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Based on the table below, what is the relationship between cups and tablespoons?

\[
\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Volume} \\
\hline
Cups & Tablespoons \\
\hline
4 & 64 \\
\hline
5 & 80 \\
\hline
6 & 96 \\
\hline
7 & 112 \\
\hline
\end{tabular}
\]

A. The number of cups is [tex]$\frac{1}{16}$[/tex] of the number of tablespoons.
B. The number of cups is [tex]$\frac{1}{4}$[/tex] of the number of tablespoons.
C. The number of cups is 4 times the number of tablespoons.
D. The number of cups is 16 times the number of tablespoons.

Answer :

Sure! Let's break down the relationship between cups and tablespoons step by step using the data given in the table.

Here’s the table once more for reference:
```
Cups | Tablespoons
-----------------------
4 | 64
5 | 80
6 | 96
7 | 112
```

To find the relationship, we will compare the values of cups and tablespoons for each row.

1. Determine the ratio for each pair:
- For 4 cups and 64 tablespoons:
[tex]\[
\frac{64 \text{ tablespoons}}{4 \text{ cups}} = 16 \text{ tablespoons per cup}
\][/tex]
- For 5 cups and 80 tablespoons:
[tex]\[
\frac{80 \text{ tablespoons}}{5 \text{ cups}} = 16 \text{ tablespoons per cup}
\][/tex]
- For 6 cups and 96 tablespoons:
[tex]\[
\frac{96 \text{ tablespoons}}{6 \text{ cups}} = 16 \text{ tablespoons per cup}
\][/tex]
- For 7 cups and 112 tablespoons:
[tex]\[
\frac{112 \text{ tablespoons}}{7 \text{ cups}} = 16 \text{ tablespoons per cup}
\][/tex]

2. Notice the consistent ratio:
- From the calculations above, you can see that for every cup, there are consistently 16 tablespoons. This consistent ratio indicates that 1 cup is equal to 16 tablespoons.

3. Interpreting cups in terms of tablespoons:
- Since 1 cup corresponds to 16 tablespoons, we can conclude that the number of cups is [tex]\(\frac{1}{16}\)[/tex] of the number of tablespoons. This is because the reciprocal of 16 is [tex]\(\frac{1}{16}\)[/tex].

So, we have confirmed that the relationship between cups and tablespoons is:

The number of cups is [tex]\(\frac{1}{16}\)[/tex] of the number of tablespoons.

This aligns with the given options, and we can confidently select the correct answer:

The number of cups is [tex]\(\frac{1}{16}\)[/tex] of the number of tablespoons.

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