1. **State the problem:** You have 3 \frac{1}{4} cups of frozen strawberries and 4 \frac{1}{2} cups of frozen blueberries. Each smoothie requires \frac{1}{2} cup of frozen berries. We need to find how many smoothies can be made. 2. **Combine the total amount of frozen berries:** Convert mixed numbers to improper fractions: $$3 \frac{1}{4} = \frac{13}{4}, \quad 4 \frac{1}{2} = \frac{9}{2}$$ 3. **Add the amounts:** $$\frac{13}{4} + \frac{9}{2} = \frac{13}{4} + \frac{18}{4} = \frac{31}{4}$$ 4. **Use the formula:** Number of smoothies = \frac{\text{Total cups of berries}}{\text{Cups per smoothie}} = \frac{31/4}{1/2} 5. **Divide the fractions:** $$\frac{31}{4} \div \frac{1}{2} = \frac{31}{4} \times \frac{2}{1} = \frac{31 \times 2}{4} = \frac{62}{4}$$ 6. **Simplify the fraction:** $$\frac{62}{4} = \frac{\cancel{62}}{\cancel{4}} \text{ (divide numerator and denominator by 2)} = \frac{31}{2} = 15 \frac{1}{2}$$ 7. **Interpret the result:** You can make 15 full smoothies and have enough berries left for half a smoothie. **Final answer:** You can make $15 \frac{1}{2}$ smoothies.