Estimate 3 + 1/4 with 3 and 1 + 7/8 with 2, so that (3 + 1/4) - (1 + 7/8) is approximately 3 - 2 = 1. But the friend's result is nearly twice this approximation.
Compare to the exact result:
(3 + 1/4) - (1 + 7/8) = 13/4 - 15/8 = (26 - 15)/8 = 9/8
Similarly, estimate 7/8 with 1, and 4/9 with 1/2. Then 7/8 + 4/9 is roughly 1 + 1/2 = 3/2, a number greater than 1. But 11/17 is less than 1.
For comparison:
7/8 + 4/9 = 63/72 + 32/72 = 95/72 (about 1.319)