Question

find the area of the following rectangle. write your answer in simplest form. be sure to include the correct unit in your answer. (3\frac{1}{3}) yd, (\frac{11}{12}) yd

Explanation:

Step1: Convert mixed number to improper fraction

The length of the rectangle is \( 3\frac{1}{3} \) yd. To convert this mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3} \) yd.

Step2: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by the formula \( A=\text{length}\times\text{width} \). Here, the length is \( \frac{10}{3} \) yd and the width is \( \frac{11}{12} \) yd.

Step3: Multiply the length and the width

We multiply \( \frac{10}{3} \) and \( \frac{11}{12} \). When multiplying fractions, we multiply the numerators together and the denominators together: \( \frac{10}{3}\times\frac{11}{12}=\frac{10\times11}{3\times12}=\frac{110}{36} \).

Step4: Simplify the fraction

We simplify \( \frac{110}{36} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{110\div2}{36\div2}=\frac{55}{18} \). We can also write this as a mixed number: \( \frac{55}{18}=3\frac{1}{18} \). But since the problem asks for the simplest form, the improper fraction \( \frac{55}{18} \) or the mixed number \( 3\frac{1}{18} \) is acceptable. However, let's check the multiplication again. Wait, \( 10\times11 = 110 \) and \( 3\times12=36 \), then \( \frac{110}{36}=\frac{55}{18} \approx 3.055\cdots \). Wait, but maybe I made a mistake in the mixed number conversion? Wait, \( 3\frac{1}{3} \) is \( \frac{10}{3} \), correct. And \( \frac{10}{3}\times\frac{11}{12}=\frac{110}{36}=\frac{55}{18} \) yd². Alternatively, \( \frac{55}{18}=3\frac{1}{18} \) yd².

Wait, let's re - do the multiplication:

\( 3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3} \)

\( \text{Area}=\frac{10}{3}\times\frac{11}{12}=\frac{10\times11}{3\times12}=\frac{110}{36}=\frac{55}{18}=3\frac{1}{18} \) square yards.

Answer:

\( \frac{55}{18} \) square yards (or \( 3\frac{1}{18} \) square yards)