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MathNet 2022-part-06 — 196 problems (EN–VI) Question 4

Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)

Question 4

Let $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, $i$ be distinct integers from $1$ to $9$. The minimum possible positive value of
$$
\frac{a \cdot b \cdot c - d \cdot e \cdot f}{g \cdot h \cdot i}
$$
can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.