Student #2 uses repeated-subtraction: 3¾ = 15/4 so: 4 rings take up 15 inches; 8 rings take up 30 inches; 12 rings take up 45 inches; 13 rings take up 45+3¾ = 48¾ inches, so we can make 13 rings, and have 50- 48¾ = 1¼ inches of wire unused. "Remainder = 1¼"

"Will the real remainder please stand up?"

But student #2 had used up 48¾ inches, so Remainder = 1¼ inches.

Student #1: 50 inches ÷ 3¾ inches/ring; = 13.333.... rings.

We have a (sort of) "remainder" of 1/3 of a ring (not 1/3 of an inch)

Check: 1/3 of a ring takes up (1/3)·(3¾) = 1¼ inches.

Summary:
Finding (an) answer was the easier part; interpreting the numbers was the harder part..