Problem 437 - Prealgebra

Question

Astronomy class There are 125 students in an astronomy class. The professor assigns them into groups of 5. How many groups of students are there?

Step-by-Step Solution

Answer

There are 25 groups of students.

Step 1: Understand the Problem

Determine the total number of students and the size of each group.

Step 2: Identify the Operation Needed

Since groups are being formed, division is the operation to use. You need to divide the total number of students by the number of students per group.

Step 3: Perform the Division

Divide 125 (students) by 5 (students per group). Solve the equation:

Step 4: Conclusion: Find the Number of Groups

After performing the division, the result is 25. Therefore, there are 25 groups of students.

Key Concepts

Grouping

In the context of the given problem, grouping refers to the process of dividing a larger set into smaller, more manageable subsets. Here, we are taking 125 students and organizing them into groups of 5. Grouping makes it easier to manage and work with large quantities.

To form groups:

• Identify the total number of items (students in this case).
• Decide the size of each group.

This method helps in organizing data systematically without any elements being left out.
For example, if there are 125 students and each group contains 5 students, you continue forming groups until you use all students.

Division Operation

The division operation is a fundamental mathematical process. It helps us determine how many times one number is contained within another. In this problem, you need to divide the total number of students by the number of students per group.

Specifically: \[ \frac{125}{5} \] Here, 125 is the dividend (total students), and 5 is the divisor (students per group). The result of the division, known as the quotient, tells us the number of groups. In our example, \[ \frac{125}{5} = 25 \] which means there are 25 groups.

Problem-Solving Steps

When tackling any division problem, following a systematic approach is crucial. Here are the steps based on the given exercise:

1. Understand the Problem: Start by identifying key values, such as the total number of students (125) and the group size (5). Understanding these figures is essential before proceeding.

2. Identify the Operation Needed: When organizing items into smaller groups, division is the go-to operation. Recognize the need to divide 125 by 5.

3. Perform the Division: Compute the division operation as instructed. Use either manual calculation or a calculator for accuracy. Here, \[ \frac{125}{5} = 25 \].

4. Conclusion: Find the Number of Groups: Interpret the quotient. In this case, the quotient is 25, meaning 125 students can be organized into 25 groups of 5.

Following these steps ensures that you systematically solve the problem without missing essential elements.