1. The problem involves comparing times given in mixed numbers and fractions to determine which is the longest or shortest time. 2. The times given are: - A: $1 \frac{11}{12}$ minutes - B: $2 \frac{12}{35}$ minutes - C: $2 \frac{11}{12}$ minutes - D: $3$ minutes 3. To compare these times, convert each mixed number to an improper fraction or decimal. 4. Convert A: $1 \frac{11}{12} = 1 + \frac{11}{12} = \frac{12}{12} + \frac{11}{12} = \frac{23}{12} \approx 1.9167$ minutes. 5. Convert B: $2 \frac{12}{35} = 2 + \frac{12}{35} = \frac{70}{35} + \frac{12}{35} = \frac{82}{35} \approx 2.3429$ minutes. 6. Convert C: $2 \frac{11}{12} = 2 + \frac{11}{12} = \frac{24}{12} + \frac{11}{12} = \frac{35}{12} \approx 2.9167$ minutes. 7. D is already a whole number: $3$ minutes. 8. Now compare the decimal values: - A: $1.9167$ - B: $2.3429$ - C: $2.9167$ - D: $3$ 9. The order from shortest to longest time is A, B, C, D. 10. This method helps in comparing mixed numbers by converting them to improper fractions or decimals for easy comparison.