To determine how many cupcakes Rashida can make with the flour she has, we first need to break down the information.
The recipe for \(1\frac{1}{4}\) dozen cupcakes (which is \(1\frac{1}{4} \times 12 = 15\) cupcakes) calls for \(1\frac{2}{3}\) cups of flour.
Now, we will convert \(1\frac{2}{3}\) and \(1\frac{1}{4}\) into improper fractions for easier calculations.
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Convert \(1\frac{2}{3}\) to an improper fraction: \[ 1\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3} \text{ cups of flour} \]
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Convert \(1\frac{1}{4}\) to an improper fraction: \[ 1\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \text{ dozen cupcakes} \]
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Find the number of cupcakes in terms of single cupcakes: \[ \frac{5}{4} \text{ dozen} = \frac{5}{4} \times 12 = 15 \text{ cupcakes} \]
So, the recipe makes 15 cupcakes using \(\frac{5}{3}\) cups of flour.
Now, we need to determine how many cupcakes Rashida can make with the 1 cup of flour she has.
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Calculate how much flour is needed for one cupcake: \[ \text{Flour per cupcake} = \frac{5/3 \text{ cups}}{15 \text{ cupcakes}} = \frac{5}{3} \div 15 = \frac{5}{3} \times \frac{1}{15} = \frac{5}{45} = \frac{1}{9} \text{ cups of flour per cupcake} \]
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Determine how many cupcakes she can make with 1 cup of flour: \[ \text{Number of cupcakes} = \frac{1 \text{ cup}}{\frac{1}{9} \text{ cup per cupcake}} = 1 \times 9 = 9 \text{ cupcakes} \]
Thus, Rashida can make 9 cupcakes with the 1 cup of flour she has.