Problem 1. The students from the seventh grade of a school are going on a winter trip. $\frac{2}{9}$ more students registered than planned. Before departure, $\frac{3}{11}$ of the registered students canceled, so 5 fewer students went on the trip than planned. How many students went on the trip?
Solution. $1+\frac{2}{9}=\frac{11}{9}$ of the planned number of students have registered. $\frac{3}{11}$ of $\frac{11}{9}$ have canceled, which means $\frac{3}{11} \cdot \frac{11}{9}=\frac{1}{3}$ of the planned number have canceled. Those who went on the trip are $\frac{11}{9}-\frac{1}{3}=\frac{11-3}{9}=\frac{8}{9}$ of the planned number of students. This means, $\frac{1}{9}$ of the planned number is 5 students, from which it follows that 45 students were planned to go on the trip. According to this, 45-5=40 students went on the trip.