Problem 72 - Prealgebra

Question

If 3 out of every 7 people who apply to medical school actually get accepted, what fraction of the people who apply get accepted?

Step-by-Step Solution

Answer

3 out of every 7 applicants are accepted, which is \( \frac{3}{7} \).

Step 1: Understanding the Problem

We are given a scenario where out of every 7 people who apply to medical school, 3 get accepted. We need to find the fraction of people who get accepted.

Step 2: Setting Up a Fraction

The fraction representing the people who get accepted is the number of people accepted divided by the total number of applicants. We know from the problem statement that 3 out of 7 applicants get accepted.

Step 3: Expressing the Fraction

We express this situation as a simple fraction: the total number of accepted applicants (3) over the total number of applicants (7). This gives us the fraction \( \frac{3}{7} \).

Key Concepts

Fraction of Applicants

In many real-world scenarios, such as applying to schools or jobs, we often encounter the concept of fractions to understand proportions. A fraction allows us to compare a part of something with its whole. When we're talking about applicants, such as those applying to medical school, we can determine what portion of these applicants achieve a specific outcome, like getting accepted.

In our example, every group of 7 people applying to medical school includes 3 who are accepted. The key here is visualization. Imagine a group of 7 applicants. Out of this group, 3 receive the news that they have been accepted, and the remaining 4 do not.

By representing this scenario with a fraction, we say that 3 out of 7 applicants are accepted. The fraction is shown as \( \frac{3}{7} \), which tells us directly about the proportion of applicants who achieve the outcome of acceptance.

Medical School Acceptance

Understanding the rate of acceptance is crucial for anyone considering applying to medical school. Not everyone who applies will be accepted, and knowing the acceptance rate can help applicants set realistic expectations and prepare accordingly.

Acceptance rates vary widely between institutions, but the concept remains similar. In our example, for every 7 applicants, 3 are accepted, which translates to an acceptance rate of \( \frac{3}{7} \). This information is vital because it helps potential students understand how competitive the process is.

• Helps in planning additional applications.
• Shows the competitiveness of different schools.
• Aids in evaluating one’s own application against typical benchmarks.

Applicants can use this fraction not just as a static number but as a tool to guide their decision-making. By preparing for the process and understanding this figure, they can optimize their chance of acceptance.

Understanding Fractions

Fractions are a fundamental part of mathematics that help us understand parts of a whole. They consist of two numbers: a numerator, which is the top number, and a denominator, which is the bottom number. In the fraction \( \frac{3}{7} \), 3 is the numerator, and 7 is the denominator.

The numerator represents the part of the whole that we are interested in, while the denominator indicates the total number that makes up that whole. In our exercise, the numerator (3) indicates how many applicants are accepted, and the denominator (7) indicates the total number of applicants.

Understanding fractions can be incredibly useful:

• They help in dividing a whole into parts.
• They allow us to compare different parts of a whole.
• Fractions are used in everyday situations, from cooking recipes to statistical reports.

Grasping how to manipulate and interpret fractions is essential for solving problems that involve parts and wholes in academic and real-world contexts.