A ratio ratio is a comparison of two ratios. It's less common than a standard ratio, but it represents a relationship between two different proportional relationships.
Here's an example to illustrate:
Imagine you're comparing the ratios of students to teachers in two different schools.
- School A: Has 100 students and 5 teachers. The ratio of students to teachers is 100:5, which simplifies to 20:1.
- School B: Has 60 students and 4 teachers. The ratio of students to teachers is 60:4, which simplifies to 15:1.
Now, to compare these two ratios (20:1 and 15:1), we can express them as a ratio ratio. In this case, the ratio ratio would be the ratio of School A's student-teacher ratio to School B's student-teacher ratio: (20:1) : (15:1).
To simplify this ratio ratio, we can divide the first ratio by the second:
(20/1) / (15/1) = 20 / 15 = 4/3
Therefore, the ratio ratio is 4:3. This means that for every 4 students per teacher in School A, there are 3 students per teacher in School B. Or, School A has a student-teacher ratio that is 4/3 (or 1.33) times the student-teacher ratio of School B.
Essentially, a ratio ratio allows us to quantify the difference or relationship between two distinct ratios. It represents a comparison of two proportional relationships.
