Question 1200301
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To get the smallest possible quotient, we want the 3-digit number to be relatively small, and we want the sum of the digits to be large.<br>
Logical analysis suggests that the number we are looking for is 199.<br>
The first digit is the smallest possible; and given that first digit 1, the largest possible sum of the digits is if the last two digits are both 9.<br>
I made an excel spreadsheet to look at the quotients for all 3-digit numbers; it verified that in fact the smallest possible quotient is if the 3-digit number is 199.<br>
ANSWER: 199/19<br>