1. **Write each fractional rate as a unit rate:** 2. For **1 1/2 cups for 3 batches**: - Convert mixed number to improper fraction: $1\ 1/2 = \frac{3}{2}$ cups. - **Cups per batch:** Divide cups by batches: $$\frac{3}{2} \div 3 = \frac{3}{2} \times \frac{1}{3} = \frac{3}{6} = \frac{1}{2}$$ So, $\frac{1}{2}$ cup per batch. - **Batches per cup:** Divide batches by cups: $$3 \div \frac{3}{2} = 3 \times \frac{2}{3} = 2$$ So, 2 batches per cup. 3. For **3 2/3 pounds for every 1/4 tablespoon**: - Convert mixed number to improper fraction: $3\ 2/3 = \frac{11}{3}$ pounds. - **Pounds per tablespoon:** Divide pounds by tablespoons: $$\frac{11}{3} \div \frac{1}{4} = \frac{11}{3} \times 4 = \frac{44}{3} = 14 \frac{2}{3}$$ So, $14 \frac{2}{3}$ pounds per tablespoon. - **Tablespoons per pound:** Divide tablespoons by pounds: $$\frac{1}{4} \div \frac{11}{3} = \frac{1}{4} \times \frac{3}{11} = \frac{3}{44}$$ So, $\frac{3}{44}$ tablespoons per pound. 4. For **2 5 miles in 1 1/2 hours**, this is likely a typo; assuming it's **2 5 = 2.5 miles** in 1 1/2 hours: - Convert 1 1/2 hours to improper fraction: $1 \frac{1}{2} = \frac{3}{2}$ hours. - **Miles per hour (speed):** $$\frac{5}{2} \div \frac{3}{2} = \frac{5}{2} \times \frac{2}{3} = \frac{5}{3} = 1 \frac{2}{3}$$ So, $1 \frac{2}{3}$ miles per hour or approximately 1.67 mph. 5. For **4 2 3/4 gallons in 3 2/3 minutes**, likely representing $4 \frac{2}{3}$ gallons and $3 \frac{2}{3}$ minutes: - Convert to improper fractions: - $4 \frac{2}{3} = \frac{14}{3}$ gallons. - $3 \frac{2}{3} = \frac{11}{3}$ minutes. - **Gallons per minute:** $$\frac{14}{3} \div \frac{11}{3} = \frac{14}{3} \times \frac{3}{11} = \frac{14}{11} = 1 \frac{3}{11}$$ So, $1 \frac{3}{11}$ gallons per minute or approximately 1.27 gallons/minute. **Final answers:** - $1 \frac{1}{2}$ cups for 3 batches = $\frac{1}{2}$ cup per batch or 2 batches per cup. - $3 \frac{2}{3}$ pounds per $\frac{1}{4}$ tablespoon = $14 \frac{2}{3}$ pounds per tablespoon or $\frac{3}{44}$ tablespoons per pound. - 2.5 miles in $1 \frac{1}{2}$ hours = $1 \frac{2}{3}$ miles per hour. - $4 \frac{2}{3}$ gallons in $3 \frac{2}{3}$ minutes = $1 \frac{3}{11}$ gallons per minute.