How many pieces?

A jewelry artisan is making earring hoops. Each hoop requires a piece of wire that is 3 ¾ inches long. If the wire comes in 50 inch coils, how many earrings can be made from one coil and how much wire is wasted? (Bassarear, 2nd ed, p. 49)



Student #1: 50 ÷ 3¾ = 13.333.... So "you can make 13 pieces and you'll have wasted 1/3"


"We have 1/3 left over, after all.." But answer is not correct.


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?"