Problem 17 - Prealgebra

Question

SCHOOL A biology class has 28 students. Four of the students transferred out of the class to take chemistry. Find the percent of change in the number of students in the biology class.

Step-by-Step Solution

Answer

The percent change is approximately 14.29%.

Step 1: Determine the Original Number of Students

The original number of students in the biology class is given as 28 students.

Step 2: Calculate the New Number of Students

After 4 students transferred out, the number of students remaining in the biology class is calculated by subtracting 4 from 28. \[ 28 - 4 = 24 \]The new number of students is 24.

Step 3: Calculate the Change in the Number of Students

The change in the number of students is the difference between the original number and the new number. \[ 28 - 24 = 4 \]So, there is a decrease of 4 students.

Step 4: Calculate the Percent Change

To find the percent change, divide the change in the number of students by the original number of students and multiply by 100. \[ \text{Percent Change} = \left( \frac{4}{28} \right) \times 100 \approx 14.29\% \]The percent change is approximately 14.29%.

Key Concepts

Prealgebra

Prealgebra lays the groundwork for understanding more advanced math concepts. It's like building a house; you need a strong foundation before adding the floors.
Prealgebra covers basic math topics such as addition, subtraction, multiplication, and division. It also includes foundational concepts like fractions, decimals, and percentages. One important aspect of prealgebra is learning how to express one quantity as a percentage of another.
In the given exercise, the concept of percent change is introduced. Percent change helps us understand how much a quantity has increased or decreased relative to its original value. Recognizing how to calculate percent change is crucial in numerous real-life situations such as discounts, interest rates, and changes in populations or quantities.
By mastering prealgebra, students can better handle these calculations, setting a solid base for algebra and beyond.

Problem Solving

Problem solving is a critical skill that involves understanding the problem, planning a method for solving it, and carrying out that plan.
In mathematics, this often means carefully reading a problem, identifying important information, and deciding which concepts and operations to use.

• Always start by determining what is being asked. In the exercise, the goal is to find the percent change in the number of biology students.
• Collect relevant information. Here, the original number of students is 28, and 4 students left, leaving 24 students.
• Calculate the change. Subtract the new number from the original (28 - 24).

After determining the numerical change, the next step is to calculate the percent change. This requires dividing the change by the original number. Multiply the result by 100 to convert it to a percentage.
Problem solving is not merely about finding the answer. It’s about understanding the process to ensure that it can be applied to similar problems, enhancing one's critical thinking and analytical skills.

Mathematics Education

Mathematics education is essential in shaping logical and analytical skills in students. It does more than teach numbers and formulas; it develops the ability to think critically and solve real-world problems.
Through exercises like the one we explored, students learn to apply mathematical concepts to various scenarios. For example, understanding percent change allows students to grasp ideas about growth and reduction in financial, scientific, and everyday contexts.
Educators play a key role in facilitating this learning by breaking down complex concepts into manageable steps. They encourage students to see the patterns and general principles behind specific problems.

• Using step-by-step solutions, teachers can guide students in mastering techniques that they can later adapt and apply independently.
• Interactive discussions and problems that require hands-on calculations enhance engagement and retention.

Moreover, mathematics education empowers students to appreciate the relevance and power of math beyond the classroom, fostering an appreciation for lifelong learning.