Adding Mixed Numbers 5

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest possible sum.

Hint

Which digits should you use/avoid?
Where should you put the 1? The 2? The…

Answer

The best answer found so far is 1 5/8 + 2 6/8 = 4 3/8.

Source: Robert Kaplinsky

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Two-Digit Multiplication – Equivalent Expressions

Directions: Using the digits 0 to 9, at most one time each, place a digit …

20 comments

  1. David Ganzman
    November 30, 2021 at 10:49 am

    9 1/8 + 2 2/8 = 11 3/8

    Reply
  2. Joyce Xue
    October 18, 2022 at 7:47 am

    6 1/8 + 6 3/8=12 4/8

    Reply
  3. Joseph Rogove
    October 25, 2022 at 10:12 pm

    What about 1 4/8 +2 5/8 = 3 9/8?

    Reply
  4. kuns
    February 7, 2023 at 5:23 pm

    1 5/8 + 2 6/8 = 4 3/8.

    Reply
  5. Rudolf Österreicher
    July 1, 2023 at 12:01 pm

    Without any further restrictions, there are 188 solutions (plus another 188 where the addends are swapped). If the mixed numbers can’t have an improper fraction as the fractional part, there are 94 solutions left:
    1 5/8 + 2 6/8 = 4 3/8
    1 6/8 + 2 5/8 = 4 3/8
    1 6/8 + 2 7/8 = 4 5/8
    1 7/8 + 2 6/8 = 4 5/8
    1 2/8 + 3 5/8 = 4 7/8
    1 5/8 + 3 2/8 = 4 7/8
    1 4/8 + 3 6/8 = 5 2/8
    1 6/8 + 3 4/8 = 5 2/8
    2 1/8 + 3 6/8 = 5 7/8
    2 6/8 + 3 1/8 = 5 7/8
    2 4/8 + 3 5/8 = 6 1/8
    2 5/8 + 3 4/8 = 6 1/8
    1 3/8 + 4 7/8 = 6 2/8
    1 7/8 + 4 3/8 = 6 2/8
    2 5/8 + 3 7/8 = 6 4/8
    2 7/8 + 3 5/8 = 6 4/8
    1 3/8 + 5 4/8 = 6 7/8
    1 4/8 + 5 3/8 = 6 7/8
    2 3/8 + 4 6/8 = 7 1/8
    2 6/8 + 4 3/8 = 7 1/8
    1 4/8 + 5 6/8 = 7 2/8
    1 6/8 + 5 4/8 = 7 2/8
    2 5/8 + 4 6/8 = 7 3/8
    2 6/8 + 4 5/8 = 7 3/8
    2 1/8 + 5 3/8 = 7 4/8
    2 3/8 + 5 1/8 = 7 4/8
    1 2/8 + 6 3/8 = 7 5/8
    1 3/8 + 6 2/8 = 7 5/8
    3 1/8 + 4 5/8 = 7 6/8
    3 5/8 + 4 1/8 = 7 6/8
    2 3/8 + 5 6/8 = 8 1/8
    2 6/8 + 5 3/8 = 8 1/8
    3 2/8 + 4 7/8 = 8 1/8
    3 7/8 + 4 2/8 = 8 1/8
    1 3/8 + 6 7/8 = 8 2/8
    1 7/8 + 6 3/8 = 8 2/8
    1 4/8 + 6 7/8 = 8 3/8
    1 7/8 + 6 4/8 = 8 3/8
    2 4/8 + 5 7/8 = 8 3/8
    2 7/8 + 5 4/8 = 8 3/8
    1 5/8 + 6 7/8 = 8 4/8
    1 7/8 + 6 5/8 = 8 4/8
    2 1/8 + 6 3/8 = 8 4/8
    2 3/8 + 6 1/8 = 8 4/8
    1 2/8 + 7 3/8 = 8 5/8
    1 3/8 + 7 2/8 = 8 5/8
    2 1/8 + 6 4/8 = 8 5/8
    2 4/8 + 6 1/8 = 8 5/8
    3 6/8 + 4 7/8 = 8 5/8
    3 7/8 + 4 6/8 = 8 5/8
    1 2/8 + 7 4/8 = 8 6/8
    1 4/8 + 7 2/8 = 8 6/8
    3 2/8 + 5 4/8 = 8 6/8
    3 4/8 + 5 2/8 = 8 6/8
    2 3/8 + 6 4/8 = 8 7/8
    2 4/8 + 6 3/8 = 8 7/8
    3 1/8 + 5 6/8 = 8 7/8
    3 6/8 + 5 1/8 = 8 7/8
    2 4/8 + 6 5/8 = 9 1/8
    2 5/8 + 6 4/8 = 9 1/8
    3 2/8 + 5 7/8 = 9 1/8
    3 7/8 + 5 2/8 = 9 1/8
    1 4/8 + 7 6/8 = 9 2/8
    1 6/8 + 7 4/8 = 9 2/8
    3 4/8 + 5 6/8 = 9 2/8
    3 6/8 + 5 4/8 = 9 2/8
    1 5/8 + 7 6/8 = 9 3/8
    1 6/8 + 7 5/8 = 9 3/8
    2 4/8 + 6 7/8 = 9 3/8
    2 7/8 + 6 4/8 = 9 3/8
    4 1/8 + 5 2/8 = 9 3/8
    4 2/8 + 5 1/8 = 9 3/8
    2 1/8 + 7 3/8 = 9 4/8
    2 3/8 + 7 1/8 = 9 4/8
    2 5/8 + 6 7/8 = 9 4/8
    2 7/8 + 6 5/8 = 9 4/8
    1 2/8 + 8 3/8 = 9 5/8
    1 3/8 + 8 2/8 = 9 5/8
    2 1/8 + 7 4/8 = 9 5/8
    2 4/8 + 7 1/8 = 9 5/8
    3 1/8 + 6 4/8 = 9 5/8
    3 4/8 + 6 1/8 = 9 5/8
    1 2/8 + 8 4/8 = 9 6/8
    1 4/8 + 8 2/8 = 9 6/8
    2 1/8 + 7 5/8 = 9 6/8
    2 5/8 + 7 1/8 = 9 6/8
    1 2/8 + 8 5/8 = 9 7/8
    1 3/8 + 8 4/8 = 9 7/8
    1 4/8 + 8 3/8 = 9 7/8
    1 5/8 + 8 2/8 = 9 7/8
    3 2/8 + 6 5/8 = 9 7/8
    3 5/8 + 6 2/8 = 9 7/8
    4 1/8 + 5 6/8 = 9 7/8
    4 6/8 + 5 1/8 = 9 7/8

