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Get Ratioed

Source: AIME I #7

February 9, 2022
AIMEAIME IAIME Qualification

Problem Statement

Let a,b,c,d,e,f,g,h,ia, b, c, d, e, f, g, h, i be distinct integers from 11 to 99. The minimum possible positive value of a⋅b⋅c−d⋅e⋅fg⋅h⋅i\frac{a \cdot b \cdot c - d \cdot e \cdot f}{g \cdot h \cdot i} can be written as mn,\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+n.m+n.
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