Answer:
2/105
Step-by-step explanation:
"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.
(8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)
We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.
The greatest rational number r is 2/105.
_____
<em>Check</em>
The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.