    There are no solutions with only fractions in their simplest form (because the numerators would all have to be uneven, but the sum of two uneven numbers is always even)

    Reply
  6. name
    July 29, 2023 at 3:07 pm

    1 5/8 plus 6 7/8 equals 8 4/8

    Reply
  7. the cool kid
    January 8, 2024 at 8:56 am

    Without any further restrictions, there are 188 solutions (plus another 188 where the addends are swapped). If the mixed numbers can’t have an improper fraction as the fractional part, there are 94 solutions left:
    1 5/8 + 2 6/8 = 4 3/8
    1 6/8 + 2 5/8 = 4 3/8
    1 6/8 + 2 7/8 = 4 5/8
    1 7/8 + 2 6/8 = 4 5/8
    1 2/8 + 3 5/8 = 4 7/8
    1 5/8 + 3 2/8 = 4 7/8
    1 4/8 + 3 6/8 = 5 2/8
    1 6/8 + 3 4/8 = 5 2/8
    2 1/8 + 3 6/8 = 5 7/8
    2 6/8 + 3 1/8 = 5 7/8
    2 4/8 + 3 5/8 = 6 1/8
    2 5/8 + 3 4/8 = 6 1/8
    1 3/8 + 4 7/8 = 6 2/8
    1 7/8 + 4 3/8 = 6 2/8
    2 5/8 + 3 7/8 = 6 4/8
    2 7/8 + 3 5/8 = 6 4/8
    1 3/8 + 5 4/8 = 6 7/8
    1 4/8 + 5 3/8 = 6 7/8
    2 3/8 + 4 6/8 = 7 1/8
    2 6/8 + 4 3/8 = 7 1/8
    1 4/8 + 5 6/8 = 7 2/8
    1 6/8 + 5 4/8 = 7 2/8
    2 5/8 + 4 6/8 = 7 3/8
    2 6/8 + 4 5/8 = 7 3/8
    2 1/8 + 5 3/8 = 7 4/8
    2 3/8 + 5 1/8 = 7 4/8
    1 2/8 + 6 3/8 = 7 5/8
    1 3/8 + 6 2/8 = 7 5/8
    3 1/8 + 4 5/8 = 7 6/8
    3 5/8 + 4 1/8 = 7 6/8
    2 3/8 + 5 6/8 = 8 1/8
    2 6/8 + 5 3/8 = 8 1/8
    3 2/8 + 4 7/8 = 8 1/8
    3 7/8 + 4 2/8 = 8 1/8
    1 3/8 + 6 7/8 = 8 2/8
    1 7/8 + 6 3/8 = 8 2/8
    1 4/8 + 6 7/8 = 8 3/8
    1 7/8 + 6 4/8 = 8 3/8
    2 4/8 + 5 7/8 = 8 3/8
    2 7/8 + 5 4/8 = 8 3/8
    1 5/8 + 6 7/8 = 8 4/8
    1 7/8 + 6 5/8 = 8 4/8
    2 1/8 + 6 3/8 = 8 4/8
    2 3/8 + 6 1/8 = 8 4/8
    1 2/8 + 7 3/8 = 8 5/8
    1 3/8 + 7 2/8 = 8 5/8
    2 1/8 + 6 4/8 = 8 5/8
    2 4/8 + 6 1/8 = 8 5/8
    3 6/8 + 4 7/8 = 8 5/8
    3 7/8 + 4 6/8 = 8 5/8
    1 2/8 + 7 4/8 = 8 6/8
    1 4/8 + 7 2/8 = 8 6/8
    3 2/8 + 5 4/8 = 8 6/8
    3 4/8 + 5 2/8 = 8 6/8
    2 3/8 + 6 4/8 = 8 7/8
    2 4/8 + 6 3/8 = 8 7/8
