Question

what is the area? write your answer as a fraction or as a whole or mixed number. \\(1\frac{1}{3}\\) ft \\(\frac{2}{3}\\) ft square feet

Explanation:

Step1: Recall area of rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). Here, the length is \( 1\frac{1}{3} \) ft and the width is \( \frac{2}{3} \) ft. First, convert the mixed number \( 1\frac{1}{3} \) to an improper fraction. \( 1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3} \).

Step2: Multiply the fractions

Now, multiply the length (\( \frac{4}{3} \)) and the width (\( \frac{2}{3} \)): \( A=\frac{4}{3}\times\frac{2}{3}=\frac{4\times2}{3\times3}=\frac{8}{9} \)? Wait, no, wait. Wait, no, wait, the length is \( 1\frac{1}{3}=\frac{4}{3} \), width is \( \frac{2}{3} \). Wait, no, maybe I mixed up length and width, but multiplication is commutative. Wait, no, let's check again. Wait, the figure is a rectangle, so area is length times width. So \( 1\frac{1}{3} \) is \( \frac{4}{3} \), and \( \frac{2}{3} \). So \( \frac{4}{3}\times\frac{2}{3}=\frac{8}{9} \)? Wait, no, that can't be. Wait, no, wait, maybe I made a mistake. Wait, \( 1\frac{1}{3} \) is \( \frac{4}{3} \), and \( \frac{2}{3} \). Wait, no, let's do it again. \( 1\frac{1}{3}=\frac{4}{3} \), so \( \frac{4}{3}\times\frac{2}{3}=\frac{8}{9} \)? Wait, but that seems small. Wait, no, maybe the length is \( \frac{2}{3} \) and the height is \( 1\frac{1}{3} \). Wait, no, the formula is correct. Wait, let's check the numbers again. The base is \( \frac{2}{3} \) ft, the height is \( 1\frac{1}{3} \) ft. So area is \( \frac{2}{3}\times1\frac{1}{3} \). Convert \( 1\frac{1}{3} \) to improper fraction: \( \frac{4}{3} \). Then \( \frac{2}{3}\times\frac{4}{3}=\frac{8}{9} \)? Wait, no, that's \( \frac{8}{9} \). Wait, but maybe I messed up the mixed number. Wait, \( 1\frac{1}{3} \) is \( 1 + \frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3} \), correct. Then \( \frac{2}{3}\times\frac{4}{3}=\frac{8}{9} \). Wait, but let's do it as mixed numbers. \( 1\frac{1}{3}\times\frac{2}{3}=(1\times\frac{2}{3})+(\frac{1}{3}\times\frac{2}{3})=\frac{2}{3}+\frac{2}{9}=\frac{6}{9}+\frac{2}{9}=\frac{8}{9} \). Yes, that's correct.

Answer:

\(\frac{8}{9}\)