Question

a recipe requires $3\frac{1}{2}$ cups of milk for every $\frac{2}{3}$ of a cup of flour. what is the ratio of cups of milk to one cup of flour? enter your answer as a whole number, proper fraction, or mixed number in simplest form.

answer attempt 1 out of 2

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Explanation:

Step1: Convert mixed number to improper fraction

The amount of milk is \(3\frac{1}{2}\) cups. Convert this to an improper fraction: \(3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}\).

Step2: Set up the ratio and solve for milk per 1 cup of flour

We know that for \(\frac{2}{3}\) cup of flour, we need \(\frac{7}{2}\) cups of milk. Let \(x\) be the amount of milk for 1 cup of flour. We can set up a proportion: \(\frac{\frac{7}{2}}{\frac{2}{3}}=x\). To divide fractions, we multiply by the reciprocal: \(x = \frac{7}{2}\times\frac{3}{2}=\frac{21}{4}\). Convert this improper fraction to a mixed number: \(\frac{21}{4}=5\frac{1}{4}\).

Answer:

\(5\frac{1}{4}\)