What Value Of $x$ Makes This Proportion True?$\frac{x}{6}=\frac{36}{24}$A. 9 B. 8 C. 7 D. 18

Understanding Proportions and Solving for x

In mathematics, proportions are used to compare two ratios or fractions. A proportion is a statement that two ratios are equal, and it can be written in the form: $\frac{a}{b}=\frac{c}{d}$. In this article, we will explore how to solve for x in a proportion, using the given equation: $\frac{x}{6}=\frac{36}{24}$.

The Importance of Proportions in Real-Life Scenarios

Proportions are used in various real-life scenarios, such as finance, engineering, and science. For example, in finance, proportions are used to calculate interest rates, investment returns, and risk management. In engineering, proportions are used to design and optimize systems, such as bridges, buildings, and electronic circuits. In science, proportions are used to understand and describe natural phenomena, such as the behavior of particles, the movement of celestial bodies, and the properties of materials.

Solving for x in a Proportion

To solve for x in a proportion, we need to follow these steps:

1. Cross-multiply: Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This will give us a new equation with x as the subject.
2. Simplify: Simplify the equation by canceling out any common factors.
3. Solve for x: Solve for x by isolating it on one side of the equation.

Applying the Steps to the Given Equation

Let's apply the steps to the given equation: $\frac{x}{6}=\frac{36}{24}$.

Step 1: Cross-multiply

To cross-multiply, we multiply the numerator of the first fraction (x) by the denominator of the second fraction (24), and vice versa. This gives us:

$x \times 24 = 6 \times 36$

Step 2: Simplify

Simplifying the equation, we get:

$24x = 216$

Step 3: Solve for x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 24:

$x = \frac{216}{24}$

$x = 9$

Conclusion

In this article, we explored how to solve for x in a proportion using the given equation: $\frac{x}{6}=\frac{36}{24}$. We followed the steps of cross-multiplying, simplifying, and solving for x to find the value of x. The final answer is x = 9.

Answer Key

The correct answer is A. 9.

Additional Examples

Here are some additional examples of proportions and how to solve for x:

• $\frac{x}{8}=\frac{32}{24}$: x = 8
• $\frac{x}{12}=\frac{36}{24}$: x = 3
• $\frac{x}{20}=\frac{40}{24}$: x = 4

Tips and Tricks

Here are some tips and tricks to help you solve proportions:

• Make sure to cross-multiply correctly.
• Simplify the equation by canceling out any common factors.
• Solve for x by isolating it on one side of the equation.
• Check your answer by plugging it back into the original equation.

Conclusion

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It can be written in the form: $\frac{a}{b}=\frac{c}{d}$.

Q: How do I solve for x in a proportion?

A: To solve for x in a proportion, you need to follow these steps:

1. Cross-multiply: Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.
2. Simplify: Simplify the equation by canceling out any common factors.
3. Solve for x: Solve for x by isolating it on one side of the equation.

Q: What is cross-multiplication?

A: Cross-multiplication is the process of multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This is done to eliminate the fractions and solve for x.

Q: How do I simplify an equation?

A: To simplify an equation, you need to cancel out any common factors. This involves dividing both sides of the equation by the common factor.

Q: What is the importance of proportions in real-life scenarios?

A: Proportions are used in various real-life scenarios, such as finance, engineering, and science. For example, in finance, proportions are used to calculate interest rates, investment returns, and risk management. In engineering, proportions are used to design and optimize systems, such as bridges, buildings, and electronic circuits. In science, proportions are used to understand and describe natural phenomena, such as the behavior of particles, the movement of celestial bodies, and the properties of materials.

Q: Can you provide more examples of proportions and how to solve for x?

A: Here are some additional examples of proportions and how to solve for x:

• $\frac{x}{8}=\frac{32}{24}$: x = 8
• $\frac{x}{12}=\frac{36}{24}$: x = 3
• $\frac{x}{20}=\frac{40}{24}$: x = 4

Q: What are some tips and tricks for solving proportions?

A: Here are some tips and tricks to help you solve proportions:

• Make sure to cross-multiply correctly.
• Simplify the equation by canceling out any common factors.
• Solve for x by isolating it on one side of the equation.
• Check your answer by plugging it back into the original equation.

Q: How do I check my answer?

A: To check your answer, you need to plug it back into the original equation. If the equation holds true, then your answer is correct.

Q: What if I get stuck or need help solving a proportion?

A: If you get stuck or need help solving a proportion, don't hesitate to ask for help. You can ask a teacher, tutor, or classmate for assistance. Additionally, you can use online resources, such as video tutorials and practice problems, to help you understand and solve proportions.

Conclusion

Proportions are an essential concept in mathematics, and solving for x in a proportion is a crucial skill to master. By following the steps of cross-multiplying, simplifying, and solving for x, you can solve proportions and apply them to real-life scenarios. Remember to check your answer by plugging it back into the original equation, and don't hesitate to ask for help if you need it.