Question

In a class of 30 students, 6 students did not pass an exam. What percentage of the students did not pass the exam?

Short answer

20% of the students did not pass.

Step-by-step solution

Determine Total Students and Failing Students

Identify the total number of students in the class, which is 30. Determine how many students did not pass the exam, which is given as 6.

Set Up the Percentage Formula

To find the percentage of students who did not pass, use the formula: \[\text{Percentage} = \left( \frac{\text{Number of students who did not pass}}{\text{Total number of students}} \right) \times 100\]

Perform the Calculation

Substitute the numbers into the formula:\[\text{Percentage} = \left( \frac{6}{30} \right) \times 100\]Calculate the result:\[\text{Percentage} = 0.2 \times 100 = 20\%\]

Conclusion

The percentage of students who did not pass the exam is 20%.

Key concepts

Mathematics

Mathematics is more than just numbers and formulas; it's a way of thinking and solving problems efficiently. At the heart of mathematical calculations, such as determining percentages, lies the ability to compare different quantities. In our example, we are tasked with finding out what percentage of students did not pass an exam. This involves basic operations like division and multiplication, but it's important to understand the logic behind them. By dividing the number of students who failed by the total number of students, we are essentially finding a "part-to-whole" relationship. This fraction represents the proportion of students who failed. Multiplying it by 100 transforms this proportion into a percentage, providing a straightforward way to express the failure rate.

Problem Solving

Problem-solving in mathematics is about breaking down a problem into manageable parts and then solving each part step by step. In this scenario, our problem involves finding a percentage, which is a common mathematical task. The first step in solving the problem is identifying the relevant numbers, in this case, the number of students who failed and the total number of students. By clearly defining these numbers, we can then set up a formula. This formula acts as a tool that helps bridge the initial questions to the final answers. We proceed by filling the formula with these numbers, which allows us to perform the calculation smoothly. Problem-solving skills are crucial because they teach us how to approach not just math problems, but challenges in various aspects of life.

Education

Education in mathematics equips students with tools that have lifelong benefits. Understanding how to calculate percentages is essential, not only for academics but also for practical life scenarios such as understanding discounts while shopping or analyzing data trends. As students learn to solve percentage problems, they also develop their cognitive abilities, like critical thinking and logical reasoning. These skills are as important as the mathematical operations themselves. By consistently practicing these exercises, students gain confidence in their numerical capabilities. Additionally, educational settings encourage collaboration, where students can discuss different approaches to solving the same problem. This interaction enriches their learning experience and enhances their problem solving toolkit.

Numerical Reasoning

Numerical reasoning refers to one's ability to interpret and work with numbers. It's about understanding the relationships between numbers and making logical deductions. Calculating percentages, like in our case, involves numerical reasoning since it requires interpreting the relationship between the number of students who did not pass and the total class size. By converting a simple fraction into a percentage, students learn to grasp the concept of scale and proportion better. These reasoning skills extend beyond math classes: they're vital in fields like finance, engineering, and even daily decision-making processes. Strong numerical reasoning skills bolster one's ability to critically analyze situations involving numerical data, leading to informed and smarter decisions.