Which algebraic expression represents "the class was divided into four equal groups"?
To represent the phrase "the class was divided into four equal groups," we first identify the total number of students in the class with the variable \(w\). The phrase "divided into" indicates the mathematical operation of division, and "four equal groups" signifies that we are partitioning the total number of students into four equal parts. Therefore, the total number of students \(w\) is being divided by the number of groups, which is \(4\).
We evaluate each given option to determine which one correctly represents the division operation:
The algebraic expression that correctly models the situation is \(\frac{w}{4}\). This correctly represents the division of the total group size \(w\) into four equal parts. Therefore, the correct option is \(\frac{w}{4}\).
In everyday life, dividing a total quantity into equal portions is a common task. For example, if you have a class of \(w = 20\) students and you want to split them into four equal working groups, you calculate the number of students per group by dividing the total number of students by the number of groups: \(\frac{20}{4} = 5\). Each of the four groups will consist of 5 students. This concept of division is essential for organizing people, distributing resources, or sharing items fairly.