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To solve this problem, we need to determine how many cupcakes Blake can make with \(2 \frac{1}{2}\) cups of flour if each cupcake requires \(\frac{2}{3}\) cup of flour.

### Step 1: Convert the Mixed Number to an Improper Fraction
Blake has \(2 \frac{1}{2}\) cups of flour. We convert this to an improper fraction:
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}
\]

### Step 2: Set Up the Division
To find out how many cupcakes Blake can make, we divide the total amount of flour he has by the amount needed for each cupcake:
\[
\frac{5}{2} \div \frac{2}{3}
\]

### Step 3: Divide Fractions by Multiplying by the Reciprocal
Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as:
\[
\frac{5}{2} \times \frac{3}{2} = \frac{5 \times 3}{2 \times 2} = \frac{15}{4}
\]

### Step 4: Simplify the Fraction
Now, we simplify \(\frac{15}{4}\) by converting it to a mixed number:
\[
\frac{15}{4} = 3 \frac{3}{4}
\]

### Conclusion
Blake can make \(3 \frac{3}{4}\) cupcakes with \(2 \frac{1}{2}\) cups of flour. This means he can make 3 full cupcakes, and he will have enough flour left for \( \frac{3}{4} \) of another cupcake.

Would you like more details or have any questions?

### Related Questions:
1. How would the answer change if Blake only had \(1 \frac{1}{2}\) cups of flour?
2. How many cupcakes can Blake make if each requires \(\frac{3}{4}\) cup of flour instead?
3. What is the leftover amount of flour if Blake only makes whole cupcakes?
4. If Blake wanted to make 5 cupcakes, how much flour would he need?
5. How many cupcakes could be made if Blake used \(3 \frac{1}{2}\) cups of flour?

### Tip:
Remember, dividing by a fraction is equivalent to multiplying by its reciprocal.

Blake has 2 1/2 cups of flour. He uses 2/3 cup of flour to make one cupcake. How many cupcakes can be made with 2 1/2 cups of flour?

Calculate how many cupcakes Blake can make with 2 1/2 cups of flour, where each cupcake requires 2/3 cup. This solution includes converting mixed numbers to improper fractions and dividing fractions by reciprocals, suitable for students in Grades 5-7.

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