Sarah Drove 40 Miles Per Hour. In 3 Hours, Sarah Drove 120 Miles. Which Is A Valid Proportion To Represent This Description?A. 40 1 = 120 3 \frac{40}{1}=\frac{120}{3} 1 40 ​ = 3 120 ​ B. 1 40 = 120 3 \frac{1}{40}=\frac{120}{3} 40 1 ​ = 3 120 ​ C. 40 3 = 120 1 \frac{40}{3}=\frac{120}{1} 3 40 ​ = 1 120 ​ D.

Introduction

Proportions are a fundamental concept in mathematics that help us understand the relationships between different quantities. In real-world scenarios, proportions are used to describe the relationships between various physical quantities, such as distance, speed, and time. In this article, we will explore how to represent a given description using a valid proportion.

The Description

Sarah drove 40 miles per hour. In 3 hours, Sarah drove 120 miles. We need to find a valid proportion to represent this description.

What is a Proportion?

A proportion is a statement that two ratios are equal. It is often written in the form:

a/b = c/d

where a, b, c, and d are numbers.

Analyzing the Description

Let's analyze the given description:

• Sarah drove 40 miles per hour.
• In 3 hours, Sarah drove 120 miles.

We can see that the distance traveled (120 miles) is related to the speed (40 miles per hour) and the time (3 hours). We can use this information to set up a proportion.

Setting Up the Proportion

To set up the proportion, we need to identify the corresponding quantities. In this case, the speed (40 miles per hour) is the ratio of distance (120 miles) to time (3 hours).

We can write the proportion as:

40/1 = 120/3

However, this is not the only possible proportion. We can also write the proportion as:

1/40 = 120/3

or

40/3 = 120/1

Evaluating the Options

Now, let's evaluate the options:

A. $\frac{40}{1}=\frac{120}{3}$

This proportion is valid because it represents the relationship between the speed (40 miles per hour), distance (120 miles), and time (3 hours).

B. $\frac{1}{40}=\frac{120}{3}$

This proportion is also valid because it represents the relationship between the speed (40 miles per hour), distance (120 miles), and time (3 hours).

C. $\frac{40}{3}=\frac{120}{1}$

This proportion is not valid because it does not represent the relationship between the speed (40 miles per hour), distance (120 miles), and time (3 hours).

D. $\frac{40}{3}=\frac{120}{1}$

This proportion is not valid because it does not represent the relationship between the speed (40 miles per hour), distance (120 miles), and time (3 hours).

Conclusion

In conclusion, the valid proportions to represent the given description are:

A. $\frac{40}{1}=\frac{120}{3}$

B. $\frac{1}{40}=\frac{120}{3}$

These proportions represent the relationship between the speed (40 miles per hour), distance (120 miles), and time (3 hours).

Real-World Applications

Proportions are used in various real-world applications, such as:

• Physics: to describe the relationships between physical quantities, such as distance, speed, and time.
• Engineering: to design and optimize systems, such as bridges, buildings, and machines.
• Economics: to analyze and predict economic trends and behaviors.

Tips and Tricks

When working with proportions, remember to:

• Identify the corresponding quantities.
• Write the proportion in the correct format.
• Evaluate the options carefully.

By following these tips and tricks, you can become proficient in working with proportions and apply them to real-world scenarios.

Common Mistakes

When working with proportions, common mistakes include:

• Failing to identify the corresponding quantities.
• Writing the proportion in the incorrect format.
• Evaluating the options incorrectly.

To avoid these mistakes, make sure to:

• Read the problem carefully.
• Identify the corresponding quantities.
• Write the proportion in the correct format.
• Evaluate the options carefully.

By avoiding these common mistakes, you can become proficient in working with proportions and apply them to real-world scenarios.

Practice Problems

Practice problems are an essential part of learning and mastering proportions. Here are some practice problems to try:

1. A car travels 60 miles per hour. In 2 hours, the car travels 120 miles. What is the valid proportion to represent this description?
2. A plane flies 300 miles per hour. In 4 hours, the plane flies 1200 miles. What is the valid proportion to represent this description?
3. A bicycle travels 20 miles per hour. In 3 hours, the bicycle travels 60 miles. What is the valid proportion to represent this description?

By practicing these problems, you can become proficient in working with proportions and apply them to real-world scenarios.

Conclusion

Frequently Asked Questions

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is often written in the form:

a/b = c/d

where a, b, c, and d are numbers.

Q: How do I set up a proportion?

A: To set up a proportion, you need to identify the corresponding quantities. For example, if you are given the speed (40 miles per hour) and the distance (120 miles) traveled in a certain time (3 hours), you can set up the proportion as:

40/1 = 120/3

Q: What is the difference between a proportion and a ratio?

A: A ratio is a comparison of two numbers, while a proportion is a statement that two ratios are equal. For example, the ratio of 2:3 is different from the proportion 2/3 = 4/6.

Q: How do I evaluate a proportion?

A: To evaluate a proportion, you need to check if the two ratios are equal. You can do this by cross-multiplying the two ratios and checking if the resulting equation is true.

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

A: Some common mistakes to avoid when working with proportions include:

• Failing to identify the corresponding quantities.
• Writing the proportion in the incorrect format.
• Evaluating the options incorrectly.

Q: How do I use proportions in real-world applications?

A: Proportions are used in various real-world applications, such as:

• Physics: to describe the relationships between physical quantities, such as distance, speed, and time.
• Engineering: to design and optimize systems, such as bridges, buildings, and machines.
• Economics: to analyze and predict economic trends and behaviors.

Q: What are some tips and tricks for working with proportions?

A: Some tips and tricks for working with proportions include:

• Identifying the corresponding quantities.
• Writing the proportion in the correct format.
• Evaluating the options carefully.

Q: How do I practice proportions?

A: You can practice proportions by working on practice problems, such as:

1. A car travels 60 miles per hour. In 2 hours, the car travels 120 miles. What is the valid proportion to represent this description?
2. A plane flies 300 miles per hour. In 4 hours, the plane flies 1200 miles. What is the valid proportion to represent this description?
3. A bicycle travels 20 miles per hour. In 3 hours, the bicycle travels 60 miles. What is the valid proportion to represent this description?

Q: What are some common types of proportions?

A: Some common types of proportions include:

• Direct proportion: a proportion where the ratio of two quantities is equal.
• Indirect proportion: a proportion where the ratio of two quantities is not equal.
• Similar proportion: a proportion where the ratio of two corresponding quantities is equal.

Q: How do I use proportions to solve problems?

A: To use proportions to solve problems, you need to:

1. Identify the corresponding quantities.
2. Write the proportion in the correct format.
3. Evaluate the options carefully.
4. Solve the resulting equation.

Conclusion

In conclusion, proportions are a fundamental concept in mathematics that help us understand the relationships between different quantities. By following the tips and tricks outlined in this article, you can become proficient in working with proportions and apply them to real-world scenarios. Remember to identify the corresponding quantities, write the proportion in the correct format, and evaluate the options carefully. With practice and patience, you can master proportions and become proficient in working with them.