Solve For W W W .${ \frac{5}{11} = W - \frac{5}{11} }$ { W = \}

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Introduction

In mathematics, solving for a variable is a fundamental concept that is used to find the value of a variable in an equation. In this article, we will focus on solving for $w$ in the given equation $\frac{5}{11} = w - \frac{5}{11}$. We will break down the solution step by step, making it easy to understand and follow.

Understanding the Equation

The given equation is $\frac{5}{11} = w - \frac{5}{11}$. To solve for $w$, we need to isolate the variable $w$ on one side of the equation. The equation can be rewritten as $\frac{5}{11} + \frac{5}{11} = w$.

Adding Fractions

To add fractions, we need to have the same denominator. In this case, the denominators are both $11$. Therefore, we can add the fractions by adding the numerators and keeping the denominator the same.

$\frac{5}{11} + \frac{5}{11} = \frac{5+5}{11} = \frac{10}{11}$

Simplifying the Equation

Now that we have added the fractions, we can simplify the equation by combining the terms on the left-hand side.

$\frac{10}{11} = w$

Isolating the Variable

To isolate the variable $w$, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by the denominator, which is $11$.

$\frac{10}{11} \times 11 = w \times 11$

Simplifying the Equation

Now that we have multiplied both sides of the equation by $11$, we can simplify the equation by canceling out the denominator.

$10 = 11w$

Dividing Both Sides

To isolate the variable $w$, we need to get rid of the coefficient $11$. We can do this by dividing both sides of the equation by $11$.

$\frac{10}{11} = w$

Simplifying the Equation

Now that we have divided both sides of the equation by $11$, we can simplify the equation by canceling out the fraction.

$w = \frac{10}{11}$

Conclusion

In this article, we have solved for $w$ in the given equation $\frac{5}{11} = w - \frac{5}{11}$. We have broken down the solution step by step, making it easy to understand and follow. We have added fractions, simplified the equation, isolated the variable, and finally solved for $w$. The final solution is $w = \frac{10}{11}$.

Tips and Tricks

• When solving for a variable, make sure to isolate the variable on one side of the equation.
• When adding fractions, make sure to have the same denominator.
• When simplifying an equation, make sure to cancel out any common factors.
• When dividing both sides of an equation, make sure to divide both sides by the same value.

Common Mistakes

• Not isolating the variable on one side of the equation.
• Not having the same denominator when adding fractions.
• Not canceling out common factors when simplifying an equation.
• Not dividing both sides of the equation by the same value.

Real-World Applications

Solving for a variable is a fundamental concept that is used in many real-world applications. For example, in physics, solving for a variable can help us understand the motion of an object. In engineering, solving for a variable can help us design and build complex systems. In finance, solving for a variable can help us make informed investment decisions.

Final Thoughts

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Introduction

In our previous article, we solved for $w$ in the given equation $\frac{5}{11} = w - \frac{5}{11}$. We broke down the solution step by step, making it easy to understand and follow. In this article, we will answer some frequently asked questions about solving for $w$.

Q: What is the first step in solving for $w$?

A: The first step in solving for $w$ is to isolate the variable $w$ on one side of the equation. This can be done by adding or subtracting the same value from both sides of the equation.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. Then, you can rewrite each fraction with the LCM as the denominator and add the fractions.

Q: What is the difference between adding and subtracting fractions?

A: Adding fractions involves combining the numerators and keeping the same denominator. Subtracting fractions involves combining the numerators and changing the sign of the second fraction.

Q: How do I simplify an equation?

A: To simplify an equation, you need to cancel out any common factors in the numerator and denominator. This can be done by dividing both the numerator and denominator by the common factor.

Q: What is the final step in solving for $w$?

A: The final step in solving for $w$ is to isolate the variable $w$ on one side of the equation. This can be done by dividing both sides of the equation by the coefficient of $w$.

Q: What are some common mistakes to avoid when solving for $w$?

A: Some common mistakes to avoid when solving for $w$ include:

• Not isolating the variable $w$ on one side of the equation
• Not having the same denominator when adding fractions
• Not canceling out common factors when simplifying an equation
• Not dividing both sides of the equation by the same value

Q: How can I apply solving for $w$ to real-world problems?

A: Solving for $w$ can be applied to many real-world problems, such as:

• Physics: Solving for $w$ can help us understand the motion of an object.
• Engineering: Solving for $w$ can help us design and build complex systems.
• Finance: Solving for $w$ can help us make informed investment decisions.

Q: What are some tips for solving for $w$?

A: Some tips for solving for $w$ include:

• Make sure to isolate the variable $w$ on one side of the equation.
• Make sure to have the same denominator when adding fractions.
• Make sure to cancel out common factors when simplifying an equation.
• Make sure to divide both sides of the equation by the same value.

Conclusion

Solving for $w$ is a crucial skill that is used in many areas of mathematics and science. By following the steps outlined in this article, you can solve for $w$ with ease. Remember to isolate the variable $w$ on one side of the equation, add fractions with the same denominator, simplify the equation by canceling out common factors, and finally solve for the variable. With practice and patience, you can become proficient in solving for $w$ and apply it to real-world problems.

Additional Resources

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

Final Thoughts

Solving for $w$ is a fundamental concept that is used in many areas of mathematics and science. By following the steps outlined in this article, you can solve for $w$ with ease. Remember to isolate the variable $w$ on one side of the equation, add fractions with the same denominator, simplify the equation by canceling out common factors, and finally solve for the variable. With practice and patience, you can become proficient in solving for $w$ and apply it to real-world problems.