Problem 117 - Elementary Algebra

Question

In a mathematics class of 44 students, one-quarter of the students signed up for a special Saturday study session. How many students signed up?

Step-by-Step Solution

Answer

11 students signed up for the special Saturday study session.

Step 1: Understand the Problem

We need to find out how many students signed up for the special Saturday study session, which is one-quarter of the total class of 44 students.

Step 2: Set Up the Fraction

The problem states that one-quarter of the students signed up. Mathematically, this can be represented as \( \frac{1}{4} \) of the total number of students.

Step 3: Calculate One-Quarter

To find one-quarter of 44, we need to multiply 44 by \( \frac{1}{4} \). This operation can be set up as: \( 44 \times \frac{1}{4} \).

Step 4: Perform the Multiplication

Calculate the product: \( 44 \times \frac{1}{4} = \frac{44}{4} \).

Step 5: Simplify the Result

Divide 44 by 4 to find the number of students: \( \frac{44}{4} = 11 \). Thus, 11 students signed up for the study session.

Key Concepts

Understanding the Mathematics Class Scenario

A mathematics class is often a place where students engage with a wide variety of mathematical concepts. In this scenario, the challenge is to determine how many students from a class of 44 opted into a special Saturday study session. Solving such problems helps build a strong foundation in handling fractions, an essential math skill. Understanding the problem vividly is the first step. We are given a class size, and a fraction of this group is interested in studying on a Saturday. By analyzing this, we can apply mathematical operations to find the exact number of participants. This step is foundational because it sets the stage for applying the correct mathematical operations.

Mastering Multiplication with Fractions

When we multiply a whole number by a fraction, it involves sharing or dividing the whole into equal parts, according to the fraction. In this problem, we find one-quarter of 44. Multiplying a number by a fraction might seem puzzling at first, but it becomes simple with practice.

• The fraction \( \frac{1}{4} \) indicates that 44 is divided into 4 equal parts.
• Multiplication is performed as \( 44 \times \frac{1}{4} \).
• This can be rewritten as \( \frac{44}{1} \times \frac{1}{4} \) which equals \( \frac{44}{4} \).
• The numerator (44) indicates the dividend, while the denominator (4) shows the divisor.

Through this multiplication, you are breaking down the whole class into the portion that signed up for the study session. This illustrates the beauty of fractions in simplifying real-world numerical problems.

Simplifying Fractions for Practical Answers

Once the fraction \( \frac{44}{4} \) is formed, the final step is simplification. Simplifying fractions is essential, as it provides us with a more comprehensible and practical answer. Here’s how it works:

• Divide the numerator (44) by the denominator (4).
• This division can also be seen as finding how many times 4 fits into 44.
• The result, 11, reveals that 11 students signed up for the session.

Simplification turns complex fractions into simpler terms. This concept not only helps in mathematics but is also applicable in everyday scenarios where dealing with fractions is needed, ensuring that you achieve clarity and precision in your answers.