Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a fraction that is as close to 5/11 as possible.
Hint
How can we measure the difference between two fractions?
Answer
Constance Wood found the closest fraction to 5/11, which is 4/9. I had previously thought it was 1/2 (and equivalent fractions) but was wrong!
Source: Robert Kaplinsky
Isn’t 4/9 closer than 4/8? 5/11 = .4545….45 and 4/9 = .44444…..4444 isn’t that closer than .5? or am I missing something
Yes, you are correct.
Thanks Constance. I’ll change the answer and give you credit for finding it. I can’t remember why I thought it was 1/2.
I used logic to find a fraction that was a little less than half, my answer is 4/9….. I’d love to hear how the author came up with his answer of all fractions equivalent to 1/2
The author came up with 1/2 because he was wrong. 😛
9 over 22 is equal to 5 over 11
10/22 is equal to 5/11
Yes, but you’re only supposed to use digits 1 – 9.
162/357 =0.454 (rounded)
or do I need to use all the numbers?
6259/13784 = 0.454 (rounded)
The answer could be 3/9
I assert that the following is the _unique_ solution:
Numerator: 9765
Denominator: 21483
This uses all of the digits 1-9 exactly once, and exactly equals 5/11.
The proof that there are no other solutions that use all 9 digits exactly once is an exercise left to the reader