What Is The Area Of A Rectangle With A Length Of 3 1 3 3 \frac{1}{3} 3 3 1 ​ Feet And A Width Of 1 2 3 1 \frac{2}{3} 1 3 2 ​ Feet?A. 2 7 9 Ft 2 2 \frac{7}{9} \, \text{ft}^2 2 9 7 ​ Ft 2 B. 3 2 9 Ft 2 3 \frac{2}{9} \, \text{ft}^2 3 9 2 ​ Ft 2 C. $5 \frac{5}{9} ,

Understanding the Problem

When dealing with mixed numbers, it's essential to convert them into improper fractions to simplify calculations. In this problem, we're given a rectangle with a length of $3 \frac{1}{3}$ feet and a width of $1 \frac{2}{3}$ feet. To find the area of the rectangle, we need to multiply the length and width.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

For the length, $3 \frac{1}{3}$, we have:

• Whole number part: 3
• Denominator: 3
• Numerator: 1

Multiplying the whole number part by the denominator: $3 \times 3 = 9$ Adding the numerator: $9 + 1 = 10$

So, the length in improper fraction form is $\frac{10}{3}$ feet.

For the width, $1 \frac{2}{3}$, we have:

• Whole number part: 1
• Denominator: 3
• Numerator: 2

Multiplying the whole number part by the denominator: $1 \times 3 = 3$ Adding the numerator: $3 + 2 = 5$

So, the width in improper fraction form is $\frac{5}{3}$ feet.

Calculating the Area

Now that we have the length and width in improper fraction form, we can multiply them to find the area of the rectangle.

Area = length × width = $\frac{10}{3} \times \frac{5}{3}$ = $\frac{10 \times 5}{3 \times 3}$ = $\frac{50}{9}$

Converting the Improper Fraction to a Mixed Number

To convert the improper fraction $\frac{50}{9}$ to a mixed number, we divide the numerator by the denominator.

$50 \div 9 = 5$ with a remainder of $5$

So, the area of the rectangle in mixed number form is $5 \frac{5}{9}$ feet.

Conclusion

In this problem, we calculated the area of a rectangle with a length of $3 \frac{1}{3}$ feet and a width of $1 \frac{2}{3}$ feet. By converting the mixed numbers to improper fractions and multiplying them, we found the area to be $\frac{50}{9}$ feet. Converting this improper fraction to a mixed number, we get $5 \frac{5}{9}$ feet.

Answer

The correct answer is C. $5 \frac{5}{9} \, \text{ft}^2$.

Real-World Applications

Calculating the area of a rectangle is a fundamental concept in mathematics with numerous real-world applications. In architecture, engineers use area calculations to determine the size of buildings, rooms, and other structures. In design, artists and designers use area calculations to determine the size of canvases, prints, and other visual elements. In everyday life, people use area calculations to determine the size of rooms, furniture, and other objects.

Tips and Tricks

When dealing with mixed numbers, it's essential to convert them into improper fractions to simplify calculations. To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

Common Mistakes

One common mistake when dealing with mixed numbers is to forget to convert them into improper fractions. This can lead to incorrect calculations and answers. Another common mistake is to multiply the whole number part by the denominator without adding the numerator, resulting in an incorrect numerator.

Conclusion

Calculating the area of a rectangle with mixed numbers requires converting them into improper fractions and multiplying them. By following these steps and avoiding common mistakes, you can accurately calculate the area of a rectangle and apply this concept to real-world problems.

Q: What is the formula for calculating the area of a rectangle?

A: The formula for calculating the area of a rectangle is length × width.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator greater than the denominator.

Q: How do I multiply mixed numbers?

A: To multiply mixed numbers, convert them into improper fractions, multiply them, and then convert the result back into a mixed number.

Q: What is the area of a rectangle with a length of $4 \frac{1}{2}$ feet and a width of $2 \frac{3}{4}$ feet?

A: To find the area, convert the mixed numbers to improper fractions: $4 \frac{1}{2} = \frac{9}{2}$ and $2 \frac{3}{4} = \frac{11}{4}$. Then, multiply them: $\frac{9}{2} \times \frac{11}{4} = \frac{99}{8}$. Finally, convert the improper fraction to a mixed number: $\frac{99}{8} = 12 \frac{3}{8}$ feet.

Q: How do I apply the concept of area to real-world problems?

A: The concept of area is used in various real-world applications, such as architecture, design, and everyday life. For example, architects use area calculations to determine the size of buildings, while designers use area calculations to determine the size of canvases and prints.

Q: What are some common mistakes to avoid when calculating the area of a rectangle with mixed numbers?

A: Some common mistakes to avoid include forgetting to convert mixed numbers to improper fractions, multiplying the whole number part by the denominator without adding the numerator, and not converting the result back into a mixed number.

Q: Can I use a calculator to calculate the area of a rectangle with mixed numbers?

A: Yes, you can use a calculator to calculate the area of a rectangle with mixed numbers. However, it's essential to understand the concept and be able to convert mixed numbers to improper fractions and vice versa.

Q: How do I check my answer for accuracy?

A: To check your answer for accuracy, convert the result back into a mixed number and verify that it matches the original problem. You can also use a calculator to check your answer.

Q: What are some real-world examples of calculating the area of a rectangle with mixed numbers?

A: Some real-world examples of calculating the area of a rectangle with mixed numbers include:

• Determining the size of a room or a building
• Calculating the area of a piece of fabric or a canvas
• Determining the size of a piece of furniture or a room
• Calculating the area of a garden or a plot of land

Q: Can I use the concept of area to solve problems involving other shapes, such as triangles or circles?

A: Yes, you can use the concept of area to solve problems involving other shapes, such as triangles or circles. However, the formulas and calculations will be different.

Q: How do I apply the concept of area to problems involving decimals?

A: To apply the concept of area to problems involving decimals, convert the decimal to a fraction or a mixed number and then calculate the area using the formula length × width.

Q: What are some common applications of the concept of area in everyday life?

A: Some common applications of the concept of area in everyday life include:

• Determining the size of a room or a building
• Calculating the area of a piece of fabric or a canvas
• Determining the size of a piece of furniture or a room
• Calculating the area of a garden or a plot of land
• Determining the size of a piece of art or a photograph