A fruit driak is made of two parts: \( 4 \frac{1}{2} \) quarts of orange joice and \( ; \frac{1}{4} \) quarts of cranberry juice. \( 1 f \frac{2}{3} \) of the fruit drink is wsed for a dinner party, how many quarts are used for the party?

It looks like there might be a few typos in your question. Let's clarify and solve it step by step. ### **Given:** 1. **Ingredients:** - **Orange juice:** \( 4 \frac{1}{2} \) quarts - **Cranberry juice:** \( \frac{1}{4} \) quarts 2. **Usage:** \( 1 \frac{2}{3} \) of the fruit drink is used for a dinner party. ### **Clarifying the Usage:** - The notation \( 1 f \frac{2}{3} \) seems to be a typo. It’s likely you meant \( 1 \frac{2}{3} \), which means "one and two-thirds" of the total fruit drink. ### **Step 1: Calculate the Total Fruit Drink** Add the orange juice and cranberry juice together: \[ 4 \frac{1}{2} + \frac{1}{4} = \frac{9}{2} + \frac{1}{4} = \frac{18}{4} + \frac{1}{4} = \frac{19}{4} \text{ quarts} = 4.75 \text{ quarts} \] ### **Step 2: Calculate the Amount Used for the Party** You mentioned using \( 1 \frac{2}{3} \) of the drink. However, using more than the total doesn't make sense. It's possible that you intended to use \( \frac{2}{3} \) of the total drink. Assuming you meant **two-thirds** of the total fruit drink: \[ \frac{2}{3} \times \frac{19}{4} = \frac{38}{12} = \frac{19}{6} \text{ quarts} \approx 3.17 \text{ quarts} \] ### **Final Answer:** Approximately **3 1⁄6 quarts** of the fruit drink are used for the dinner party.