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

### Hint

How can we make a really big fraction? If improper fractions are allowed, the numerators should be as big as possible and the denominators as small as possible.

### Answer

The best I have found is 9 6/7 + 8 4/5 or 9 4/5 + 8 6/7. Otherwise 9 8/1 + 7 6/2 or 9 6/2 + 7 8/1 would be best, assuming improper fractions could be allowed.

Source: Robert Kaplinsky

No big deal, but I don’t think you’ve completely closed the end since 9 7/1 + 8 6/2 is the same (of course you can swap the order of the mixed numbers, too.)

You are totally right Jim. Thanks for adding to the discussion!

Also no big deal, but 9 4/5 + 8 6/7 is just as good as 9 6/7 + 8 4/5. Never hurts to emphasize that the whole number and fraction are added together, and addition’s commutative…

Actually it is a big deal Julie, you are absolutely right, thank you!

The way I read this was to multiply each whole number times the fraction first, then add the two terms. This adds a little twist, but works out to the same answer of 9(8/1) + 7(6/2) for a total of 93.

Interesting approach, but with the title it is assumed they are adding mixed numbers. Thank you for your response!