Use an example to represent the given ratio as the number of men to the number of women. Then, find the ratio of the same number of women to the same number of men.
B
Begin by finding the total number of students using the ratio from the exercise.
C
Begin by finding the total number of students using the ratio from the exercise. Recall the definition of a percent.
D
Begin by finding the total number of students using the ratio from the exercise. Recall the definition of a fraction.
A
3:2
B
3:5
C
40 %
D
3/5
Practice makes perfect
We want to find the ratio of women to men in a college. First, recall that a ratio is a comparison of two quantities. It describes how much of
one thing there is compared to another. In our case, we compare the number of men to women in college's student body. Let's take a look.
1{{\color{#0000FF}{\text{number of men}}} \,
&:\, {\color{#009600}{\text{ number of women}}} \\ &\! \Updownarrow \\ {\color{#0000FF}{2}} \, &: \, {\color{#009600}{3}}}
To better understand this ratio, we can use an example. Let's say that there are 200 men and 300 women in the student body. Notice that this ratio is the same as 2:3.
2 &: 3 & ⇕ 200 &: 300
Now, we can find the ratio of women to men in the college using our example.
number of women &: number of men & ⇕ 300 &: 200
We can simplify this ratio to write the final answer.
300 &: 200 & ⇕ 3 &: 2
We found that the ratio of women to men in the college is 3:2.
In Part B, we want to find the ratio of women to the total number of students. To do so, we will use the example from Part A. Let's say there are 200 men and 300 women in the student body. To calculate the total number of students, we add these two numbers together.
200+ 300= 500
Next, let's use the information we found to write the ratio.
number of women &: total number of students & ⇕ 300 &: 500
We can simplify this ratio to write the final answer.
300 &: 500 & ⇕ 3 &: 5
We found that the ratio of women to the total number of students in the college is 3:5.
Now we want to find what percent of the college is men. Recall that a percent is a ratio of a number to 100. Keeping this in mind, let's consider our example. We know that there are 200 men in students body and there is a total of 500 students. We will this as a fraction and simplify. Let's take a look.
In Part D, we want to find what fraction of the college is women. Recall that fractions are a specific type of ratio that compares a part to a whole. Let's use the example from the previous parts to write this fraction.
