Posted by **Tiffany** on Tuesday, March 22, 2011 at 9:37pm.

the numbers M and N are different numbers selected from the first 25 counting numbers: If M is larger than N, what is the smallest value that M * N over M-N could have?

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**Reiny**, Tuesday, March 22, 2011 at 10:12pm
the smallest value of MN/(M-N) is obtained when

MN is as small as possible and M-N is as large as possible

since M and N are from the first 25 natural numbers

the smallest product is 1x2 or 2

and the largest difference is 25-1 or 24

the smallest value of MN/(M-N) is 2/24 or 1/12

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**Tiffany**, Tuesday, March 22, 2011 at 10:30pm
I thought in this problem M and N had to be the same numbers so how could we do 1*2 over 25-1. Also, M has to be larger than N........still confused.

- Math -
**Reiny**, Tuesday, March 22, 2011 at 10:52pm
In the first line of your problem you said

"M and N are **different ** numbers".

when I formed 25 - 1 for M-N , wasn't my M > N ???

- Math -
**Tiffany**, Wednesday, March 23, 2011 at 7:44pm
ok, thanks. I was just thinking I had to use the same number for M & M on the top and bottom of the fraction. I understand now. Thanks so much!

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