A ratio is a comparison of two numbers, represented by a division of their amounts. The ratio between a and b can be represented as a fraction a/b. For example: The number of girls in the class is 22 and the number of boys in the class is 11. The ratio of boys to the total in the class is 11/33=1/3.
To calculate a ratio from a two- way frequency table we need to find the 2 relevant values in the table and divide them. If possible, simplify the result.
For example:
The table below shows the number of students that passed and failed the exam in two classes.
Class 1 Class 2 Total
Passed 20 15 35
Failed 10 15 25
Total 30 30 60
After reading the table we can see that:
The fraction of the students that failed the exam study in class 1 is:
We need to calculate the ratio of the students in class 1 that failed the exam from the total students that failed the exam.
The denominator is the number of students that failed the exam, we see in the table that 25 students failed the exam.
The numerator is the number of students that study in class 1 and failed the exam, we see in the table that 10 students study in class 1 and failed the exam.
The fraction is 10/25=2/5.
The ratio of students that study in class 1 from the total number of students is:
The denominator is the number of students in 2 classes, we see in the table that it is 60 students.
The numerator is the number of students that study in class 1, we see in the table that it is 30 students.
The ratio of the students that study in class 1 from the total numbers of students is 30/60=1/2.
The ratio of students that study in class 1 and passed the exam from the number of students that study in class 2 and passed the exam is:
The denominator is the number of students that study in class 2 and passed the exam, we see in the table that it is 15 students.
The numerator is the number of students that study in class 1 and passed the exam, we see in the table that it is 20 students.
The ratio is 20/15=4/3.