Solve The Proportion Below.${ \frac{5}{x} = \frac{1}{4} }$x = A. 8 B. 15 C. 10 D. 20

Understanding Proportions

A proportion is a statement that two ratios are equal. It is often written in the form of an equation, where the ratios are set equal to each other. In this article, we will focus on solving proportions, specifically the proportion $\frac{5}{x} = \frac{1}{4}$.

What is a Proportion?

A proportion is a mathematical statement that two ratios are equal. It is often written in the form of an equation, where the ratios are set equal to each other. For example, the proportion $\frac{a}{b} = \frac{c}{d}$ states that the ratio of $a$ to $b$ is equal to the ratio of $c$ to $d$.

Why are Proportions Important?

Proportions are an essential concept in mathematics, and they have numerous real-world applications. They are used in various fields, such as finance, engineering, and science, to solve problems and make informed decisions. In this article, we will focus on solving proportions, specifically the proportion $\frac{5}{x} = \frac{1}{4}$.

Solving the Proportion

To solve the proportion $\frac{5}{x} = \frac{1}{4}$, we need to find the value of $x$. We can do this by cross-multiplying, which means multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.

Step 1: Cross-Multiply

Cross-multiplying the proportion $\frac{5}{x} = \frac{1}{4}$ gives us:

$$5 \cdot 4 = x \cdot 1$$

Step 2: Simplify

Simplifying the equation $5 \cdot 4 = x \cdot 1$ gives us:

$$20 = x$$

Step 3: Check the Answer

To check our answer, we can plug the value of $x$ back into the original proportion and see if it is true.

$$\frac{5}{20} = \frac{1}{4}$$

Since this is true, we can conclude that the value of $x$ is indeed 20.

Conclusion

In this article, we solved the proportion $\frac{5}{x} = \frac{1}{4}$ by cross-multiplying and simplifying the equation. We found that the value of $x$ is 20. This is an important concept in mathematics, and it has numerous real-world applications. We hope that this article has helped you understand how to solve proportions and has provided you with a better understanding of this important mathematical concept.

Answer

The correct answer is D. 20.

Additional Examples

Here are a few additional examples of proportions:

• $\frac{2}{x} = \frac{3}{5}$
• $\frac{x}{4} = \frac{2}{3}$
• $\frac{1}{x} = \frac{2}{5}$

Try solving these proportions on your own, and see if you can find the correct values of $x$.

Tips and Tricks

Here are a few tips and tricks for solving proportions:

• Make sure to cross-multiply correctly.
• Simplify the equation as much as possible.
• Check your answer by plugging it back into the original proportion.

By following these tips and tricks, you can become a pro at solving proportions and can apply this important mathematical concept to real-world problems.

Real-World Applications

Proportions have numerous real-world applications. Here are a few examples:

• Finance: Proportions are used to calculate interest rates and investment returns.
• Engineering: Proportions are used to design and build structures, such as bridges and buildings.
• Science: Proportions are used to measure and analyze data in various scientific fields, such as physics and biology.

By understanding how to solve proportions, you can apply this important mathematical concept to real-world problems and can make informed decisions in various fields.

Conclusion

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is often written in the form of an equation, where the ratios are set equal to each other.

Q: How do I solve a proportion?

A: To solve a proportion, you need to cross-multiply and simplify the equation. This involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.

Q: What is cross-multiplication?

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

Q: How do I check my answer?

A: To check your answer, you need to plug the value of the unknown variable back into the original proportion and see if it is true.

Q: What are some common mistakes to avoid when solving proportions?

A: Some common mistakes to avoid when solving proportions include:

• Not cross-multiplying correctly
• Not simplifying the equation
• Not checking the answer

Q: Can you give me an example of a proportion?

A: Here is an example of a proportion:

$\frac{5}{x} = \frac{1}{4}$

To solve this proportion, you would cross-multiply and simplify the equation to find the value of $x$.

Q: How do I know if a proportion is true or false?

A: To determine if a proportion is true or false, you need to check if the ratios are equal. If the ratios are equal, then the proportion is true. If the ratios are not equal, then the proportion is false.

Q: Can you give me some real-world examples of proportions?

A: Here are some real-world examples of proportions:

• A recipe for baking a cake calls for a ratio of 2 cups of flour to 1 cup of sugar. If you want to make a larger cake, you would need to increase the ratio of flour to sugar.
• A car's fuel efficiency is measured in miles per gallon. If a car gets 25 miles per gallon, and you drive 100 miles, you would need to calculate the amount of fuel used to determine the cost of the trip.
• A builder needs to calculate the amount of materials required to build a house. If the house requires a ratio of 2:1 of bricks to mortar, and the builder wants to build a house that is twice as large, they would need to increase the ratio of bricks to mortar.

Q: How do I apply proportions to real-world problems?

A: To apply proportions to real-world problems, you need to identify the ratios and relationships between the variables. You can then use the proportion to solve for the unknown variable and make informed decisions.

Q: Can you give me some tips for solving proportions?

A: Here are some tips for solving proportions:

• Make sure to cross-multiply correctly
• Simplify the equation as much as possible
• Check your answer by plugging it back into the original proportion
• Use real-world examples to help you understand the concept of proportions
• Practice, practice, practice! The more you practice solving proportions, the more comfortable you will become with the concept.