Solve For { A $}$ In The Equation:$ \frac{1}{3} + A = \frac{5}{4} }$Choose The Correct Value Of { A $}$ From The Options Below A. { \frac{11 {12}$}$B. { \frac{6}{7}$}$C. { \frac{4}{3}$}$D.

Introduction

In this article, we will delve into the world of algebra and solve for the variable 'a' in a given equation. The equation in question is $\frac{1}{3} + a = \frac{5}{4}$. We will use a step-by-step approach to isolate the variable 'a' and find its correct value.

Understanding the Equation

The given equation is a linear equation, which means it can be solved using basic algebraic operations. The equation is $\frac{1}{3} + a = \frac{5}{4}$. Our goal is to isolate the variable 'a' and find its value.

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

To isolate the variable 'a', we need to get rid of the constant term $\frac{1}{3}$ on the left-hand side of the equation. We can do this by subtracting $\frac{1}{3}$ from both sides of the equation.

$\frac{1}{3} + a - \frac{1}{3} = \frac{5}{4} - \frac{1}{3}$

Simplifying the left-hand side, we get:

$a = \frac{5}{4} - \frac{1}{3}$

Step 2: Find a Common Denominator

To subtract the fractions on the right-hand side, we need to find a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can rewrite the fractions with a common denominator of 12.

$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$

$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Now, we can subtract the fractions:

$a = \frac{15}{12} - \frac{4}{12}$

Step 3: Simplify the Fraction

Simplifying the fraction, we get:

$a = \frac{15 - 4}{12}$

$a = \frac{11}{12}$

Conclusion

We have successfully solved for the variable 'a' in the equation $\frac{1}{3} + a = \frac{5}{4}$. The correct value of 'a' is $\frac{11}{12}$.

Answer Options

A. $\frac{11}{12}$ B. $\frac{6}{7}$ C. $\frac{4}{3}$ D. $\frac{3}{4}$

The correct answer is A. $\frac{11}{12}$.

Discussion

This problem is a great example of how to solve linear equations using basic algebraic operations. By following the steps outlined above, we can isolate the variable 'a' and find its correct value. This type of problem is commonly seen in algebra and is an essential skill to master for anyone studying mathematics.

Related Topics

• Solving linear equations
• Algebraic operations
• Fractions and decimals
• Linear equations with variables on both sides

Practice Problems

Try solving the following problems on your own:

1. Solve for x in the equation $2x + 3 = 7$.
2. Solve for y in the equation $y - 2 = 5$.
3. Solve for z in the equation $z + 1 = 9$.

Conclusion

$$$$

Introduction

In our previous article, we solved for the variable 'a' in the equation $\frac{1}{3} + a = \frac{5}{4}$. We used a step-by-step approach to isolate the variable 'a' and find its correct value. In this article, we will answer some frequently asked questions (FAQs) related to solving linear equations.

Q&A

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

A: The first step in solving a linear equation is to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator. You can then divide both the numerator and denominator by the GCD to simplify the fraction.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, $2x + 3 = 7$ is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a linear equation with variables on both sides?

A: To solve a linear equation with variables on both sides, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the importance of solving linear equations?

A: Solving linear equations is an essential skill in mathematics and is used in a wide range of applications, including physics, engineering, economics, and computer science. It is also a fundamental concept in algebra and is used to solve more complex equations.

Q: How do I check my answer?

A: To check your answer, you need to plug the value of the variable back into the original equation and see if it is true. If it is true, then your answer is correct.

Common Mistakes

• Not isolating the variable on one side of the equation
• Not simplifying the fraction
• Not checking the answer
• Not using the correct order of operations (PEMDAS)

Tips and Tricks

• Always read the problem carefully and understand what is being asked
• Use a step-by-step approach to solve the equation
• Simplify the fraction as much as possible
• Check the answer to make sure it is correct
• Use the correct order of operations (PEMDAS)

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to solving linear equations. We also discussed common mistakes and provided tips and tricks for solving linear equations. By following these tips and tricks, you can become proficient in solving linear equations and move on to more complex equations.

Practice Problems

Try solving the following problems on your own:

1. Solve for x in the equation $2x + 3 = 7$.
2. Solve for y in the equation $y - 2 = 5$.
3. Solve for z in the equation $z + 1 = 9$.

Related Topics

• Solving quadratic equations
• Solving systems of linear equations
• Graphing linear equations
• Linear inequalities

Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations