Adding Mixed Numbers

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

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Directions: Using the digits 1 to 9 at most one time each, place a digit …

10 comments

  1. 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.)

  2. 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.

  3. Rudolf Österreicher

    Smallest sum:
    1 3/8 + 2 4/9 = 3.8194

    Greatest sum:
    Allowing improper fractions in mixed numbers:
    7 6/2 + 8 9/1 = 27.0
    7 6/2 + 9 8/1 = 27.0
    8 6/2 + 9 7/1 = 27.0

    Not allowing improper fractions in mixed numbers:
    8 4/5 + 9 6/7 = 18.6571

    Note: Each of the results given can also be obtained by swapping the fractional parts or the whole parts of the mixed numbers, each of the two swaps multiplying the number of solutions by 2. So 27 can actually be gotten in 3 * 2 * 2 = 12 ways.

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