Solve For The Variable In $\frac{7}{28} = \frac{25}{x}$.A) 4 B) 20 C) 5 D) 100
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Introduction
In mathematics, solving for a variable in a fractional equation is a fundamental concept that involves manipulating the equation to isolate the variable. This process requires a deep understanding of algebraic operations and the properties of fractions. In this article, we will explore how to solve for the variable in the equation $\frac{7}{28} = \frac{25}{x}$.
Understanding the Equation
The given equation is a simple fractional equation, where the left-hand side is equal to the right-hand side. To solve for the variable x, we need to manipulate the equation to isolate x. The equation can be rewritten as:
Step 1: Simplify the Left-Hand Side
The first step in solving the equation is to simplify the left-hand side. We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 7 and 28 is 7.
Step 2: Cross-Multiply
Now that we have simplified the left-hand side, we can cross-multiply to eliminate the fractions. Cross-multiplying involves multiplying both sides of the equation by the denominators of the fractions.
Conclusion
In this article, we have demonstrated how to solve for the variable in the equation $\frac{7}{28} = \frac{25}{x}$. By simplifying the left-hand side and cross-multiplying, we were able to isolate the variable x and find its value. The final answer is x = 100.
Final Answer
The final answer is D) 100.
Frequently Asked Questions
Q: What is the greatest common divisor (GCD) of 7 and 28?
A: The GCD of 7 and 28 is 7.
Q: How do I simplify the left-hand side of the equation?
A: To simplify the left-hand side, divide both the numerator and the denominator by their greatest common divisor (GCD).
Q: What is cross-multiplication?
A: Cross-multiplication involves multiplying both sides of the equation by the denominators of the fractions.
Q: How do I isolate the variable x?
A: To isolate the variable x, simplify the left-hand side and cross-multiply.
Additional Resources
For more information on solving fractional equations, check out the following resources:
- Khan Academy: Solving Equations with Fractions
- Mathway: Solving Equations with Fractions
- Wolfram Alpha: Solving Equations with Fractions
Related Topics
- Solving Linear Equations
- Solving Quadratic Equations
- Solving Systems of Equations
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Introduction
In our previous article, we explored how to solve for the variable in the equation $\frac{7}{28} = \frac{25}{x}$. We demonstrated the steps involved in simplifying the left-hand side and cross-multiplying to isolate the variable x. In this article, we will address some of the most frequently asked questions related to solving for the variable in a fractional equation.
Q&A
Q: What is the greatest common divisor (GCD) of 7 and 28?
A: The GCD of 7 and 28 is 7.
Q: How do I simplify the left-hand side of the equation?
A: To simplify the left-hand side, divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, we divided both 7 and 28 by 7 to get $\frac{1}{4}$.
Q: What is cross-multiplication?
A: Cross-multiplication involves multiplying both sides of the equation by the denominators of the fractions. In this case, we multiplied both sides by x to get $1 \cdot x = 25 \cdot 4$.
Q: How do I isolate the variable x?
A: To isolate the variable x, simplify the left-hand side and cross-multiply. In this case, we simplified the left-hand side to $\frac{1}{4}$ and then cross-multiplied to get $x = 100$.
Q: What if the equation has a variable in the denominator?
A: If the equation has a variable in the denominator, you will need to multiply both sides of the equation by the denominator to eliminate it. For example, if the equation is $\frac{7}{x} = \frac{25}{28}$, you would multiply both sides by x to get $7 = \frac{25x}{28}$.
Q: Can I use a calculator to solve for the variable?
A: Yes, you can use a calculator to solve for the variable. However, it's always a good idea to check your work by plugging the solution back into the original equation.
Q: What if I get a negative solution?
A: If you get a negative solution, it's possible that the solution is extraneous. You should plug the solution back into the original equation to check if it's true.
Tips and Tricks
- Always simplify the left-hand side of the equation before cross-multiplying.
- Make sure to multiply both sides of the equation by the same value.
- Check your work by plugging the solution back into the original equation.
- If you get a negative solution, it's possible that the solution is extraneous.
Common Mistakes
- Failing to simplify the left-hand side of the equation.
- Not multiplying both sides of the equation by the same value.
- Not checking the solution by plugging it back into the original equation.
- Getting a negative solution without checking if it's extraneous.
Conclusion
Solving for the variable in a fractional equation can be a challenging task, but with practice and patience, you can master it. Remember to simplify the left-hand side, cross-multiply, and check your work to ensure that your solution is correct. If you have any further questions or concerns, feel free to ask.
Final Answer
The final answer is D) 100.
Additional Resources
For more information on solving fractional equations, check out the following resources:
- Khan Academy: Solving Equations with Fractions
- Mathway: Solving Equations with Fractions
- Wolfram Alpha: Solving Equations with Fractions
Related Topics
- Solving Linear Equations
- Solving Quadratic Equations
- Solving Systems of Equations