To solve this, we need to first convert all the fractions to have the same denominator.

So, 3 3/8 = 3 + 3/8 = 24/8 + 3/8 = 27/8
1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4

Now we can rewrite the equation as:

27/8 - 5/4 - 15/32

Next, we need to find a common denominator for the fractions. The least common multiple of 8, 4, and 32 is 32.

So, we rewrite the equation again with a common denominator of 32:

(274)/32 - (58)/32 - 15/32
(108/32) - (40/32) - 15/32

Now, we can subtract the fractions:

(108 - 40 - 15)/32
(53/32)

Therefore, 3 3/8 - 1 1/4 - 15/32 = 53/32 or 1 21/32.