\frac3628800120 \cdot 6 \cdot 2 = \frac36288001440 = 2520

Mastering Fraction Simplification: Solving $\frac{3628800}{120 \cdot 6 \cdot 2} = 2520$

Simplifying complex fractions can seem intimidating at first, but with the right approach, even large numbers become manageable. In this article, we’ll break down the calculation of $\frac{3628800}{120 \cdot 6 \cdot 2} = 2520$ step by step, showing how reasoning and arithmetic lead straight to the solution.

Understanding the Context

Understanding the Expression

We begin by examining the denominator:
\[
120 \cdot 6 \cdot 2
\]

These multiplying factors represent a product that helps reduce a large numerator efficiently. Our task is to simplify:
\[
\frac{3628800}{120 \cdot 6 \cdot 2} = \frac{3628800}{1440}
\]

$SOLVED:Sum the series 1 \cdot 2 \cdot 5+2 \cdot 3 \cdot 6+3 \cdot 4 ...$

Image Gallery

$SOLVED:Sum the series 1 \cdot 2 \cdot 5+2 \cdot 3 \cdot 6+3 \cdot 4 ...$

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$[where θ is the angle between P and Q ] \[ =\frac{(2 \cdot 1)+[(-3) \cdot..$

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

$sequences and series - Prove that $\frac{5}{1 \cdot 2 \cdot 3} + \frac ...$

Key Insights

Step 1: Calculate the Denominator

Let’s compute the product in the denominator:
\[
120 \cdot 6 = 720
\]
\[
720 \cdot 2 = 1440
\]

So, the equation becomes:
\[
\frac{3628800}{1440}
\]

Step 2: Perform the Division

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Final Thoughts

Now divide 3,628,800 by 1,440.
To simplify, we can perform long division or identify prime factorizations, but let's use step-by-step simplification.

We start by simplifying the fraction algebraically:

Notice that both numerator and denominator are divisible by small factors. However, since this is specific, we compute directly:

\[
3628800 \div 1440 = ?
\]

Break 1440 into prime factors:
\[
1440 = 144 \cdot 10 = (12^2) \cdot (2 \cdot 5) = (2^2 \cdot 3)^2 \cdot 2 \cdot 5 = 2^4 \cdot 3^2 \cdot 2 \cdot 5 = 2^5 \cdot 3^2 \cdot 5
\]

Now factor 3,628,800:

It turns out that
\[
3628800 = 720 \cdot 5040
\]
and
\[
720 \cdot 1440 = 3628800
\]

But for direct computation:

Using calculator-level precision or step division:
\[
3628800 \div 1440 = 2520
\]