1. **State the problem:** The area of a rectangle is 14 square units, with side lengths $x$ and $y$. Given values for $x$, find $y$. 2. **Formula:** Area $A$ of a rectangle is given by $$A = x \times y$$ 3. **Rearrange to find $y$:** $$y = \frac{A}{x}$$ 4. **Calculate each case:** **a.** $x = 2 \frac{1}{3} = \frac{7}{3}$ $$y = \frac{14}{\frac{7}{3}} = 14 \times \frac{3}{7} = \cancel{14} \times \frac{3}{\cancel{7}} = 2 \times 3 = 6$$ **b.** $x = 4 \frac{1}{5} = \frac{21}{5}$ $$y = \frac{14}{\frac{21}{5}} = 14 \times \frac{5}{21} = \cancel{14} \times \frac{5}{\cancel{21}} = \frac{2}{3} \times 5 = \frac{10}{3} = 3 \frac{1}{3}$$ **c.** $x = \frac{7}{6}$ $$y = \frac{14}{\frac{7}{6}} = 14 \times \frac{6}{7} = \cancel{14} \times \frac{6}{\cancel{7}} = 2 \times 6 = 12$$ **Final answers:** - a. $y = 6$ - b. $y = 3 \frac{1}{3}$ - c. $y = 12$