Separate them wisely

Logic Level 5

\[ \large \frac{5823}{17469} , \frac{5832}{17496} \]

Above shows 2 distinct ways to segregate and concatenate the integers from 1 to 9 inclusive such that their ratio is equals to \( \frac13 \).

What is the number of ways to segregate and concatenate the integers from 1 to 9 inclusive (using each digit exactly once) to form two integers such that their ratio equals to \( \frac{1}{12} \)?

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