11. The principal of a local middle school surveyed 600 students about their method of transportation to school. Two-hundred students came to school on their bikes. a. Write the ratio of students who ride bikes to school to the total number of students surveyed. b. Write the ratio of students who do not ride bikes to school to the total number of students surveyed. c. Write the ratios in parts a and bas fractions and find their sum as a fraction. What does this ratio mean?

Let's break down the problem step by step. ### a. Ratio of students who ride bikes to school to the total number of students surveyed The number of students who ride bikes is 200, and the total number of students surveyed is 600. The ratio can be written as: \[ \text{Ratio} = \frac{200}{600} \] ### b. Ratio of students who do not ride bikes to school to the total number of students surveyed To find the number of students who do not ride bikes, we subtract the number of students who ride bikes from the total number of students: \[ \text{Students who do not ride bikes} = 600 - 200 = 400 \] The ratio can be written as: \[ \text{Ratio} = \frac{400}{600} \] ### c. Write the ratios in parts a and b as fractions and find their sum as a fraction Now, we can simplify both fractions: 1. For the ratio of students who ride bikes: \[ \frac{200}{600} = \frac{1}{3} \quad \text{(dividing both numerator and denominator by 200)} \] 2. For the ratio of students who do not ride bikes: \[ \frac{400}{600} = \frac{2}{3} \quad \text{(dividing both numerator and denominator by 200)} \] Now, we can find the sum of these two fractions: \[ \frac{1}{3} + \frac{2}{3} = \frac{1 + 2}{3} = \frac{3}{3} = 1 \] ### What does this ratio mean? The sum of the ratios \( \frac{1}{3} \) (students who ride bikes) and \( \frac{2}{3} \) (students who do not ride bikes) equals 1, which means that together, they account for all the students surveyed. This indicates that every student either rides a bike or does not ride a bike, confirming that the ratios represent the entire population of students surveyed.