Explaining the Correct Answer

Oct 13, 2025 by miodeya.com 4 views

Introduction

Mathematics is a vast and fascinating subject that encompasses various branches, including arithmetic, algebra, geometry, and more. In this article, we will delve into two fundamental concepts: arranging numbers in order and understanding trapezoids. We will explore the correct arrangement of given numbers and calculate the fraction of the area of a trapezoid.

Arranging Numbers

The Task

We are given a set of numbers: 45, 60, 0, -13, and -22. The task is to arrange these numbers from highest to lowest.

The Correct Arrangement

To arrange the numbers correctly, we need to compare each number with the others. We start by comparing the positive numbers: 45 and 60. Since 60 is greater than 45, we place 60 first. Next, we compare the remaining positive numbers: 45 and 0. Since 45 is greater than 0, we place 45 next. Now, we have 60, 45, and 0. We are left with the negative numbers: -13 and -22. Since -13 is greater than -22, we place -13 next. Finally, we place -22 last. Therefore, the correct arrangement of the numbers from highest to lowest is:

60, 45, 0, -13, -22

Explaining the Correct Answer

The correct answer is not a simple matter of comparing numbers. It requires a thorough understanding of the concept of order and the properties of numbers. When arranging numbers, we need to consider both the magnitude and the sign of the numbers. In this case, we had to compare positive numbers with each other and negative numbers with each other before combining the results.

Understanding Trapezoids

The Task

We are given a trapezoid with the following dimensions:

The length of the shorter base is 6 cm.
The length of the longer base is 10 cm.
The height of the trapezoid is 4 cm.

The task is to calculate the fraction of the area of the trapezoid.

The Formula

The formula for the area of a trapezoid is:

A = (1/2) × (a + b) × h

where A is the area, a and b are the lengths of the bases, and h is the height.

The Calculation

We can now plug in the values given in the problem:

A = (1/2) × (6 + 10) × 4 A = (1/2) × 16 × 4 A = 32

The Fraction

To find the fraction of the area, we need to divide the area by the total area of the trapezoid. However, the total area of the trapezoid is not given. Instead, we are asked to find the fraction of the area. This means that we need to find the ratio of the area to the total area.

Since the total area of the trapezoid is not given, we cannot find the fraction of the area. However, we can find the ratio of the area to the total area. Let's assume that the total area of the trapezoid is 100 cm². Then, the fraction of the area is:

Fraction = (32/100) = 0.32

Explaining the Correct Answer

The correct answer is not a simple matter of plugging in numbers into a formula. It requires a thorough understanding of the concept of area and the properties of trapezoids. When calculating the area of a trapezoid, we need to consider the lengths of the bases and the height. In this case, we had to use the formula for the area of a trapezoid and plug in the given values.

Conclusion

In this article, we explored two fundamental concepts in mathematics: arranging numbers in order and understanding trapezoids. We learned how to arrange numbers from highest to lowest and how to calculate the fraction of the area of a trapezoid. We also discussed the importance of understanding the properties of numbers and the formula for the area of a trapezoid. By mastering these concepts, we can solve a wide range of mathematical problems and gain a deeper understanding of the subject.

References

[1] Khan Academy. (n.d.). Trapezoids. Retrieved from https://www.khanacademy.org/math/geometry/geometry-trapezoids
[2] Math Open Reference. (n.d.). Trapezoid. Retrieved from https://www.mathopenref.com/trapezoid.html

Glossary

Trapezoid: A quadrilateral with one pair of parallel sides.
Area: The amount of space inside a shape.
Fraction: A way of expressing a part of a whole as a ratio of the part to the whole.
Order: The arrangement of numbers from highest to lowest or lowest to highest.
Frequently Asked Questions: Arranging Numbers and Understanding Trapezoids ====================================================================

Q: What is the correct order of the numbers 45, 60, 0, -13, and -22?

A: The correct order of the numbers from highest to lowest is: 60, 45, 0, -13, -22.

Q: How do I arrange numbers from highest to lowest?

A: To arrange numbers from highest to lowest, you need to compare each number with the others. Start by comparing the positive numbers, then the negative numbers, and finally combine the results.

Q: What is the formula for the area of a trapezoid?

A: The formula for the area of a trapezoid is: A = (1/2) × (a + b) × h, where A is the area, a and b are the lengths of the bases, and h is the height.

Q: How do I calculate the area of a trapezoid?

A: To calculate the area of a trapezoid, you need to plug in the values of the lengths of the bases and the height into the formula: A = (1/2) × (a + b) × h.

Q: What is the fraction of the area of a trapezoid?

A: The fraction of the area of a trapezoid is the ratio of the area to the total area of the trapezoid.

Q: How do I find the fraction of the area of a trapezoid?

A: To find the fraction of the area of a trapezoid, you need to divide the area by the total area of the trapezoid.

Q: What is the total area of a trapezoid?

A: The total area of a trapezoid is not given in the problem. However, you can assume a total area of 100 cm² to find the fraction of the area.

Q: How do I find the ratio of the area to the total area of a trapezoid?

A: To find the ratio of the area to the total area of a trapezoid, you need to divide the area by the total area of the trapezoid.

Q: What is the ratio of the area to the total area of a trapezoid?

A: The ratio of the area to the total area of a trapezoid is 0.32.

Q: What is the importance of understanding the properties of numbers and the formula for the area of a trapezoid?

A: Understanding the properties of numbers and the formula for the area of a trapezoid is crucial in solving mathematical problems and gaining a deeper understanding of the subject.

Q: How can I apply the concepts of arranging numbers and understanding trapezoids in real-life situations?

A: You can apply the concepts of arranging numbers and understanding trapezoids in real-life situations such as calculating the area of a room, the volume of a container, or the distance between two points.

Q: What are some common mistakes to avoid when arranging numbers and understanding trapezoids?

A: Some common mistakes to avoid when arranging numbers and understanding trapezoids include:

Not comparing the positive and negative numbers separately
Not using the correct formula for the area of a trapezoid
Not plugging in the correct values into the formula
Not assuming a total area of the trapezoid

Q: How can I practice and improve my skills in arranging numbers and understanding trapezoids?

A: You can practice and improve your skills in arranging numbers and understanding trapezoids by:

Solving mathematical problems and exercises
Practicing with different types of numbers and trapezoids
Reviewing and understanding the concepts and formulas
Seeking help from a teacher or tutor

Conclusion

In this article, we have answered some frequently asked questions about arranging numbers and understanding trapezoids. We have covered topics such as the correct order of numbers, the formula for the area of a trapezoid, and how to calculate the area and fraction of the area of a trapezoid. We have also discussed the importance of understanding the properties of numbers and the formula for the area of a trapezoid, and how to apply these concepts in real-life situations.