Adding Fractions 7

Directions: Use the digits 1 to 9, at most one time each, to make a true statement.

Hint

What digits would be challenging as denominators?
What digits would be challenging as numerators?

Answer

There are many answers. Here are two possibilities:
2/8 + 1/4 = 3/6
1/2 + 3/9 = 5/6

Source: Owen Kaplinsky

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8 comments

  1. Another two answers discovered by my students: 1/2 + 9/6 = 8/4 and 5/3 + 2/6 = 8/4

  2. 2/4 + 1/3 = 12/10 simply it and get 5/6

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

  4. 9/3 + 4/2 = 5/1

  5. 2/1 + 6/9 = 8/3
    7/2 + 3/6 = 4/1
    8/2 + 9/3 = 7/1

  6. 8/4 + 6/2 = 5/1
    8/4 + 9/3 = 5/1
    4/2 + 6/2 = 5/1

  7. 2/8 + 6/3 = 9/4

  8. Rudolf Österreicher

    54 unique solutions (times 2, if you count it as a different solution if you swap the two addends):
    1/4 + 2/8 = 3/6 = 0.5
    1/6 + 3/9 = 2/4 = 0.5
    1/6 + 3/9 = 4/8 = 0.5
    1/6 + 4/8 = 2/3 = 0.6667
    1/2 + 3/9 = 5/6 = 0.8333
    1/3 + 2/4 = 5/6 = 0.8333
    1/3 + 4/8 = 5/6 = 0.8333
    2/4 + 3/9 = 5/6 = 0.8333
    3/9 + 4/8 = 5/6 = 0.8333
    2/3 + 4/8 = 7/6 = 1.1667
    1/2 + 6/8 = 5/4 = 1.25
    1/2 + 5/6 = 4/3 = 1.3333
    2/8 + 5/4 = 9/6 = 1.5
    1/2 + 7/6 = 5/3 = 1.6667
    2/4 + 7/6 = 5/3 = 1.6667
    4/8 + 7/6 = 5/3 = 1.6667
    2/8 + 9/6 = 7/4 = 1.75
    1/2 + 9/6 = 8/4 = 2.0
    2/6 + 5/3 = 8/4 = 2.0
    2/8 + 7/4 = 6/3 = 2.0
    4/3 + 6/9 = 2/1 = 2.0
    4/8 + 9/6 = 2/1 = 2.0
    5/4 + 6/8 = 2/1 = 2.0
    2/8 + 6/3 = 9/4 = 2.25
    3/2 + 6/8 = 9/4 = 2.25
    2/6 + 8/4 = 7/3 = 2.3333
    1/6 + 7/3 = 5/2 = 2.5
    3/6 + 8/4 = 5/2 = 2.5
    4/3 + 7/6 = 5/2 = 2.5
    4/8 + 6/3 = 5/2 = 2.5
    6/8 + 7/4 = 5/2 = 2.5
    1/6 + 5/2 = 8/3 = 2.6667
    2/1 + 4/6 = 8/3 = 2.6667
    2/1 + 6/9 = 8/3 = 2.6667
    4/2 + 6/9 = 8/3 = 2.6667
    4/8 + 5/2 = 3/1 = 3.0
    4/8 + 5/2 = 9/3 = 3.0
    6/8 + 9/4 = 3/1 = 3.0
    3/1 + 4/8 = 7/2 = 3.5
    4/8 + 9/3 = 7/2 = 3.5
    5/6 + 8/3 = 7/2 = 3.5
    8/4 + 9/6 = 7/2 = 3.5
    3/6 + 7/2 = 4/1 = 4.0
    5/2 + 9/6 = 4/1 = 4.0
    3/1 + 6/4 = 9/2 = 4.5
    3/6 + 4/1 = 9/2 = 4.5
    3/6 + 9/2 = 5/1 = 5.0
    4/2 + 9/3 = 5/1 = 5.0
    4/8 + 9/2 = 5/1 = 5.0
    6/2 + 8/4 = 5/1 = 5.0
    6/4 + 7/2 = 5/1 = 5.0
    7/2 + 9/6 = 5/1 = 5.0
    8/4 + 9/3 = 5/1 = 5.0
    8/2 + 9/3 = 7/1 = 7.0

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