Problem 88 - Prealgebra

Question

Studies indicate that approximately \(\frac{3}{4}\) of all undergraduate college students work while attending school. A local community college has a student enrollment of 8,500 students. How many of these students work while attending college?

Step-by-Step Solution

Answer

6,375 students work while attending college.

Step 1: Understand the Fraction

The problem states that \(\frac{3}{4}\) of all undergraduate students work. This means that for every 4 students, 3 students work and 1 student does not work.

Step 2: Identify Total Student Enrollment

The total number of students enrolled at the community college is given as 8,500 students. This is the total number of students we're considering for the calculation.

Step 3: Multiply Enrollment by Fraction

To find out how many students work, multiply the total enrollment by the fraction that represents working students. Thus, you calculate: \(8500 \times \frac{3}{4}\).

Step 4: Perform the Calculation

Now, perform the multiplication: \(8500 \times \frac{3}{4} = 8500 \times 0.75 = 6375\).

Step 5: Interpret the Result

The result from the calculation gives the number of students who work. So, 6,375 students work while attending the community college.

Key Concepts

Understanding Fractions

Fractions are an essential part of mathematics, representing parts of a whole. A fraction consists of two numbers: the numerator and the denominator. The numerator, the top number, indicates how many parts we are considering. The denominator, the bottom number, tells us into how many parts the whole is divided. For example, in the fraction \(\frac{3}{4}\), the denominator '4' signifies that the whole is divided into 4 parts, while the numerator '3' denotes that we are considering 3 out of those 4 parts.

Fractions can describe real-world scenarios, like the problem we're discussing. Seeing \(\frac{3}{4}\) in this scenario helps us understand that 3 out of every 4 students are likely to be working. This way, fractions provide a clear visual and conceptual way to consider portions and percentages of a population.

Solving Word Problems

Word problems translate real-life situations into mathematical calculations. By understanding the scenario, we can apply mathematical concepts to find solutions. The key is to break down the problem into manageable parts. Analyze what is given and what needs to be figured out.

In our example, the problem provides a fractional value of \(\frac{3}{4}\) representing the students who work, and the total number of students, which is 8,500. By extracting these key pieces of information, we simplify the situation into a straightforward mathematical operation: multiplying the total number of students by the fraction of those who work.

• Understand the setup: What is given?
• Determine what needs to be calculated.
• Apply the appropriate mathematical operation to find the solution.

Word problems ground mathematical concepts in real-world application, making the numbers more than just abstract symbols.

Calculating Percentages

Percentages are another essential concept linked with fractions, representing a number out of a hundred. They offer another way to understand parts of a whole. When we multiply fractions, like \(\frac{3}{4}\), with a total amount, we are converting it into a percentage equivalent. Specifically, multiplying \(\frac{3}{4}\) by a total approximates to multiplying the total by 75%, as \(\frac{3}{4}\) is equivalent to 75%.

For student enrollment of 8,500, multiplying by 75% (or 0.75) indicates that 75% of the students are working. This calculation provides the answer of 6,375 students.

• Fractions easily convert to percentages by considering their equivalent out of 100.
• Understanding both fractions and percentages helps greatly in solving real-world problems.
• Converting fractions to percentages allows for simplified communication of data and its implications.

This connection between fractions and percentages enriches our ability to comprehend and convey proportions effortlessly.