Open Middle®
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
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
I did 2/1 times 9/6=3
ok
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.
I got 8/1 x 6/2 = 21
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. 🙁
2/3×1/3=3/3 or 1
2/3 x 1/3 is 2/9, not 1.
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.
I got 8/6 x 3/4=1. Im 10! This is not really 5th grade level if you know how to multiply fractions.
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
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.