Find the ratio of students who chose science as their favorite subject to the total number of students. Then construct an equivalent ratio with a denominator of 400.
60 students
Practice makes perfect
We are given a table showing which school subjects are favored by a group of students. We want to predict the number of students out of 400 that would choose science as their favorite subject. Consider the given table.
Favorite Subject
Subject
Number of Responses
Math
6
Science
3
English
4
History
7
Before we can predict that number, we need to determine what the ratio of students who chose science as their favorite subject to the total number of students is. Let's find the total number of students who gave responses by adding up all the entries from the table.
6+3+4+7=20
There were 20 students in the considered group. Now we can find the ratio by dividing the number of students who chose science as their favorite subject, 3, by the total number of students, 20.
Students Who Picked Science/Total Number of Students=3/20
Out of every 20 students asked, we can expect 3 of them to choose science as their favorite subject. Next, we want to predict how many students out of 400 would pick science as their favorite subject. Let's write an equivalent ratio with 400 in the denominator. Notice that 400=20 * 20. This means that we can write the equivalent ratio if we multiply both the numerator and the denominator of our original ratio by 20. Let's do it!
Assuming that the ratio of the students choosing science to total number of students stays the same, we found the equivalent ratio 60:400. This means that we can predict that 60 out of 400 students would choose science as their favorite subject.
Alternative Solution
Alternative Solution Process
We can also solve this problem using a bar diagram. Let's make a bar diagram representing 400 students. We will divide the diagram into 20 equal parts because we know how many students per group of 20 prefer science.
We already know that the ratio of students who prefer science to the total number of students is 320, so let's mark 3 out of the 20 equal parts on our diagram. These parts will represent the students who chose science as their favorite subject.
Finally, we need to determine how many students are included in each of the 20 equal parts. Since 400÷20=20, each group represents 20 students.
The number of students who would choose science as their favorite subject is 3 times a group containing 20 students. Because of this, we can predict that 20* 3=60 out of 400 students would choose science as their favorite subject!
