To find the number of cups of fruit punch mix per 1 cup of water in Elyse's fruit punch recipe, we can set up a ratio based on the information provided.
You have:
- 1 cup of water corresponds to \( \frac{1}{2} \) cup of fruit punch mix.
So the ratio of fruit punch mix to water can be expressed as:
\[ \frac{\text{Fruit Punch Mix (cups)}}{\text{Water (cups)}} = \frac{\frac{1}{2}}{1} \]
To find out how many cups of fruit punch mix there are per cup of water, we can observe that:
\[ \text{Fruit Punch Mix per 1 cup of water} = \frac{1}{2} \text{ cup} \]
Thus, if you want to find 1 cup of water from this ratio, you can think of it as:
To find how much fruit punch mix you have per 1 cup of water, you already have the answer from the recipe:
- Fruit Punch Mix per 1 cup of water = \( \frac{1}{2} \) cup.
So, you do not need to divide \( \frac{1}{2} \) by anything to find the amount of mix for 1 cup of water, since it is already provided directly in the recipe.
Therefore:
\[ 1 \text{ cup of water corresponds to } \frac{1}{2} \text{ cup of fruit punch mix.} \]