    3 1/8 + 5 6/8 = 8 7/8
    3 6/8 + 5 1/8 = 8 7/8
    2 4/8 + 6 5/8 = 9 1/8
    2 5/8 + 6 4/8 = 9 1/8
    3 2/8 + 5 7/8 = 9 1/8
    3 7/8 + 5 2/8 = 9 1/8
    1 4/8 + 7 6/8 = 9 2/8
    1 6/8 + 7 4/8 = 9 2/8
    3 4/8 + 5 6/8 = 9 2/8
    3 6/8 + 5 4/8 = 9 2/8
    1 5/8 + 7 6/8 = 9 3/8
    1 6/8 + 7 5/8 = 9 3/8
    2 4/8 + 6 7/8 = 9 3/8
    2 7/8 + 6 4/8 = 9 3/8
    4 1/8 + 5 2/8 = 9 3/8
    4 2/8 + 5 1/8 = 9 3/8
    2 1/8 + 7 3/8 = 9 4/8
    2 3/8 + 7 1/8 = 9 4/8
    2 5/8 + 6 7/8 = 9 4/8
    2 7/8 + 6 5/8 = 9 4/8
    1 2/8 + 8 3/8 = 9 5/8
    1 3/8 + 8 2/8 = 9 5/8
    2 1/8 + 7 4/8 = 9 5/8
    2 4/8 + 7 1/8 = 9 5/8
    3 1/8 + 6 4/8 = 9 5/8
    3 4/8 + 6 1/8 = 9 5/8
    1 2/8 + 8 4/8 = 9 6/8
    1 4/8 + 8 2/8 = 9 6/8
    2 1/8 + 7 5/8 = 9 6/8
    2 5/8 + 7 1/8 = 9 6/8
    1 2/8 + 8 5/8 = 9 7/8
    1 3/8 + 8 4/8 = 9 7/8
    1 4/8 + 8 3/8 = 9 7/8
    1 5/8 + 8 2/8 = 9 7/8
    3 2/8 + 6 5/8 = 9 7/8
    3 5/8 + 6 2/8 = 9 7/8
    4 1/8 + 5 6/8 = 9 7/8
    4 6/8 + 5 1/8 = 9 7/8

    There are no solutions with only fractions in their simplest form (because the numerators would all have to be uneven, but the sum of two uneven numbers is always even)

    Reply
  8. Riley the GREAT!!
    January 8, 2024 at 8:58 am

    I think the least possible sum is 1 5/8 + 2 3/8 = 4

    Reply
  9. lucas frings
    January 8, 2024 at 8:59 am

    the answer is 1/8+2/8 =3/8

    Reply
  10. Josephine Hockley
    January 8, 2024 at 9:00 am

    I think its 1 5/8 + 2 6/8 = 4 3/8. 🙂

    Reply
  11. the cool kid
    January 8, 2024 at 9:00 am

    1 5/8 + 2 6/8 = 4 3/8 that is the least one you can do

    Reply
  12. Anonymous
    January 8, 2024 at 9:01 am

    1 2/8 + 3 5/8 = 4 7/8.

    Reply
  13. Scarlett Foreman
    January 8, 2024 at 9:08 am

    I think that the amount of answer combinations go into hundreds, therefore there are many options

    Reply
  14. lebron james
    January 8, 2024 at 9:11 am

    its 4 3/8

    Reply

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