1. **State the problem:** We are given weights of puppies as mixed numbers: 3 3/4 lb, 4 1/4 lb, 3 1/2 lb, 3 3/4 lb, 3 1/4 lb, 4 1/4 lb, and 3 3/4 lb. We want to understand or analyze these weights, possibly by finding the average or comparing them. 2. **Convert mixed numbers to improper fractions:** - $3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4}$ - $4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}$ - $3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$ - $3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}$ 3. **List all weights as improper fractions:** $\frac{15}{4}, \frac{17}{4}, \frac{7}{2}, \frac{15}{4}, \frac{13}{4}, \frac{17}{4}, \frac{15}{4}$ 4. **Convert all fractions to have a common denominator (4):** - $\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}$ So the weights are: $\frac{15}{4}, \frac{17}{4}, \frac{14}{4}, \frac{15}{4}, \frac{13}{4}, \frac{17}{4}, \frac{15}{4}$ 5. **Sum all weights:** $$\frac{15}{4} + \frac{17}{4} + \frac{14}{4} + \frac{15}{4} + \frac{13}{4} + \frac{17}{4} + \frac{15}{4} = \frac{15 + 17 + 14 + 15 + 13 + 17 + 15}{4} = \frac{106}{4}$$ 6. **Find the average weight:** There are 7 weights, so $$\text{Average} = \frac{\frac{106}{4}}{7} = \frac{106}{4} \times \frac{1}{7} = \frac{106}{28}$$ 7. **Simplify the fraction:** $$\frac{106}{28} = \frac{\cancel{2}53}{\cancel{2}14} = \frac{53}{14}$$ 8. **Convert back to mixed number:** $$53 \div 14 = 3 \text{ remainder } 11$$ So, $$\frac{53}{14} = 3 \frac{11}{14}$$ **Final answer:** The average weight of the puppies is $3 \frac{11}{14}$ pounds.