1. The problem asks: About how many months did it take the wagon train to travel from Missouri to Utah if it took 1 \frac{2}{3} months from Missouri to Wyoming and \frac{3}{5} month from Wyoming to Utah? 2. To find the total time, we add the two times together: $$1 \frac{2}{3} + \frac{3}{5}$$ 3. Convert the mixed number to an improper fraction: $$1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}$$ 4. Now add the fractions \frac{5}{3} and \frac{3}{5} by finding a common denominator. The least common denominator (LCD) of 3 and 5 is 15. 5. Convert each fraction to have denominator 15: $$\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}$$ $$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$$ 6. Add the fractions: $$\frac{25}{15} + \frac{9}{15} = \frac{25 + 9}{15} = \frac{34}{15}$$ 7. Convert the improper fraction back to a mixed number: $$\frac{34}{15} = 2 \frac{4}{15}$$ 8. So, the wagon train took about $2 \frac{4}{15}$ months to travel from Missouri to Utah. This means approximately 2.27 months.