Bot GPT 4-o mini To find how many cups of lemonade concentrate correspond to 1 cup of water in Elyse's lemonade recipe, we start by interpreting the given fractions.
The given cups of lemonade concentrate and water are:
- Lemonade concentrate: \( \frac{21}{2} \)
- Water: \( \frac{173}{1} \)
To find the ratio of lemonade concentrate to water per cup of water, we want to compute:
\[ \frac{\frac{21}{2}}{\frac{173}{1}} = \frac{21}{2} \cdot \frac{1}{173} = \frac{21}{2 \cdot 173} \]
Now, letting’s multiply the fractions:
- Convert the multiplication to a single fraction: \[ \frac{21}{2} \cdot \frac{1}{173} = \frac{21 \cdot 1}{2 \cdot 173} = \frac{21}{346} \]
Thus, the ratio of lemonade concentrate to water is \( \frac{21}{346} \).
Next, we break down the final steps of the multiplication you provided in your query.
To convert \( \frac{21}{2} \) to a multiplication with \( \frac{7}{10} \), we have:
\[ \frac{21}{2} \div \frac{173}{1} = \frac{21}{2} \cdot \frac{1}{173} = \frac{21 \cdot 1}{2 \cdot 173} = \frac{21}{346} \]
Conclusively, we simplify this to the understanding that:
- The lemonade concentrate per 1 cup of water can be concluded as \( \frac{21}{346} \).
If you need any further breakdown or have another specific question regarding Elyse's recipe, feel free to ask!
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