Multiplying Fractions to Make a Whole Number

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make a whole number product.

Hint

How can you use equivalent fractions to find the answer?

Answer

6/2 * 1/3 = 1, 8/4 * 1/2 = 1, 2/4 * 6/3 = 1

Source: Owen Kaplinsky

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12 comments

  1. My students came up with more solutions:

    2/1 X 9/6 = 3
    4/1 X 6/3 = 8
    6/4 X 2/3 = 1
    3/2 X 6/9 = 1
    4/2 X 3/1 = 6
    3/6 X 4/2 = 1
    2/3 X 9/6 = 1
    4/8 X 6/3 = 1
    9/3 X 4/2 = 6

  2. I had 6/2 x 3/1 = 9. I got this by finding a number that times by something would be under ten. I first got 6/2 and that got me 3. Then i got 3 from 3/1. Lastly i multiplied 3 by 3 and got 9. I agree it was a challenging puzzle.

  3. I got 8/1 x 6/2 = 21

  4. This is not what I was looking for please be more accurate with the answers I really HATE it when I get the answers wrong. 🙁

  5. 2/3×1/3=3/3 or 1

  6. I don’t agree with the first two provided answers. If you use a unit fraction as a factor, you cannot reuse the “1” tile in the answer. In fact, I don’t think there is an answer with a unit fraction as a factor. The third supplied answer works, though.

  7. I got 8/6 x 3/4=1. Im 10! This is not really 5th grade level if you know how to multiply fractions.

  8. Vanessa Churchill

    Today we found:

    9/6 x 2/3 = 1
    6/9 x 3/2 = 1
    6/3 x 2/4 = 1
    6/8 x 4/3 = 1
    4/6 x 3/2 = 1
    1/8 x 4/3 = 6
    6/4 x 8/3 = 2

  9. Rudolf Österreicher

    The 24 unique solutions are
    2/3 * 6/4 = 1
    2/3 * 9/6 = 1
    3/4 * 8/6 = 1
    3/6 * 4/2 = 1
    3/9 * 6/2 = 1
    4/8 * 6/3 = 1
    3/6 * 4/1 = 2
    3/9 * 6/1 = 2
    4/3 * 9/6 = 2
    2/4 * 6/1 = 3
    2/6 * 9/1 = 3
    4/6 * 9/2 = 3
    4/8 * 6/1 = 3
    8/6 * 9/4 = 3
    2/1 * 6/3 = 4
    3/6 * 8/1 = 4
    8/6 * 9/3 = 4
    2/1 * 9/3 = 6
    3/2 * 4/1 = 6
    3/4 * 8/1 = 6
    4/2 * 9/3 = 6
    8/4 * 9/3 = 6
    4/3 * 6/1 = 8
    3/1 * 6/2 = 9

    You can always swap the fractions, the numerators or the denominators to get another solution.

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