Solve The Proportion Below.${ \frac{x}{29} = \frac{2}{5.8} }$What Is The Value Of { X $}$?A. 5 B. 11.6 C. 10 D. 25.2

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 $\frac{x}{29} = \frac{2}{5.8}$.

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 $\frac{x}{29} = \frac{2}{5.8}$ states that the ratio of $x$ to $29$ is equal to the ratio of $2$ to $5.8$.

Why are Proportions Important?

Proportions are an essential concept in mathematics, particularly in algebra and geometry. They are used to solve problems involving ratios, proportions, and percentages. In real-life situations, proportions are used to compare quantities, such as the ratio of a car's speed to the distance traveled, or the ratio of a recipe's ingredients to the number of servings.

How to Solve a Proportion

To solve a proportion, we need to find the value of the variable (in this case, $x$) that makes the two ratios equal. Here are the steps to solve a proportion:

1. Write the proportion as an equation: Write the proportion as an equation, with the ratios set equal to each other.
2. Cross-multiply: Cross-multiply the two ratios, which means multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.
3. Solve for the variable: Solve for the variable (in this case, $x$) by dividing both sides of the equation by the coefficient of the variable.

Solving the Proportion

Now, let's apply these steps to solve the proportion $\frac{x}{29} = \frac{2}{5.8}$.

Step 1: Write the proportion as an equation

$\frac{x}{29} = \frac{2}{5.8}$

Step 2: Cross-multiply

$x \times 5.8 = 2 \times 29$

Step 3: Solve for the variable

$x = \frac{2 \times 29}{5.8}$

$x = \frac{58}{5.8}$

$x = 10$

Conclusion

In this article, we have learned how to solve a proportion, specifically the proportion $\frac{x}{29} = \frac{2}{5.8}$. We have applied the steps to solve a proportion, which include writing the proportion as an equation, cross-multiplying, and solving for the variable. We have also seen the importance of proportions in mathematics and real-life situations.

Answer

The value of $x$ is $\boxed{10}$.

Discussion

What do you think is the most challenging part of solving proportions? How do you apply proportions in real-life situations? Share your thoughts and experiences in the comments below!

Related Topics

• Ratios and proportions
• Algebra and geometry
• Percentages and fractions
• Real-life applications of proportions

References

• [1] Khan Academy. (n.d.). Ratios and proportions. Retrieved from https://www.khanacademy.org/math/algebra/x2f6f7c0d/x2f6f7c0d/x2f6f7c0d
• [2] Math Open Reference. (n.d.). Proportions. Retrieved from https://www.mathopenref.com/proportions.html
• [3] Wolfram MathWorld. (n.d.). Proportion. Retrieved from https://mathworld.wolfram.com/Proportion.html
  Frequently Asked Questions (FAQs) about Solving Proportions ================================================================

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: Why are proportions important?

A: Proportions are an essential concept in mathematics, particularly in algebra and geometry. They are used to solve problems involving ratios, proportions, and percentages. In real-life situations, proportions are used to compare quantities, such as the ratio of a car's speed to the distance traveled, or the ratio of a recipe's ingredients to the number of servings.

Q: How do I solve a proportion?

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

1. Write the proportion as an equation: Write the proportion as an equation, with the ratios set equal to each other.
2. Cross-multiply: Cross-multiply the two ratios, which means multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.
3. Solve for the variable: Solve for the variable (in this case, $x$) by dividing both sides of the equation by the coefficient of the variable.

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to solve proportions. It involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.

Q: How do I apply proportions in real-life situations?

A: Proportions are used in many real-life situations, such as:

• Comparing the ratio of a car's speed to the distance traveled
• Comparing the ratio of a recipe's ingredients to the number of servings
• Calculating the area of a rectangle or a triangle
• Finding the volume of a cylinder or a sphere

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

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

• Not cross-multiplying the ratios
• Not solving for the variable correctly
• Not checking the units of the answer

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

A: Here is an example of a proportion:

$\frac{x}{29} = \frac{2}{5.8}$

To solve this proportion, you would follow the steps outlined above.

Q: How do I check my answer when solving a proportion?

A: To check your answer when solving a proportion, you should:

• Plug the answer back into the original equation
• Check that the ratios are equal
• Check that the units of the answer are correct

Q: What are some real-life applications of proportions?

A: Some real-life applications of proportions include:

• Architecture: Proportions are used to design buildings and structures
• Engineering: Proportions are used to design machines and mechanisms
• Art: Proportions are used to create balanced and harmonious compositions
• Science: Proportions are used to describe the relationships between variables in scientific experiments

Q: Can you give me some practice problems to try?

A: Here are some practice problems to try:

1. $\frac{x}{12} = \frac{3}{4}$
2. $\frac{y}{15} = \frac{2}{3}$
3. $\frac{z}{20} = \frac{5}{6}$

Try solving these proportions using the steps outlined above.

Conclusion

In this article, we have answered some frequently asked questions about solving proportions. We have covered topics such as what a proportion is, why proportions are important, and how to solve a proportion. We have also provided some practice problems to try and some real-life applications of proportions.