Subtracting Two-Digit Numbers (Middle School)

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) difference.


What does the number on the left represent?  What does the number on the right represent?


98 – 12 is the largest difference.  There are several answers for the smallest difference including 81-79.

Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both.

Source: Robert Kaplinsky

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  1. We were just thinking of doing a question like this next week, but pretty simple. Subtract integers between -10 and +10, can’t use it twice, and make largest and smallest value possible.

    Which is different than smallest difference I guess. Technically this question can make a negative…so your resulting “difference” would be a smaller value than 2?

    And i just realized this is tagged as 1st, 2nd, and 7th grade, so it all depends on your limits.

    But since I started this…is 80-79 (or anything like it) the smallest difference? A difference of 1?

    Or can you do something like -97 – 86, and get -183? Would that be the smallest difference, or is that just a smaller value? Obviously depends on grade level…but at the 7th grade level, what’s the proper distinction? Is difference about distance apart on a number line, or is the resulting value the “difference”?

  2. I have a similar question as to the addition problem like this one. Can’t I choose if a number is negative or positive? If I can, then what about 97 – (-86) as the largest difference?

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