To Fit Between Two Windows, The Width Of A Bookshelf Must Be No Greater Than 6 1 2 6 \frac{1}{2} 6 2 1 ​ Feet. Mrs. Aguilar Purchases A Bookshelf That Is 77 Inches Wide. Which Statement Describes The Relationship Between The Width Of The Bookshelf And The

Introduction

In everyday life, we often encounter situations where we need to compare measurements in different units. This can be a challenging task, especially when dealing with fractions and mixed numbers. In this article, we will explore the relationship between the width of a bookshelf and the maximum allowed width to fit between two windows.

The Problem

Mrs. Aguilar purchases a bookshelf that is 77 inches wide. However, the width of the bookshelf must be no greater than $6 \frac{1}{2}$ feet to fit between two windows. The question is, which statement describes the relationship between the width of the bookshelf and the maximum allowed width?

Converting Measurements

To compare the measurements, we need to convert the width of the bookshelf from inches to feet. There are 12 inches in 1 foot, so we can convert 77 inches to feet by dividing by 12.

$$77 \text{ inches} = \frac{77}{12} \text{ feet}$$

Calculating the Result

Now, let's calculate the result of the division.

$$\frac{77}{12} \approx 6.42 \text{ feet}$$

Comparing Measurements

The width of the bookshelf is approximately 6.42 feet, which is greater than the maximum allowed width of $6 \frac{1}{2}$ feet. To compare the measurements, we can convert the maximum allowed width from feet to inches.

$$6 \frac{1}{2} \text{ feet} = 6.5 \text{ feet} = 6.5 \times 12 = 78 \text{ inches}$$

Conclusion

The width of the bookshelf is greater than the maximum allowed width. Therefore, the statement that describes the relationship between the width of the bookshelf and the maximum allowed width is:

• The width of the bookshelf is greater than the maximum allowed width.

Key Takeaways

• To compare measurements in different units, we need to convert them to a common unit.
• When dealing with fractions and mixed numbers, we can convert them to decimal form to make calculations easier.
• The width of the bookshelf is greater than the maximum allowed width.

Real-World Applications

This problem has real-world applications in various fields, such as:

• Furniture shopping: When purchasing a bookshelf, it's essential to consider the maximum allowed width to fit between two windows.
• Interior design: When designing a room, it's crucial to consider the measurements of furniture and fixtures to ensure they fit comfortably.
• Construction: When building a house or a room, it's essential to consider the measurements of windows and doors to ensure they fit properly.

Conclusion

Q: What is the maximum allowed width for a bookshelf to fit between two windows?

A: The maximum allowed width for a bookshelf to fit between two windows is $6 \frac{1}{2}$ feet.

Q: How do I convert inches to feet?

A: To convert inches to feet, you can divide the number of inches by 12. For example, 77 inches is equal to $\frac{77}{12}$ feet.

Q: What is the width of the bookshelf in feet?

A: The width of the bookshelf is approximately 6.42 feet.

Q: Is the width of the bookshelf greater than the maximum allowed width?

A: Yes, the width of the bookshelf is greater than the maximum allowed width.

Q: How do I compare measurements in different units?

A: To compare measurements in different units, you need to convert them to a common unit. In this case, we converted the width of the bookshelf from inches to feet to compare it with the maximum allowed width.

Q: What are some real-world applications of this problem?

A: Some real-world applications of this problem include:

• Furniture shopping: When purchasing a bookshelf, it's essential to consider the maximum allowed width to fit between two windows.
• Interior design: When designing a room, it's crucial to consider the measurements of furniture and fixtures to ensure they fit comfortably.
• Construction: When building a house or a room, it's essential to consider the measurements of windows and doors to ensure they fit properly.

Q: How can I make informed decisions in various aspects of life?

A: To make informed decisions, you need to understand the relationship between measurements and compare them to ensure they fit comfortably. This requires converting measurements to a common unit and considering the maximum allowed width.

Q: What are some tips for working with fractions and mixed numbers?

A: Some tips for working with fractions and mixed numbers include:

• Converting fractions to decimal form: This can make calculations easier and more manageable.
• Using a calculator: A calculator can help you perform calculations quickly and accurately.
• Breaking down complex problems: Break down complex problems into smaller, more manageable parts to make them easier to solve.

Q: How can I practice working with fractions and mixed numbers?

A: You can practice working with fractions and mixed numbers by:

• Solving problems: Practice solving problems that involve fractions and mixed numbers.
• Using online resources: There are many online resources available that can help you practice working with fractions and mixed numbers.
• Seeking help: Don't be afraid to seek help if you're struggling with fractions and mixed numbers.

Q: What are some common mistakes to avoid when working with fractions and mixed numbers?

A: Some common mistakes to avoid when working with fractions and mixed numbers include:

• Not converting fractions to decimal form: Failing to convert fractions to decimal form can make calculations more difficult.
• Not considering the maximum allowed width: Failing to consider the maximum allowed width can lead to errors and mistakes.
• Not breaking down complex problems: Failing to break down complex problems into smaller, more manageable parts can make them more difficult to solve.