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Among all fractions  that have a positive integer numerator and denominator and satisfy 9/11 <= x <= 9/10, which fraction has the smallest denominator?

 Apr 28, 2022
 #1
avatar+124598 
+1

9 /11 ≤ x ≤ 9/10

 

90 / 110  ≤ x ≤  99 / 110

 

 Possible  fractions

90  /110  , 91/110 , 92  /110  , 94 /110  , 95  / 110   , 96 /110   , 97/110 , 98/110 , 99/ 110

 

95  / 110  =     19  /  22     has the smallest denominator

 

 

cool cool cool

 Apr 28, 2022
 #2
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+1

How about 5/6  = 0.83333...   ?

( 9/11 = 0.81818...  ,  9/10 = 0.90000... )

 Apr 28, 2022
 #3
avatar+124598 
0

Yep....your answer is  correct!!!

 

Thanks  !!!

 

cool cool cool

CPhill  Apr 28, 2022

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