I'm using this shell script to identify the maximum and minimum of the performed arithmetic operation but facing issue with float value in if block

Question

read -p "enter first number : " a
read -p "enter second number : " b
read -p "enter third number : " c
if [ $b -gt 0  ]
then
   w=`echo $a  $b  $c | awk '{print $1+$2*$3}'`;
      echo $w;
   x=`echo $a  $b  $c | awk '{print $1%$2+$3}'`
      echo $x
   y=`echo $c  $a  $b | awk '{print $1+$2/$3}'`
      echo $y
   z=`echo $a $b $c | awk '{print $1*$2+$3}'`
      echo $z

   if [ $w -gt $x ] && [ "($w -gt $y | bc)" ] && [ $w -gt $z ]
   then
      echo $w"w"
   elif [ $x -gt $w ] && [ "( $x -gt $y | bc )" ] && [ $x -gt $z ]
     then
        echo $x"x"
     elif [ $z -gt $w ] && [ $z -gt $x ] && [ "($z -gt $y | bc)" ]
     then
        echo $z"z"
     else
        echo $y"y"
   fi

   if [ $w -lt $x ] && [ "( $w -lt $y | bc )" ] && [ $w -lt $z ]
   then
      echo $w"w"
   elif [ $x -lt $w ] && [ "( $x -lt $y | bc )" ] && [ $x -lt $z ]
     then
        echo $x"x"
     elif [ $z -lt $w ] && [ $z -lt $x ] && [ "($z -lt $y | bc )" ]
       then
          echo $y"y"
       else
          echo $z"z"
   fi
fi