Lucy saws a wooden rod into two pieces. The larger piece is 7 3/4 inches long. The original rod was 9 1/8 inches long. How many inches long is the resulting smaller piece?
The larger piece is 7 3/4 inches long, which is 31/4 inches.
The original length of the rod was 9 1/8 inches, which is 73/8 inches.
So the length of the smaller piece is 73/8 - 31/4 = 73/8 - 31/8 = 42/8 = <<73/8-31/4=5 1/4>>5 1/4 inches. Answer: \boxed{5\frac{1}{4}}.