Question

3. In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second graders. If there are 96 students in the auditorium, how many second graders are there?

Answer 1

So there are 96 students in total, and you know 1/6 of 96 are fifth graders:
96 x 1/6 = 16
and you know 1/3 of 96 are fourth graders:
96 x 1/3 = 32
so to find the remaining kids:
96-16-32= 48
1/4 of the remaining kids are second graders:
48 x 1/4 = 12
therefore, there are 12 second graders

Answer 2

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.

$\boxed{ \ = 3 \times 4 \ }$

$\boxed{\boxed{ \ = 12 \ students \ }}$

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