Solve For { X $}$ In The Equation:${ \frac{x}{24} = \frac{28}{36} }$

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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 ${ x }$ in the equation ${ \frac{x}{24} = \frac{28}{36} }$. This equation involves fractions, and we will use various techniques to simplify and solve for ${ x }$.

Understanding the Equation

The given equation is ${ \frac{x}{24} = \frac{28}{36} }$. To solve for ${ x }$, we need to isolate the variable ${ x }$ on one side of the equation. The equation involves two fractions, and we can start by simplifying the fractions to make the equation easier to solve.

Simplifying the Fractions

To simplify the fractions, we can find the greatest common divisor (GCD) of the numerator and denominator of each fraction. The GCD of 24 and 36 is 12. We can divide both the numerator and denominator of each fraction by 12 to simplify them.

${ \frac{x}{24} = \frac{28}{36} }$

${ \frac{x}{2 \times 12} = \frac{2 \times 14}{2 \times 18} }$

${ \frac{x}{2 \times 12} = \frac{14}{18} }$

Cross-Multiplication

Now that we have simplified the fractions, we can use cross-multiplication to eliminate the fractions. Cross-multiplication involves multiplying both sides of the equation by the denominators of the fractions.

${ \frac{x}{2 \times 12} = \frac{14}{18} }$

${ x \times 18 = 14 \times 2 \times 12 }$

${ 18x = 336 }$

Solving for ${ x }$

Now that we have eliminated the fractions, we can solve for ${ x }$ by dividing both sides of the equation by 18.

${ 18x = 336 }$

${ x = \frac{336}{18} }$

${ x = 18.67 }$

Conclusion

In this article, we solved for ${ x }$ in the equation ${ \frac{x}{24} = \frac{28}{36} }$. We simplified the fractions, used cross-multiplication to eliminate the fractions, and finally solved for ${ x }$ by dividing both sides of the equation by 18. The value of ${ x }$ is approximately 18.67.

Tips and Tricks

• When solving equations involving fractions, it's essential to simplify the fractions to make the equation easier to solve.
• Cross-multiplication is a useful technique to eliminate fractions in equations.
• When solving for ${ x }$, make sure to isolate the variable ${ x }$ on one side of the equation.

Real-World Applications

Solving equations involving fractions has numerous real-world applications. For example, in finance, we often use equations involving fractions to calculate interest rates, investment returns, and other financial metrics. In science, we use equations involving fractions to model physical systems, such as the motion of objects and the behavior of electrical circuits.

Common Mistakes

• When simplifying fractions, make sure to find the greatest common divisor (GCD) of the numerator and denominator.
• When using cross-multiplication, make sure to multiply both sides of the equation by the denominators of the fractions.
• When solving for ${ x }$, make sure to isolate the variable ${ x }$ on one side of the equation.

Final Thoughts

Solving equations involving fractions is a fundamental concept in mathematics that has numerous real-world applications. By simplifying fractions, using cross-multiplication, and solving for ${ x }$, we can solve a wide range of equations and make informed decisions in various fields.

Introduction

In our previous article, we discussed how to solve equations involving fractions. However, we understand that there may be some questions and doubts that readers may have. In this article, we will address some of the frequently asked questions (FAQs) on solving equations involving fractions.

Q: What is the greatest common divisor (GCD) and how do I find it?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. To find the GCD, you can use the Euclidean algorithm or simply list the factors of each number and find the largest common factor.

Q: How do I simplify fractions?

A: To simplify fractions, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What is cross-multiplication and how do I use it?

A: Cross-multiplication is a technique used to eliminate fractions in equations. To use cross-multiplication, you multiply both sides of the equation by the denominators of the fractions.

Q: How do I solve for x in an equation involving fractions?

A: To solve for x in an equation involving fractions, you need to isolate the variable x on one side of the equation. You can do this by simplifying the fractions, using cross-multiplication, and then solving for x.

Q: What are some common mistakes to avoid when solving equations involving fractions?

A: Some common mistakes to avoid when solving equations involving fractions include:

• Not simplifying the fractions before solving the equation
• Not using cross-multiplication to eliminate fractions
• Not isolating the variable x on one side of the equation
• Not checking the solution for accuracy

Q: How do I check the solution for accuracy?

A: To check the solution for accuracy, you can plug the solution back into the original equation and verify that it is true.

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

A: Solving equations involving fractions has numerous real-world applications, including:

• Finance: calculating interest rates, investment returns, and other financial metrics
• Science: modeling physical systems, such as the motion of objects and the behavior of electrical circuits
• Engineering: designing and optimizing systems, such as bridges and buildings

Q: Can I use a calculator to solve equations involving fractions?

A: Yes, you can use a calculator to solve equations involving fractions. However, it's essential to understand the underlying math and be able to solve the equation by hand.

Q: How do I practice solving equations involving fractions?

A: To practice solving equations involving fractions, you can try the following:

• Start with simple equations and gradually move to more complex ones
• Use online resources, such as worksheets and practice problems
• Work with a partner or tutor to get feedback and guidance
• Review and practice regularly to build your skills and confidence

Conclusion

Solving equations involving fractions is a fundamental concept in mathematics that has numerous real-world applications. By understanding the concepts and techniques discussed in this article, you can build your skills and confidence in solving equations involving fractions. Remember to practice regularly and seek help when needed to become proficient in solving equations involving fractions.

Additional Resources

• Online resources, such as Khan Academy and Mathway, offer video lessons and practice problems on solving equations involving fractions.
• Textbooks and workbooks, such as "Algebra and Trigonometry" by Michael Sullivan, provide comprehensive coverage of solving equations involving fractions.
• Online communities, such as Reddit's r/learnmath, offer a platform to ask questions and get feedback from experienced mathematicians and educators.

Final Thoughts

Solving equations involving fractions is a skill that takes practice and patience to develop. By following the tips and techniques discussed in this article, you can build your skills and confidence in solving equations involving fractions. Remember to practice regularly and seek help when needed to become proficient in solving equations involving fractions.