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In a proper fraction the numerator is smaller than the denominator. Since every two-digit number is larger than every one-digit number, there must be a one-digit numerator and two-digit denominator comprising 3 digits total. The greatest fraction will be the one with the largest possible numerator and smallest possible denominator.

Choose a numerator of 9 (the largest one-digit number) and a denominator of 10 (the smallest 2-digit number). All 3 digits are different.

The answer is 9/10.

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Q: What is the greatest proper fraction that has 3 different digits?
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