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

### Hint

### Hint

Where should the biggest numbers go?

What does smallest difference mean? In this case, we want the two numbers as close together as possible. A less 5th grade friendly way of saying it would be “Make the absolute value of the difference as small as possible by…”

A conversation may come up regarding whether improper fractions are allowed.

### Answer

### Answer

If improper fractions are allowed, many solutions with zero are possible including 7 2/8 – 6 5/4

Source: Robert Kaplinsky

The smallest difference is not zero. Any negative answer will be smaller than a difference of zero.

The smallest difference I could find is:

( 2 3/7 ) – ( 8 9/1 ) = – 14 5/7

Hi Robert. I tried to address your concern by revising the hint. What language do you suggest to get it closer to what I want without saying “absolute value” or using “distance” which may be too big of an initial hint?

you might consider taking out the operation all together, and phrase the question as create two numbers that are as ‘almost’ equal. Then extend with explain how you know they are almost equal. This should bring up subtraction as a method for comparison, but could provide some other really interesting discussions as well.

That is a really neat idea Mark. I’ve never tried that but I can see how that could lead to interesting discussions.

( 9 4/6) – (8 5/3)=0

I found it helpful to use the language you suggested, two numbers that are “almost” equal. This prompted me to think about fractions that might be at the same point on a number line (equal), represented differently, thus having a difference of 0.

Yeah, I wonder about being “least helpful” (a la http://robertkaplinsky.com/want-least-helpful-teacher-possible/) with this problem. Initially I don’t talk much about being almost equal. I want them to try and do brute force procedurally to see that this is not an effective way of doing it. Then they are ready to think about it conceptually.