Converting the Fraction to a Mixed Number

Oct 13, 2025 by magicalceylontours.com 13 views

Understanding the Problem

Melissa has created a school banner that is 3 yards long and $\frac{11}{12}$ yard wide. To find the area of the banner, we need to multiply the length by the width. In this article, we will explore how to calculate the area of the banner and provide the correct answer among the given options.

What is Area?

Area is a measure of the amount of space inside a two-dimensional shape. It is calculated by multiplying the length by the width. In the case of the school banner, we need to multiply the length (3 yards) by the width ( $\frac{11}{12}$ yard) to find the area.

Calculating the Area

To calculate the area of the banner, we can use the formula:

Area = Length x Width

In this case, the length is 3 yards and the width is $\frac{11}{12}$ yard. We can multiply these two values together to find the area.

Area = 3 x $\frac{11}{12}$

To multiply a whole number by a fraction, we can multiply the whole number by the numerator (11) and then divide by the denominator (12).

Area = $\frac{3 x 11}{12}$

Area = $\frac{33}{12}$

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator (33) and the denominator (12) by their greatest common divisor (GCD). The GCD of 33 and 12 is 3.

Area = $\frac{33 ÷ 3}{12 ÷ 3}$

Area = $\frac{11}{4}$

Converting the Fraction to a Mixed Number

To convert the fraction to a mixed number, we can divide the numerator (11) by the denominator (4). The quotient is 2 and the remainder is 3.

Area = 2 $\frac{3}{4}$

Conclusion

The area of the school banner is 2 $\frac{3}{4}$ square yards. This is the correct answer among the given options.

Answer

The correct answer is:

C. $2 \frac{3}{4}$ sq yd

Discussion

This problem requires the application of basic arithmetic operations, including multiplication and division. It also requires the conversion of a fraction to a mixed number. The correct answer can be verified by multiplying the length by the width and simplifying the resulting fraction.

Practice Problems

Find the area of a rectangle with a length of 5 yards and a width of $\frac{3}{4}$ yard.
Find the area of a triangle with a base of 3 yards and a height of $\frac{5}{6}$ yard.
Find the area of a circle with a radius of 2 yards.

Conclusion

$In this article, we have calculated the area of a school banner that is 3 yards long and $\frac{11}{12}$ yard wide. We have used the formula Area = Length x Width and simplified the resulting fraction to find the correct answer. The correct answer is 2 $\frac{3}{4}$ square yards.<br/> **Frequently Asked Questions (FAQs) About Calculating the Area of a School Banner**$

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

A: The formula for calculating the area of a school banner is Area = Length x Width.

Q: How do I multiply a whole number by a fraction?

A: To multiply a whole number by a fraction, you can multiply the whole number by the numerator (the top number of the fraction) and then divide by the denominator (the bottom number of the fraction).

Q: How do I simplify a fraction?

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

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

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

A: To convert a fraction to a mixed number, you can divide the numerator by the denominator and write the quotient as the whole number part and the remainder as the fraction part.

Q: What is the area of a rectangle with a length of 5 yards and a width of $\frac{3}{4}$ yard?

A: To find the area of the rectangle, you can multiply the length by the width.

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

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

Area = $\frac{15}{4}$

Area = 3 $\frac{3}{4}$ square yards

Q: What is the area of a triangle with a base of 3 yards and a height of $\frac{5}{6}$ yard?

A: To find the area of the triangle, you can use the formula Area = $\frac{1}{2}$ x Base x Height.

Area = $\frac{1}{2}$ x 3 x $\frac{5}{6}$

Area = $\frac{1}{2}$ x $\frac{15}{6}$

Area = $\frac{15}{12}$

Area = 1 $\frac{3}{12}$ square yards

Q: What is the area of a circle with a radius of 2 yards?

A: To find the area of the circle, you can use the formula Area = $\pi$ x Radius^2.

Area = $\pi$ x 2^2

Area = $\pi$ x 4

Area = 12.57 square yards (approximately)

Conclusion

In this article, we have answered some frequently asked questions about calculating the area of a school banner. We have covered topics such as multiplying a whole number by a fraction, simplifying a fraction, converting a fraction to a mixed number, and calculating the area of different shapes. We hope that this article has been helpful in understanding the concepts of area and how to calculate it.