Understanding Fractions and Proportions in a Classroom Scenario

The question asks: 'A history class has 15 boys and 20 girls. What fraction of the class are boys?' Such questions are often used to help students understand the concept of proportions and how they can be represented as fractions.

Introduction to the Problem

First, let's address the initial statement: if 3/7 of the learners are girls, what fraction of the learners are boys? We can deduce that the fraction of learners who are boys would be 4/7.

Calculation Steps:

1) Start with the fraction of learners who are girls: 3/7. 2) To find the fraction of learners who are boys, subtract: 1 - 3/7 7/7 - 3/7 4/7. 3) So, 4/7 of the learners are boys.

Verification and Validation

To verify, let’s use the given number of girls (20) and solve for the total number of learners (x).

4/7x 20 so x 7/4 * 20 70. Therefore, there are 70 learners, 20 boys, and 50 girls.

Alternative Calculation Method

Let's consider an alternative method by scaling the numbers in a way that the sum is easier to manage. For example, if we assume a class of 25 students with 15 girls and 10 boys, the fraction of boys becomes 10/25.

The fraction 10/25 can be simplified to 2/5. This means:

2/5 of the students are boys. 3/5 of the students are girls.

Expressing these as percentages:

1/5 is 20% thus 2/5 is 40%. So, 40% of the students are boys. 3/5 is 60% thus 3/5 is 60%. So, 60% of the students are girls.

Conclusion on the Initial Problem

The initial fractions given in the problem (3/7 and 4/7) were derived from a total class of 35 learners (20 girls and 15 boys). This means the fraction of boys in the class is 15/35, which simplifies to 3/7. The fraction of girls is 20/35, which simplifies to 4/7.

Additional Considerations

If the class had 12 boys and 18 girls (a total of 30 students), the fraction of boys would be 12/30, which simplifies to 2/5 or two fifths.

This example demonstrates the flexibility in using fractions to represent proportions in a classroom setting, helping students better understand and solve related problems in mathematics.