12
Given:
In an auditorium,
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.
[tex]96 \div 6 \ units = 16 \rightarrow \boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16} = 96 \ students[/tex]
The remainder is 6 units - (1 unit + 2 units) = 3 units, that is [tex]\boxed{16}\boxed{16}\boxed{16} = 48 \ students[/tex]. Or, 96 - 16 - 32 = 48 students.
[tex]\frac{1}{4}[/tex] of the remaining students are second graders.
Let us count how many second graders are there.
[tex]\boxed{ \ \frac{1}{4} \times 48 \ students = ? \ }[/tex]
Thus, there are 12 second-graders in the auditorium.
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Quick Steps
[tex]\boxed{ \ \frac{1}{4} \times \bigg(1 - \frac{1}{6} - \frac{1}{3} \bigg) \times 96 = ? \ }[/tex]
[tex]\boxed{ \ = \frac{1}{4} \times \bigg(\frac{6}{6} - \frac{1}{6} - \frac{2}{6} \bigg) \times 96 \ }[/tex]
[tex]\boxed{ \ = \frac{1}{4} \times \frac{3}{6} \times 96 \ }[/tex]
[tex]\boxed{ \ = \frac{3}{24} \times 96 \ }[/tex]
We crossed out 24 and 96.
[tex]\boxed{ \ = 3 \times 4 \ }[/tex]
[tex]\boxed{\boxed{ \ = 12 \ students \ }}[/tex]
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