Problem 52 - Basic College Mathematics

Question

Of the students in the freshman class, \(\frac{4}{5}\) have digital cameras; \(\frac{1}{4}\) of these students also join the college photography club. What fraction of the students in the freshman class join the photography club?

Step-by-Step Solution

Answer

The fraction of the students in the freshman class who join the photography club is \(\frac{1}{5}\).

Step 1 - Determine the fraction of students with digital cameras

Given that \(\frac{4}{5}\) of the students in the freshman class have digital cameras.

Step 2 - Calculate the fraction of students with digital cameras who join the photography club

Of the students with digital cameras, \(\frac{1}{4}\) join the photography club. To find this fraction, multiply \(\frac{4}{5}\) by \(\frac{1}{4}\).

Step 3 - Perform the multiplication

Multiply the fractions: \(\frac{4}{5} \times \frac{1}{4} = \frac{4 \times 1}{5 \times 4} = \frac{4}{20}\)

Step 4 - Simplify the fraction

Simplify the fraction \(\frac{4}{20}\): \(\frac{4}{20} = \frac{1}{5}\).

Step 5: Conclusion

The fraction of students in the freshman class who join the photography club is \(\frac{1}{5}\).

Key Concepts

Digital Cameras

Digital cameras are popular devices among photography enthusiasts. These cameras use electronic sensors to capture and store images digitally. For students, owning a digital camera opens up a world of creativity. The freshman class in our example has \(\frac{4}{5}\) of its students equipped with digital cameras. This high percentage shows a strong interest in photography among the students. Considering how accessible digital photography has become, it's not surprising that so many students have digital cameras. This access encourages them to experiment with different techniques and styles, enhancing their skills and creativity.

Photography Club

Joining a photography club offers many benefits to students. A photography club provides a platform to share knowledge, discover new techniques, and gain feedback on one's work. In our example, \(\frac{1}{4}\) of the students with digital cameras join the college photography club. This fraction indicates that some students are eager to further their interest in photography through community interaction. Being part of a club facilitates learning through collaborative efforts and organized events like photo walks and exhibitions. These experiences allow students to grow their passion and competence in photography.

Freshman Class

The freshman class is typically made up of first-year students who are just beginning their college journey. This period is crucial for students as they explore different interests and activities. In the given problem, we note that there is a considerable interest in photography within the freshman class. A large portion, \(\frac{4}{5}\) to be exact, owns digital cameras. This statistic highlights how hobbies and interests like photography can play an essential role in the students' freshman experience, aiding in socialization and skill development.

Simplifying Fractions

Simplifying fractions is a key mathematical skill that helps make numbers easier to work with. When multiplying fractions, the result must often be simplified. For example, in our problem, we needed to find what fraction of the freshman class joined the photography club. We multiplied \(\frac{4}{5}\) (students with cameras) by \(\frac{1}{4}\) (those joining the club) to get \(\frac{4}{20}\). Simplifying this involves finding the greatest common divisor (GCD) of 4 and 20, which is 4. Dividing both the numerator and the denominator by 4, we get \(\frac{1}{5}\). Thus, \(\frac{1}{5}\) of the entire freshman class join the photography club. Mastering simplification makes handling fractions much more manageable and improves numerical literacy.