Evaluate (6!7!)/(4!9!)

$\frac{6! 7!}{4! 9!}$

Rewrite $9!$ as $9 \cdot 8 \cdot 7!$ .

$\frac{6! 7!}{4! (9 \cdot 8 \cdot 7!)}$

Cancel the common factor of $7!$ .

Cancel the common factor.

$\frac{6! 7!}{4! (9 \cdot 8 \cdot 7!)}$

Rewrite the expression.

$\frac{6!}{4! (9 \cdot 8)}$

$\frac{6!}{4! (9 \cdot 8)}$

Rewrite $6!$ as $6 \cdot 5 \cdot 4!$ .

$\frac{6 \cdot 5 \cdot 4!}{4! (9 \cdot 8)}$

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6 \cdot 5 \cdot 4!$ .

$\frac{3 (2 \cdot 5 \cdot 4!)}{4! (9 \cdot 8)}$

Cancel the common factors.

Factor $3$ out of $4! (9 \cdot 8)$ .

$\frac{3 (2 \cdot 5 \cdot 4!)}{3 (4! (3 \cdot 8))}$

Cancel the common factor.

$\frac{3 (2 \cdot 5 \cdot 4!)}{3 (4! (3 \cdot 8))}$

Rewrite the expression.

$\frac{2 \cdot 5 \cdot 4!}{4! (3 \cdot 8)}$

$\frac{2 \cdot 5 \cdot 4!}{4! (3 \cdot 8)}$

$\frac{2 \cdot 5 \cdot 4!}{4! (3 \cdot 8)}$

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2 \cdot 5 \cdot 4!$ .

$\frac{2 (5 \cdot 4!)}{4! (3 \cdot 8)}$

Cancel the common factors.

Factor $2$ out of $4! (3 \cdot 8)$ .

$\frac{2 (5 \cdot 4!)}{2 (4! (3 \cdot 4))}$

Cancel the common factor.

$\frac{2 (5 \cdot 4!)}{2 (4! (3 \cdot 4))}$

Rewrite the expression.

$\frac{5 \cdot 4!}{4! (3 \cdot 4)}$

$\frac{5 \cdot 4!}{4! (3 \cdot 4)}$

$\frac{5 \cdot 4!}{4! (3 \cdot 4)}$

Cancel the common factor of $4!$ .

Cancel the common factor.

$\frac{5 \cdot 4!}{4! (3 \cdot 4)}$

Rewrite the expression.

$\frac{5}{3 \cdot 4}$

$\frac{5}{3 \cdot 4}$

Multiply $3$ by $4$ .

$\frac{5}{12}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$

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