Digits are chosen without replacement from the set {1,3,5,7,9}

Question

and placed in the boxes such that the sum of the two fractions is less than one. What is the greatest possible sum of the two fractions. Express your answer as a common fraction. 

 

?/? + ?/? < 1.

Answer 1

possible fractions are:

1/3, 1/5, 1/7, 1/9, 3/5, 3/7, 3/9, 5/7, 5/9, and 7/9

the greatest possible denominator is 9*7=63

(3/7)+(5/9)=(27/63)+(35/63)=62/63 is the largest fractional sum less than 1