Question

Which ratios have a unit rate of 3? Choose ALL that apply.2 cups : ⅔ cup⅔ cup : 1 cup2½ cups : ⅚ cup3¾ cups : 2 cups 1 cup : ¼ cup15/2 cups : 2½ cups

Answer 1

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

`\begin{gathered} 2cups\colon(2)/(3)cup \\ \text{Divide through by ''2/3'' to have the ratio in unit rate, we have:} \\ (2)/((2)/(3))cups\colon((2)/(3))/((2)/(3))cup \\ 3cups\colon1cup(TRUE) \\ \\ (2)/(3)cup\colon1cup \\ \text{Divide through by ''2/3'' to have the ratio in unit rate, we have:} \\ ((2)/(3))/((2)/(3))cup\colon(1)/((2)/(3))cup \\ 1cup\colon`1(1)/(2)cup(FALSE) \\ \\ 2(1)/(2)cups\colon(5)/(6)cup \\ \text{Divide through by ''5/6'' to have the ratio in unit rate, we have:} \\ (2(1)/(2))/((5)/(6))cups\colon((5)/(6))/((5)/(6))cup \\ 3cups\colon1cup(TRUE) \end{gathered}`

We will do the same for the remaining

`\begin{gathered} 3(3)/(4)cups\colon2cups \\ \text{Divide both sides by ''2'', we have:} \\ (3(3)/(4))/(2)cups\colon(2)/(2)cups \\ 1(7)/(8)cups\colon1cup(FALSE) \\ \\ 1cup\colon(1)/(4)cup \\ \text{Divide both sides by ''1/4'', we have:} \\ (1)/((1)/(4))cup\colon((1)/(4))/((1)/(4))cup \\ 4cups\colon1cup(FALSE) \\ \\ (15)/(2)cups\colon2(1)/(2)cups​ \\ \text{Divide both sides by ''2 1/2'', we have:} \\ ((15)/(2))/(2(1)/(2))cups\colon(2(1)/(2))/(2(1)/(2))cups \\ 3cups\colon1cup(TRUE) \end{gathered}`

Therefore, the first, third & sixth options are correct