Question: Bill has 5 cups of strawberries. He used 2 1/6 cups to make smoothies. He uses the rest of the strawberries to make jars of jam. He needs 2/3 cups of strawberries for each jar of jam. How many jars of jam can he make?
1. **State the problem:**
Bill starts with $5$ cups of strawberries. He uses $2 \frac{1}{6}$ cups for smoothies. The remaining strawberries are used to make jars of jam, each requiring $\frac{2}{3}$ cups. We need to find how many jars he can make.
2. **Convert mixed number to improper fraction:**
$$2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{13}{6}$$
3. **Calculate remaining strawberries:**
$$5 - \frac{13}{6} = \frac{30}{6} - \frac{13}{6} = \frac{17}{6}$$
4. **Find number of jars:**
Each jar needs $\frac{2}{3}$ cups, so number of jars is:
$$\frac{\frac{17}{6}}{\frac{2}{3}} = \frac{17}{6} \times \frac{3}{2} = \frac{17 \times 3}{6 \times 2} = \frac{51}{12}$$
5. **Simplify fraction:**
$$\frac{51}{12} = \frac{\cancel{51}}{\cancel{12}} \text{ (no common factors except 3)}$$
Actually, $51 = 3 \times 17$ and $12 = 3 \times 4$, so:
$$\frac{51}{12} = \frac{3 \times 17}{3 \times 4} = \frac{17}{4} = 4 \frac{1}{4}$$
6. **Interpret result:**
Bill can make $4$ full jars of jam, and will have some strawberries left over.
**Final answer:**
Bill can make **4 jars** of jam.