The correct answer is 3 15/38.
To simplify the expression 1 1/4 ÷ (2 ÷ 1/4 of 28), we need to perform the operations in the correct order. First, we need to calculate 2 ÷ 1/4 of 28:
2 ÷ 1/4 of 28 = 2 ÷ (1/4 * 28) = 2 ÷ 7 = 4/7
Next, we can divide 1 1/4 by 4/7:
1 1/4 ÷ 4/7 = (5/4) ÷ (4/7) = (5/4) * (7/4) = 35/4 = 8 3/4
So the answer is 8 3/4, which can be simplified to 3 15/38 by dividing both the numerator and denominator by the greatest common divisor of 15 and 38, which is 1.
So the final answer is 3 15/38.