, we can isolate the variable $b$ by subtracting 6 from both sides of the equation.

$6 + 4b = 7$

Subtracting 6 from both sides:

$4b = 1$

Step 3: Solve for b

To solve for $b$, we can divide both sides of the equation by 4.

$4b = 1$

Dividing both sides by 4:

$b = \frac{1}{4}$

Conclusion

In this article, we solved for the variable $b$ in the equation $\frac{3}{2} + b = \frac{7}{4}$. We used algebraic techniques to isolate the variable $b$ and found that $b = \frac{1}{4}$. This equation involves fractions, and we used the concept of equivalent ratios to simplify the equation.

Tips and Tricks

• When solving equations involving fractions, it's essential to find the least common multiple (LCM) of the denominators to simplify the equation.
• Use algebraic techniques to isolate the variable on one side of the equation.
• Be careful when multiplying or dividing both sides of the equation by a fraction, as this can affect the value of the variable.

Real-World Applications

Solving equations involving fractions has many real-world applications, such as:

• Finance: When calculating interest rates or investment returns, fractions are often used to represent the interest or return on investment.
• Science: In physics and chemistry, fractions are used to represent measurements and calculations.
• Engineering: In engineering, fractions are used to represent dimensions and calculations.

Final Thoughts

Solving equations involving fractions requires a strong understanding of algebraic techniques and the concept of equivalent ratios. By following the steps outlined in this article, you can solve for the variable $b$ in the equation $\frac{3}{2} + b = \frac{7}{4}$. Remember to be careful when working with fractions and to use algebraic techniques to isolate the variable on one side of the equation.

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Introduction

In our previous article, we solved for the variable $b$ in the equation $\frac{3}{2} + b = \frac{7}{4}$. We used algebraic techniques to isolate the variable $b$ and found that $b = \frac{1}{4}$. In this article, we will answer some frequently asked questions (FAQs) related to solving equations involving fractions.

Q&A

Q: What is the least common multiple (LCM) of 2 and 4?

A: The least common multiple (LCM) of 2 and 4 is 4.

Q: Why do we need to find the LCM of the denominators?

A: We need to find the LCM of the denominators to simplify the equation and eliminate the fractions.

Q: How do we simplify the equation?

A: We can simplify the equation by multiplying both sides of the equation by the LCM of the denominators.

Q: What is the first step in solving the equation?

A: The first step in solving the equation is to simplify the equation by finding the LCM of the denominators and multiplying both sides of the equation by the LCM.

Q: How do we isolate the variable $b$?

A: We can isolate the variable $b$ by subtracting 6 from both sides of the equation.

Q: What is the final answer for the variable $b$?

A: The final answer for the variable $b$ is $\frac{1}{4}$.

Q: What are some real-world applications of solving equations involving fractions?

A: Some real-world applications of solving equations involving fractions include finance, science, and engineering.

Q: What are some tips and tricks for solving equations involving fractions?

A: Some tips and tricks for solving equations involving fractions include finding the LCM of the denominators, using algebraic techniques to isolate the variable, and being careful when multiplying or dividing both sides of the equation by a fraction.

Common Mistakes

• Not finding the LCM of the denominators before simplifying the equation.
• Not using algebraic techniques to isolate the variable.
• Not being careful when multiplying or dividing both sides of the equation by a fraction.

Conclusion

Solving equations involving fractions requires a strong understanding of algebraic techniques and the concept of equivalent ratios. By following the steps outlined in this article and answering the FAQs, you can solve for the variable $b$ in the equation $\frac{3}{2} + b = \frac{7}{4}$. Remember to be careful when working with fractions and to use algebraic techniques to isolate the variable on one side of the equation.

Additional Resources

• For more information on solving equations involving fractions, check out our previous article on the topic.
• For practice problems and exercises, try solving equations involving fractions on your own or with a partner.
• For additional resources and support, consider consulting a math tutor or teacher.

Final Thoughts

Solving equations involving fractions is an essential skill in mathematics, and with practice and patience, you can become proficient in solving these types of equations. Remember to be careful when working with fractions and to use algebraic techniques to isolate the variable on one side of the equation.