A school choir is made up of girls and boys in the ratio 4 :3. There are 35 students in the choir altogether. a. How many of the students are boys? b. What fraction of the students are boys?

a. The ratio of girls to boys in the choir is 4:3. This means for every 7 students (4+3), 4 are girls and 3 are boys. To find out how many boys there are in a choir of 35, we first need to find out how many 'groups' of 7 students there are in 35. We do this by dividing 35 by 7, which gives us 5. This means there are 5 'groups' of 7 students in the choir. Since we know that in each group of 7, 3 are boys, we multiply 5 (the number of groups) by 3 (the number of boys in each group) to get 15. So, there are 15 boys in the choir.

b. To find out what fraction of the students are boys, we divide the number of boys by the total number of students. So, we divide 15 (the number of boys) by 35 (the total number of students) to get 15/35. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5. So, 15/35 simplifies to 3/7. Therefore, the fraction of students that are boys is 3/7.