Problem 39 - Prealgebra

Question

In a recent year, about \(41 \%\) of twelfth graders participated in school performing arts. If a high school had 1800 students, one-fourth of which were twelfth graders, about how many twelfth graders participated in school performing arts?

Step-by-Step Solution

Answer

About 185 twelfth graders participated in performing arts.

Step 1: Find the Number of Twelfth Graders

First, determine how many twelfth graders are in the high school. Since one-fourth of the students are twelfth graders, we multiply the total number of students by one-fourth: \[ \text{Number of twelfth graders} = \frac{1}{4} \times 1800 = 450 \]

Step 2: Calculate Participation in Performing Arts

Now, calculate the number of twelfth graders who participated in performing arts. Given that 41% of them participate, we find 41% of the 450 twelfth graders:\[ \text{Participating twelfth graders} = 0.41 \times 450 = 184.5 \]Since the number of students must be a whole number, we round 184.5 to the nearest whole number, which is 185.

Key Concepts

Twelfth Graders

Twelfth graders are students typically in their last year of high school. They are often on the brink of the next stage in their lives, be it higher education or entering the workforce. Understanding the number of twelfth graders in any given school can help in understanding school dynamics and planning school activities effectively.

• Twelfth grade is also known as senior year.
• These students often have more responsibilities, including college applications and preparing for graduation.
• By determining the number of twelfth graders in a school, one can plan resources effectively, particularly for activities and events that are specific to this group.

The key to getting the right count involves understanding the overall student population and knowing what fraction of it comprises twelfth graders.

Performing Arts Participation

Participating in the performing arts can significantly benefit students. It involves activities such as theater, music, and dance. These activities are not only about having fun, but they also help in developing teamwork and creative thinking skills.

• Performing arts provide students with an outlet to express themselves and build confidence.
• It can create a sense of community both within the school and with audiences from the area.
• Knowing how many students participate can help schools allocate funds and resources to enhance these programs.

In this exercise, determining how many twelfth graders participate in the arts can help understand the popularity and impact of such programs within the school.

Fraction to Percentage Conversion

Converting fractions to percentages is an essential math skill that allows us to express proportions in a more universally understandable format. This process involves basic arithmetic and a simple rule: multiply the fraction by 100 to get the percentage.

• To convert, first express the fraction as a decimal by dividing the numerator by the denominator.
• Next, multiply the decimal by 100 to get the percentage.
• This makes it easier to communicate and compare different portions effectively.

For example, when determining student participation, understanding that 41% of twelfth graders participate in performing arts means being able to convert that percentage to an actual student count, which involves reversing the process.

Whole Number Approximation

When dealing with numbers in a practical, real-world context, approximation is often necessary. Whole number approximation is particularly crucial in contexts like counting people, where fractional numbers don't make sense.

• Rounding helps simplify complex numbers into understandable figures.
• The rules of rounding depend on whether the decimal part is less than or greater than 0.5.
• Approximating to the nearest whole number provides a realistic view of quantities.

In this exercise, 184.5 twelfth graders means rounding to 185 because you cannot have half a student. Simple rules and understanding of rounding can help in making precise yet straightforward decisions in any study or school program.