Basic Math Examples

$\frac{2! \cdot 4! \cdot 6!}{1! \cdot 7!}$

Step 1

Rewrite $7!$ as $7 \cdot 6!$ .

$\frac{2! \cdot 4! \cdot 6!}{1! \cdot (7 \cdot 6!)}$

Step 2

Cancel the common factor of $6!$ .

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Step 2.1

Cancel the common factor.

$\frac{2! \cdot 4! \cdot 6!}{1! \cdot (7 \cdot 6!)}$

Step 2.2

Rewrite the expression.

$\frac{2! \cdot 4!}{1! \cdot (7)}$

Step 3

Simplify the numerator.

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Step 3.1

Expand $2!$ to $2 \cdot 1$ .

$\frac{2 \cdot 14!}{1! \cdot 7}$

Step 3.2

Multiply $2$ by $1$ .

$\frac{24!}{1! \cdot 7}$

Step 3.3

Expand $4!$ to $4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{2 (4 \cdot 3 \cdot 2 \cdot 1)}{1! \cdot 7}$

Step 3.4

Multiply $4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.4.1

Multiply $4$ by $3$ .

$\frac{2 (12 \cdot 2 \cdot 1)}{1! \cdot 7}$

Step 3.4.2

Multiply $12$ by $2$ .

$\frac{2 (24 \cdot 1)}{1! \cdot 7}$

Step 3.4.3

Multiply $24$ by $1$ .

$\frac{2 \cdot 24}{1! \cdot 7}$

Step 4

Simplify the denominator.

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Step 4.1

Expand $1!$ to $1$ .

$\frac{2 \cdot 24}{1 \cdot 7}$

Step 4.2

Multiply $7$ by $1$ .

$\frac{2 \cdot 24}{7}$

Step 5

Multiply $2$ by $24$ .

$\frac{48}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{48}{7}$

Decimal Form:

$6.\overline{857142}$

Mixed Number Form:

$6 \frac{6}{7}$