4 pieces of pipe need 4 cuts to separate them from a length of pipe so that means 4/6=2/3" is wasted.
20' less ⅔"=19'11⅓". Total length of pipes required=2'1¼"+4'2¾"+5'1⁹⁄₁₆"+6'3⅝"=17'+7"+(4+12+9+10)/16".
The fraction comes to 35/16=2³⁄₁₆". So total length cut is 17'9³⁄₁₆".
What’s left is 19' 11⅓"-17'9³⁄₁₆"=2'2+(16-9)/48"=2'2+7/48=2'2⁷⁄₄₈".