Question

Dr. James has 32 students in his math class. 14 of the students are boys.

I. WRITE IN SIMPLEST FORM
II. THE FORM 1:n
III. THE FORM n:1

Answer 1

In Dr. James's math class, the ratio of boys to girls is 14:18, which simplifies to 7:9 in simplest form, approximately 1:1.29 in the form 1:n, and approximately 1.29:1 in the form n:1.

Step-by-step explanation:

The subject question pertains to the representation of the proportion of boys to girls in Dr. James's math class. Since there are 32 students and 14 of them are boys, there must be 32 - 14 = 18 girls. We are asked to represent this in simplest form, in the format of 1:n, and in the format of n:1.

Simplest Form

The simplest form of the ratio of boys to girls would be the reduced form of the ratio 14:18, which simplifies to 7:9 because both numbers can be divided by 2.

FORM 1:n

To express the ratio of boys to girls as 1:n, we would have to set the number of boys (which we will consider as 1) in relation to the number of girls. Since there are 18 girls and 14 boys, the ratio would be 1:(18/14), which simplifies to 1:(9/7) or approximately 1:1.29 when we divide 9 by 7.

FORM n:1

Conversely, to express the ratio of girls to boys as n:1, we simply flip the ratio to get the number of girls first. The ratio will be (18/14):1, which can be simplified to (9/7):1 or approximately 1.29:1.