Question

1. Consider the rational numbers 4/13 and 3/10 .

Answer 1

There are infinite rational numbers between the two numbers you have given 
Why not start with the one midway between the two? 
Since 3/10 = 39/130 < 4/13 = 40/130
a = (39 + 40)/260 = 79/260 
will do for a start.

Answer 2

A.      4/13      3/10

find a common denominator which is 130

    mult. by 10/10   and the second one by 13/13

   40/130    and 39/130

so, that means 4/13 is larger because after you find a common denominator, compare the top numbers to find the larger and 40 is larger than 39.

B.   a rational number between them would be 39.5/130