A Rectangular-shaped Mural Has A Length Of $1 \frac{2}{3}$ Feet And A Width Of $1 \frac{1}{4}$ Feet. What Is The Area Of The Mural?A. $1 \frac{1}{12} \text{ Sqft}$B. $1 \frac{2}{12} \text{ Sqft}$C. $2

When dealing with problems involving the area of a rectangular shape, it's essential to understand the relationship between the length, width, and area. In this case, we're given a rectangular-shaped mural with a length of $1 \frac{2}{3}$ feet and a width of $1 \frac{1}{4}$ feet. Our goal is to calculate the area of the mural.

Converting Mixed Numbers to Improper Fractions

Before we can calculate the area, we need to convert the mixed numbers to improper fractions. To do this, we'll multiply the whole number part by the denominator and then add the numerator.

• For the length, $1 \frac{2}{3}$, we have:
  • Whole number part: 1
  • Denominator: 3
  • Numerator: 2
  • Multiply whole number part by denominator: 1 × 3 = 3
  • Add numerator: 3 + 2 = 5
  • So, the length is $\frac{5}{3}$ feet.
• For the width, $1 \frac{1}{4}$, we have:
  • Whole number part: 1
  • Denominator: 4
  • Numerator: 1
  • Multiply whole number part by denominator: 1 × 4 = 4
  • Add numerator: 4 + 1 = 5
  • So, the width is $\frac{5}{4}$ feet.

Calculating the Area

Now that we have the length and width in improper fraction form, we can calculate the area using the formula:

Area = length × width

Substituting the values, we get:

Area = $\frac{5}{3}$ × $\frac{5}{4}$

To multiply fractions, we multiply the numerators and denominators separately:

Area = $\frac{5 \times 5}{3 \times 4}$

Area = $\frac{25}{12}$

Simplifying the Fraction

The fraction $\frac{25}{12}$ is already in its simplest form, so we don't need to simplify it further.

Conclusion

The area of the rectangular-shaped mural is $\frac{25}{12}$ square feet. To convert this to a mixed number, we can divide the numerator by the denominator:

$\frac{25}{12}$ = 2 $\frac{1}{12}$

Therefore, the area of the mural is 2 $\frac{1}{12}$ square feet.

Answer

The correct answer is C. 2 $\frac{1}{12}$ sqft.

Discussion

This problem requires a basic understanding of fractions and how to multiply them. It's essential to follow the order of operations and convert mixed numbers to improper fractions before calculating the area. The solution involves multiplying the length and width of the mural and simplifying the resulting fraction.

Related Topics

• Converting mixed numbers to improper fractions
• Multiplying fractions
• Simplifying fractions
• Calculating the area of a rectangle

Practice Problems

• A rectangular-shaped painting has a length of 2 feet and a width of $\frac{3}{4}$ feet. What is the area of the painting?
• A rectangular-shaped table has a length of $\frac{5}{6}$ feet and a width of 2 feet. What is the area of the table?
  Frequently Asked Questions: Calculating the Area of a Rectangular-Shaped Mural ====================================================================================

In this article, we'll address some common questions and concerns related to calculating the area of a rectangular-shaped mural.

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

A: The formula for calculating the area of a rectangle is:

Area = length × width

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

A: To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number part by the denominator.
2. Add the numerator to the result.
3. Write the result as an improper fraction.

For example, to convert $1 \frac{2}{3}$ to an improper fraction:

1. Multiply 1 by 3: 1 × 3 = 3
2. Add 2: 3 + 2 = 5
3. Write the result as an improper fraction: $\frac{5}{3}$

Q: How do I multiply fractions?

A: To multiply fractions, multiply the numerators and denominators separately:

$\frac{a}{b}$ × $\frac{c}{d}$ = $\frac{a \times c}{b \times d}$

For example, to multiply $\frac{2}{3}$ and $\frac{3}{4}$:

$\frac{2}{3}$ × $\frac{3}{4}$ = $\frac{2 \times 3}{3 \times 4}$ = $\frac{6}{12}$

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD.

For example, to simplify $\frac{6}{12}$:

1. Find the GCD of 6 and 12: 6
2. Divide both the numerator and denominator by the GCD: $\frac{6 ÷ 6}{12 ÷ 6}$ = $\frac{1}{2}$

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

A: To calculate the area, multiply the length and width:

Area = length × width = 3 × $\frac{1}{2}$ = $\frac{3 \times 1}{2}$ = $\frac{3}{2}$

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

A: To calculate the area, multiply the length and width:

Area = length × width = $\frac{2}{3}$ × 4 = $\frac{2 \times 4}{3}$ = $\frac{8}{3}$

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator:

$\frac{a}{b}$ = $\frac{a}{b}$ ÷ 1

For example, to convert $\frac{3}{4}$ to a decimal:

$\frac{3}{4}$ = $\frac{3}{4}$ ÷ 1 = 0.75

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, follow these steps:

1. Determine the place value of the last digit in the decimal.
2. Multiply the decimal by a power of 10 to eliminate the decimal point.
3. Write the result as a fraction.

For example, to convert 0.75 to a fraction:

1. Determine the place value of the last digit: hundredths
2. Multiply by 100 to eliminate the decimal point: 0.75 × 100 = 75
3. Write the result as a fraction: $\frac{75}{100}$

Conclusion

Calculating the area of a rectangular-shaped mural requires a basic understanding of fractions and how to multiply them. By following the steps outlined in this article, you can confidently calculate the area of a rectangle and convert between mixed numbers, improper fractions, and decimals.