### Sample Problem

The ratio of the number of teachers to the number of boys to the number of girls at a kindergarten is 2:6:8.

(a) The number of teachers is what fraction of the number of boys? (Not simplify your answer)

(b) How many times as many girls are there as teachers?

(c) The number of teachers is what fraction of the total number of people?(Not simplify your answer)

(d) The total number of people is times the total number of girls.

#### Solution

(a) The ratio of the number of teachers to the number of boys is 2:6. Both 2:6 and express the same relationship between the number of teachers and boys. So, the number of teachers is of the number of boys.

(b) The ratio of girls to teachers is 8:2. Then, 8 ÷ 2 = 4.

Thus, there are 4 times as many girls as teachers.

(c) Set the number of teachers as 2 units, so the total amount of people is (2 + 6 + 8 = 16) units. Then, the ratio of teachers to total people to  is 2:16: Thus, the fraction is 2/16 = 1/8.

(d) The ratio of total people to girls is 16:8.

Then, 16 ÷ 8 = 2

Thus, there are 2 times as many total people as girls.