12
Further explanation
Given:
In an auditorium,
- \(\frac{1}{6}\) of the students are fifth graders,
- \(\frac{1}{3}\) are fourth graders, and
- \(\frac{1}{4}\) of the remaining students are second graders.
There are 96 students in the auditorium.
Question:
How many second graders are there?
The Process:
The least common multiple (LCM) of 3 and 6 is 6.
Let us draw the diagram of all students.
\(96 \div 6 \ units = 16 \rightarrow \boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16} = 96 \ students\)
- \(\frac{1}{6}\) of the students are fifth graders, or 1 of 6 units above, that is \(\boxed{16} = 16 \ students\)
- \(\frac{1}{3} = \frac{2}{6}\) are fourth graders, or 2 of 6 units above, that is \(\boxed{16}\boxed{16} = 32 \ students\)
The remainder is 6 units - (1 unit + 2 units) = 3 units, that is \(\boxed{16}\boxed{16}\boxed{16} = 48 \ students\). Or, 96 - 16 - 32 = 48 students.
\(\frac{1}{4}\) of the remaining students are second graders.
Let us count how many second graders are there.
\(\boxed{ \ \frac{1}{4} \times 48 \ students = ? \ }\)
Thus, there are 12 second-graders in the auditorium.
- - - - - - - - - -
Quick Steps
\(\boxed{ \ \frac{1}{4} \times \bigg(1 - \frac{1}{6} - \frac{1}{3} \bigg) \times 96 = ? \ }\)
\(\boxed{ \ = \frac{1}{4} \times \bigg(\frac{6}{6} - \frac{1}{6} - \frac{2}{6} \bigg) \times 96 \ }\)
\(\boxed{ \ = \frac{1}{4} \times \frac{3}{6} \times 96 \ }\)
\(\boxed{ \ = \frac{3}{24} \times 96 \ }\)
We crossed out 24 and 96.
\(\boxed{ \ = 3 \times 4 \ }\)
\(\boxed{\boxed{ \ = 12 \ students \ }}\)
Learn more
- How long did it take Charlotte to finish the word search brainly.com/question/8561495
- What fraction of all Sarah's photos is of her friends brainly.com/question/1020296
- Create and solve a story problem about two friends and their weekly allowance brainly.com/question/2968321
Keywords: In an auditorium, 1/6 of the students, fifth graders, 1/3, fourth, 1/4, the remaining students, second, 96, how many, second graders
