Question

find the area of the following rectangle. write your answer in simplest form. be sure to include the correct unit in your answer. 5\\(\frac{1}{3}\\) yd, \\(\frac{1}{2}\\) yd (with a rectangle diagram and a keypad for unit selection).

Explanation:

Step1: Convert mixed number to improper fraction

The length of the rectangle is \( 5\frac{1}{3} \) 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, \( 5\frac{1}{3}=\frac{5\times3 + 1}{3}=\frac{16}{3} \) yd.

Step2: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the formula \( A=\text{length}\times\text{width} \). Here, the length is \( \frac{16}{3} \) yd and the width is \( \frac{1}{2} \) yd.

Step3: Multiply the length and the width

We multiply \( \frac{16}{3} \) by \( \frac{1}{2} \). When multiplying fractions, we multiply the numerators together and the denominators together: \( \frac{16}{3}\times\frac{1}{2}=\frac{16\times1}{3\times2}=\frac{16}{6} \).

Step4: Simplify the fraction

We simplify \( \frac{16}{6} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{16\div2}{6\div2}=\frac{8}{3} \). We can also write this as a mixed number: \( 2\frac{2}{3} \). The unit for the area of a rectangle (since we are multiplying lengths) is square yards (\( \text{yd}^2 \)).

Answer:

\( 2\frac{2}{3} \) square yards (or \( \frac{8}{3} \text{yd}^2 \))