Question

A recipe for
1
1
4
dozen cupcakes calls for
1
2
3
cups of flour, but Rashida has only
1
cup of flour.

How many cupcakes can she make? Hint: Pay close attention to the units!

Answer 1

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.

1. **Convert \(1\frac{2}{3}\) to an improper fraction:**
\[
1\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3} \text{ cups of flour}
\]

2. **Convert \(1\frac{1}{4}\) to an improper fraction:**
\[
1\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \text{ dozen cupcakes}
\]

3. **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.

4. **Calculate how much flour is needed for one cupcake:**
\[
\text{Flour per cupcake} = \frac{5/3 \text{ cups}}{15 \text{ cupcakes}} = \frac{5}{3} \div 15 = \frac{5}{3} \times \frac{1}{15} = \frac{5}{45} = \frac{1}{9} \text{ cups of flour per cupcake}
\]

5. **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.