Solving the Fractional Problem: How Many Girls Studied French?

Math problems often require a clear understanding of the information provided. Let's dive into a simple yet intriguing problem: Half of the students in a class are girls, and half of the girls studied French. If there are 40 students in the class, how many girls studied French?

The Reasoning Process

First, we need to establish the given information clearly:

Total number of students in the class: 40 Half of the students are girls: 40 / 2 20 girls

Next, we know that half of the girls studied French. Now, let's break down the problem step-by-step:

Step 1: Calculate the Number of Girls

Since half of the students are girls, the number of girls in the class is:

[frac{40}{2} 20 text{ girls}]

Step 2: Calculate the Number of Girls Who Studied French

Half of the girls studied French. Therefore, the number of girls who studied French is:

[frac{20}{2} 10 text{ girls}]

So, 10 girls in the class studied French.

Understanding the Calculation

The problem can also be solved using fractions. Let's break it down as follows:

Using Fractions:

Given that half of the students are girls, the fraction of girls is:

[frac{1}{2}]

Since half of the girls studied French, we can represent this as:

[frac{1}{2} times frac{1}{2} frac{1}{4}]

To find the number of girls who studied French, we need to calculate 1/4 of the total number of students:

[frac{1}{4} times 40 10 text{ girls}]

This confirms that 10 girls in the class studied French.

Conclusion

In summary, the problem involves understanding fractions and basic arithmetic. Given the constraints of the problem, we can confidently state that 10 girls in the class studied French. This solution can be applied to similar problems by using the provided fractions and total numbers.