Question

To continue finding the number of cups of lemonade concentrate per 1 cup of water in Elyse’s recipe, multiply
2
1
​
•
10
7
​
. Start by writing
2
1
​
•
10
7
​
as a single fraction.

Elyse's Lemonade Recipe
÷ 1
7
3
​

÷ 1
7
3
​

Water
(cups) Lemonade Concentrate
(cups)
1
7
3
​

2
1
​

1 ?

2
1
​
÷ 1
7
3
​


=
2
1
​
÷
10
7

=
2
1
​
•
7
10

=
•
•

Answer 1

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:

1. **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:

1. 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!