Answer :
To determine the relationship between cups and tablespoons, we look at the ratios given in the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Cups} & \text{Tablespoons} \\
\hline
4 & 64 \\
\hline
5 & 80 \\
\hline
6 & 96 \\
\hline
7 & 112 \\
\hline
\end{array}
\][/tex]
For each row, we calculate the ratio of cups to tablespoons:
1. For 4 cups and 64 tablespoons:
[tex]\[
\frac{4}{64} = \frac{1}{16}
\][/tex]
2. For 5 cups and 80 tablespoons:
[tex]\[
\frac{5}{80} = \frac{1}{16}
\][/tex]
3. For 6 cups and 96 tablespoons:
[tex]\[
\frac{6}{96} = \frac{1}{16}
\][/tex]
4. For 7 cups and 112 tablespoons:
[tex]\[
\frac{7}{112} = \frac{1}{16}
\][/tex]
Since the ratio is [tex]$\frac{1}{16}$[/tex] in every case, we conclude that:
[tex]\[
\text{The number of cups is } \frac{1}{16} \text{ of the number of tablespoons.}
\][/tex]
Thus, the correct answer is: The number of cups is [tex]$\frac{1}{16}$[/tex] of the number of tablespoons.
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Cups} & \text{Tablespoons} \\
\hline
4 & 64 \\
\hline
5 & 80 \\
\hline
6 & 96 \\
\hline
7 & 112 \\
\hline
\end{array}
\][/tex]
For each row, we calculate the ratio of cups to tablespoons:
1. For 4 cups and 64 tablespoons:
[tex]\[
\frac{4}{64} = \frac{1}{16}
\][/tex]
2. For 5 cups and 80 tablespoons:
[tex]\[
\frac{5}{80} = \frac{1}{16}
\][/tex]
3. For 6 cups and 96 tablespoons:
[tex]\[
\frac{6}{96} = \frac{1}{16}
\][/tex]
4. For 7 cups and 112 tablespoons:
[tex]\[
\frac{7}{112} = \frac{1}{16}
\][/tex]
Since the ratio is [tex]$\frac{1}{16}$[/tex] in every case, we conclude that:
[tex]\[
\text{The number of cups is } \frac{1}{16} \text{ of the number of tablespoons.}
\][/tex]
Thus, the correct answer is: The number of cups is [tex]$\frac{1}{16}$[/tex] of the number of tablespoons.
