Let's begin by identifying key information given to us:
To know which ratios have a unit rate of 3, we will check them all one after the other as shown below
[tex]\begin{gathered} 2cups\colon\frac{2}{3}cup \\ \text{Divide through by ''2/3'' to have the ratio in unit rate, we have:} \\ \frac{2}{\frac{2}{3}}cups\colon\frac{\frac{2}{3}}{\frac{2}{3}}cup \\ 3cups\colon1cup(TRUE) \\ \\ \frac{2}{3}cup\colon1cup \\ \text{Divide through by ''2/3'' to have the ratio in unit rate, we have:} \\ \frac{\frac{2}{3}}{\frac{2}{3}}cup\colon\frac{1}{\frac{2}{3}}cup \\ 1cup\colon`1\frac{1}{2}cup(FALSE) \\ \\ 2\frac{1}{2}cups\colon\frac{5}{6}cup \\ \text{Divide through by ''5/6'' to have the ratio in unit rate, we have:} \\ \frac{2\frac{1}{2}}{\frac{5}{6}}cups\colon\frac{\frac{5}{6}}{\frac{5}{6}}cup \\ 3cups\colon1cup(TRUE) \end{gathered}[/tex]We will do the same for the remaining
[tex]\begin{gathered} 3\frac{3}{4}cups\colon2cups \\ \text{Divide both sides by ''2'', we have:} \\ \frac{3\frac{3}{4}}{2}cups\colon\frac{2}{2}cups \\ 1\frac{7}{8}cups\colon1cup(FALSE) \\ \\ 1cup\colon\frac{1}{4}cup \\ \text{Divide both sides by ''1/4'', we have:} \\ \frac{1}{\frac{1}{4}}cup\colon\frac{\frac{1}{4}}{\frac{1}{4}}cup \\ 4cups\colon1cup(FALSE) \\ \\ \frac{15}{2}cups\colon2\frac{1}{2}cups \\ \text{Divide both sides by ''2 1/2'', we have:} \\ \frac{\frac{15}{2}}{2\frac{1}{2}}cups\colon\frac{2\frac{1}{2}}{2\frac{1}{2}}cups \\ 3cups\colon1cup(TRUE) \end{gathered}[/tex]Therefore, the first, third & sixth options are correct
