Solve For X. X 20 = 6 8 \frac{x}{20} = \frac{6}{8} 20 X ​ = 8 6 ​

$$

Introduction

Solving equations involving fractions can be a challenging task, especially for those who are new to algebra. However, with the right approach and a clear understanding of the concepts, solving these types of equations can become a breeze. In this article, we will focus on solving the equation $\frac{x}{20} = \frac{6}{8}$, and we will break down the solution into simple, easy-to-follow steps.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at what it means. The equation $\frac{x}{20} = \frac{6}{8}$ states that the ratio of $x$ to $20$ is equal to the ratio of $6$ to $8$. In other words, if we were to divide $x$ by $20$, we would get the same result as if we were to divide $6$ by $8$.

Step 1: Simplify the Fractions

To solve the equation, we need to simplify the fractions on both sides. We can do this by finding the greatest common divisor (GCD) of the numerator and denominator of each fraction. In this case, the GCD of $6$ and $8$ is $2$, so we can simplify the fractions as follows:

$$\frac{x}{20} = \frac{6}{8} \Rightarrow \frac{x}{20} = \frac{3}{4}$$

Step 2: Cross-Multiply

Now that we have simplified the fractions, we can cross-multiply to get rid of the fractions. To do this, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us:

$$x \cdot 4 = 20 \cdot 3$$

Step 3: Solve for x

Now that we have cross-multiplied, we can solve for $x$ by dividing both sides of the equation by $4$. This gives us:

$$x = \frac{20 \cdot 3}{4}$$

Step 4: Simplify the Expression

To simplify the expression, we can divide $20$ by $4$ to get $5$, and then multiply $5$ by $3$ to get $15$. This gives us:

$$x = 15$$

Conclusion

And there you have it! We have successfully solved the equation $\frac{x}{20} = \frac{6}{8}$ by simplifying the fractions, cross-multiplying, and solving for $x$. The final answer is $x = 15$.

Tips and Tricks

• When solving equations involving fractions, it's often helpful to simplify the fractions first.
• Cross-multiplying can be a useful technique for getting rid of fractions.
• Make sure to check your work by plugging the solution back into the original equation.

Real-World Applications

Solving equations involving fractions has many real-world applications. For example, in finance, you may need to calculate the interest rate on a loan or investment. In science, you may need to calculate the concentration of a solution or the rate of a chemical reaction. In engineering, you may need to calculate the stress on a material or the flow rate of a fluid.

Common Mistakes

• Failing to simplify the fractions before solving the equation.
• Forgetting to cross-multiply.
• Not checking the solution by plugging it back into the original equation.

Conclusion

Solving equations involving fractions can be a challenging task, but with the right approach and a clear understanding of the concepts, it can become a breeze. By simplifying the fractions, cross-multiplying, and solving for $x$, we can successfully solve equations like $\frac{x}{20} = \frac{6}{8}$. Remember to check your work and to apply the concepts to real-world problems.

Final Answer

The final answer is: $\boxed{15}$

$$

Introduction

In our previous article, we solved the equation $\frac{x}{20} = \frac{6}{8}$ by simplifying the fractions, cross-multiplying, and solving for $x$. However, we know that practice makes perfect, and the best way to learn is by doing. In this article, we will provide a Q&A guide to help you practice solving equations like $\frac{x}{20} = \frac{6}{8}$.

Q&A Guide

Q: What is the first step in solving the equation $\frac{x}{20} = \frac{6}{8}$?

A: The first step in solving the equation $\frac{x}{20} = \frac{6}{8}$ is to simplify the fractions. We can do this by finding the greatest common divisor (GCD) of the numerator and denominator of each fraction.

Q: How do I simplify the fractions?

A: To simplify the fractions, we need to find the GCD of the numerator and denominator of each fraction. In this case, the GCD of $6$ and $8$ is $2$, so we can simplify the fractions as follows:

$$\frac{x}{20} = \frac{6}{8} \Rightarrow \frac{x}{20} = \frac{3}{4}$$

Q: What is the next step in solving the equation?

A: The next step in solving the equation is to cross-multiply. To do this, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.

Q: How do I cross-multiply?

A: To cross-multiply, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us:

$$x \cdot 4 = 20 \cdot 3$$

Q: What is the final step in solving the equation?

A: The final step in solving the equation is to solve for $x$ by dividing both sides of the equation by $4$.

Q: How do I solve for $x$?

A: To solve for $x$, we divide both sides of the equation by $4$. This gives us:

$$x = \frac{20 \cdot 3}{4}$$

Q: What is the final answer?

A: The final answer is $x = 15$.

Practice Problems

Problem 1

Solve the equation $\frac{x}{15} = \frac{4}{5}$.

Solution

To solve the equation, we need to simplify the fractions. We can do this by finding the GCD of the numerator and denominator of each fraction.

$$\frac{x}{15} = \frac{4}{5} \Rightarrow \frac{x}{15} = \frac{8}{10}$$

Next, we need to cross-multiply. To do this, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.

$$x \cdot 10 = 15 \cdot 8$$

Finally, we need to solve for $x$ by dividing both sides of the equation by $10$.

$$x = \frac{15 \cdot 8}{10}$$

The final answer is $x = 12$.

Problem 2

Solve the equation $\frac{x}{12} = \frac{3}{4}$.

Solution

To solve the equation, we need to simplify the fractions. We can do this by finding the GCD of the numerator and denominator of each fraction.

$$\frac{x}{12} = \frac{3}{4} \Rightarrow \frac{x}{12} = \frac{9}{12}$$

Next, we need to cross-multiply. To do this, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.

$$x \cdot 12 = 12 \cdot 9$$

Finally, we need to solve for $x$ by dividing both sides of the equation by $12$.

$$x = \frac{12 \cdot 9}{12}$$

The final answer is $x = 9$.

Conclusion

Solving equations involving fractions can be a challenging task, but with practice and patience, you can become a pro. Remember to simplify the fractions, cross-multiply, and solve for $x$ to get the final answer. With this Q&A guide, you can practice solving equations like $\frac{x}{20} = \frac{6}{8}$ and become more confident in your math skills.

Final Answer

The final answer is: $\boxed{15}$