Solving the Equation: Why 3628800 ÷ (6 × 120 × 2) = 2520

Have you ever encountered a complex fraction and wondered how to simplify it quickly? Let’s break down a classic math problem step by step to reveal how window dressing the expression leads neatly to 2520.

Understanding the Context

The expression in focus is:

\[
\frac{3628800}{6 \cdot 120 \cdot 2} = \frac{3628800}{1440} = 2520
\]

At first glance, this fraction might look intimidating due to large numbers and multiplication in the denominator. But with some strategic simplification, the solution becomes clear and fast.

If \( \frac{1}{2 \cdot 3^{10}}+\frac{2}{2^{2} \cdot 3^{9}}+\frac{3}{2 ...

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If \( \frac{1}{2 \cdot 3^{10}}+\frac{2}{2^{2} \cdot 3^{9}}+\frac{3}{2 ...
sequences and series - Prove that $\frac{5}{1 \cdot 2 \cdot 3} + \frac ...
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[where θ is the angle between P and Q ]\[=\frac{(2 \cdot 1)+[(-3) \cdot..
SOLVED:Simplify. \frac{5}{6} \cdot \frac{3}{10} \cdot \frac{8}{3}

Key Insights

Step 1: Understand the Denominator

Start by simplifying the denominator:
\[
6 \cdot 120 \cdot 2
\]

Multiply the constants step by step:

  • First, compute \(6 \ imes 2 = 12\)
    - Then multiply by 120:
    \[
    12 \ imes 120 = 1440
    \]

So, the entire denominator simplifies neatly to 1440. Now the expression becomes:

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Final Thoughts

\[
\frac{3628800}{1440}
\]

Step 2: Divide 3,628,800 by 1440

Instead of brute-force division, simplify using factorization or known value insights.

Notice that:
\[
3628800 = 7! = 7 \ imes 6 \ imes 5 \ imes 4 \ imes 3 \ imes 2 \ imes 1 = 5040 \ imes 720
\]

But more directly, observe:

\[
\frac{3628800}{1440} = \frac{3628800 \div 10}{1440 \div 10} = \frac{362880}{144}
\]

Still large—but now compare with familiar factorials or multiples:

Alternatively, recognize that:
\[
\frac{7! \ imes 7}{1440} \quad \ ext{is indicator of permutations or combination calculations}
\]

Yet, straight numeral division confirms: