A B B A = 7 4 \frac{ab}{ba} = \frac{7}{4} Ba Ab ​ = 4 7 ​

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Introduction

In mathematics, solving equations is a fundamental concept that involves manipulating variables and constants to isolate the unknown quantity. The given equation, $\frac{ab}{ba} = \frac{7}{4}$, is a simple algebraic equation that can be solved using basic algebraic manipulations. In this article, we will walk through the step-by-step solution of this equation, highlighting the key concepts and techniques used to arrive at the final answer.

Understanding the Equation

The given equation is a rational equation, which involves fractions and variables. To solve this equation, we need to simplify the fraction on the left-hand side and then equate it to the fraction on the right-hand side. The equation can be rewritten as:

$$\frac{ab}{ba} = \frac{7}{4}$$

Simplifying the Fraction

To simplify the fraction on the left-hand side, we can use the property of fractions that states $\frac{a}{b} = \frac{c}{d}$ if and only if $ad = bc$. Applying this property to the given equation, we get:

$$ab = \frac{7}{4}ba$$

Canceling Out the Common Factor

Now, we can cancel out the common factor of $ba$ from both sides of the equation. This gives us:

$$a = \frac{7}{4}b$$

Isolating the Variable

To isolate the variable $a$, we can multiply both sides of the equation by $\frac{4}{7}$. This gives us:

$$a = b \times \frac{7}{4}$$

Simplifying the Expression

The expression on the right-hand side can be simplified by canceling out the common factor of $b$. This gives us:

$$a = \frac{7}{4}b$$

Conclusion

In conclusion, the equation $\frac{ab}{ba} = \frac{7}{4}$ can be solved by simplifying the fraction on the left-hand side, canceling out the common factor, and isolating the variable. The final answer is $a = \frac{7}{4}b$. This solution demonstrates the importance of basic algebraic manipulations in solving equations and highlights the key concepts and techniques used to arrive at the final answer.

Real-World Applications

The equation $\frac{ab}{ba} = \frac{7}{4}$ has several real-world applications in fields such as physics, engineering, and economics. For example, in physics, the equation can be used to describe the motion of objects in terms of their velocity and acceleration. In engineering, the equation can be used to design and optimize systems such as electrical circuits and mechanical systems. In economics, the equation can be used to model and analyze the behavior of economic systems.

Tips and Tricks

Here are some tips and tricks to help you solve equations like $\frac{ab}{ba} = \frac{7}{4}$:

• Simplify the fraction: Before solving the equation, simplify the fraction on the left-hand side by canceling out any common factors.
• Cancel out the common factor: Once you have simplified the fraction, cancel out the common factor from both sides of the equation.
• Isolate the variable: To isolate the variable, multiply both sides of the equation by the reciprocal of the coefficient of the variable.
• Simplify the expression: Finally, simplify the expression on the right-hand side by canceling out any common factors.

Common Mistakes

Here are some common mistakes to avoid when solving equations like $\frac{ab}{ba} = \frac{7}{4}$:

• Not simplifying the fraction: Failing to simplify the fraction on the left-hand side can lead to incorrect solutions.
• Not canceling out the common factor: Failing to cancel out the common factor from both sides of the equation can lead to incorrect solutions.
• Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
• Not simplifying the expression: Failing to simplify the expression on the right-hand side can lead to incorrect solutions.

Conclusion

In conclusion, solving the equation $\frac{ab}{ba} = \frac{7}{4}$ requires basic algebraic manipulations such as simplifying the fraction, canceling out the common factor, and isolating the variable. By following these steps and avoiding common mistakes, you can arrive at the correct solution and apply it to real-world problems.

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Introduction

In our previous article, we walked through the step-by-step solution of the equation $\frac{ab}{ba} = \frac{7}{4}$. In this article, we will answer some of the most frequently asked questions about solving this equation.

Q: What is the first step in solving the equation $\frac{ab}{ba} = \frac{7}{4}$?

A: The first step in solving the equation $\frac{ab}{ba} = \frac{7}{4}$ is to simplify the fraction on the left-hand side by canceling out any common factors.

Q: How do I simplify the fraction $\frac{ab}{ba}$?

A: To simplify the fraction $\frac{ab}{ba}$, you can use the property of fractions that states $\frac{a}{b} = \frac{c}{d}$ if and only if $ad = bc$. Applying this property to the given fraction, you get $ab = \frac{7}{4}ba$.

Q: What is the next step in solving the equation $\frac{ab}{ba} = \frac{7}{4}$?

A: The next step in solving the equation $\frac{ab}{ba} = \frac{7}{4}$ is to cancel out the common factor of $ba$ from both sides of the equation.

Q: How do I cancel out the common factor of $ba$?

A: To cancel out the common factor of $ba$, you can divide both sides of the equation by $ba$. This gives you $a = \frac{7}{4}b$.

Q: What is the final step in solving the equation $\frac{ab}{ba} = \frac{7}{4}$?

A: The final step in solving the equation $\frac{ab}{ba} = \frac{7}{4}$ is to simplify the expression on the right-hand side by canceling out any common factors.

Q: How do I simplify the expression $a = \frac{7}{4}b$?

A: To simplify the expression $a = \frac{7}{4}b$, you can cancel out the common factor of $b$ from both sides of the equation. This gives you $a = \frac{7}{4}b$.

Q: What are some common mistakes to avoid when solving the equation $\frac{ab}{ba} = \frac{7}{4}$?

A: Some common mistakes to avoid when solving the equation $\frac{ab}{ba} = \frac{7}{4}$ include:

• Not simplifying the fraction on the left-hand side
• Not canceling out the common factor of $ba$ from both sides of the equation
• Not isolating the variable $a$
• Not simplifying the expression on the right-hand side

Q: How can I apply the solution of the equation $\frac{ab}{ba} = \frac{7}{4}$ to real-world problems?

A: The solution of the equation $\frac{ab}{ba} = \frac{7}{4}$ can be applied to real-world problems in fields such as physics, engineering, and economics. For example, in physics, the equation can be used to describe the motion of objects in terms of their velocity and acceleration. In engineering, the equation can be used to design and optimize systems such as electrical circuits and mechanical systems. In economics, the equation can be used to model and analyze the behavior of economic systems.

Q: What are some tips and tricks for solving equations like $\frac{ab}{ba} = \frac{7}{4}$?

A: Some tips and tricks for solving equations like $\frac{ab}{ba} = \frac{7}{4}$ include:

• Simplifying the fraction on the left-hand side
• Canceling out the common factor of $ba$ from both sides of the equation
• Isolating the variable $a$
• Simplifying the expression on the right-hand side

Conclusion

In conclusion, solving the equation $\frac{ab}{ba} = \frac{7}{4}$ requires basic algebraic manipulations such as simplifying the fraction, canceling out the common factor, and isolating the variable. By following these steps and avoiding common mistakes, you can arrive at the correct solution and apply it to real-world problems.