You've indicated that you prefer not to use regular expressions. In that case, you're still working too hard. In that case, you should look for a library function that does the job, such as the standard scanf library.

require 'scanf'

def eval_binary_expr(expr)
  l_operand, op, r_operand = expr.scanf('%f %c %f')
  if l_operand.nil?
    raise ArgumentError, "Missing or invalid left operand"
  end

  begin
    case op
      when '/' then l_operand / r_operand
      when '*' then l_operand * r_operand
      when '+' then l_operand + r_operand
      when '-' then l_operand - r_operand
      else raise ArgumentError, "Missing or invalid operator"
    end
  rescue TypeError
    raise ArgumentError, "Missing or invalid right operand"
  end
end

This implementation is better than the original, in that it can handle negative operands and explicitly positive operands. It also examines the string from left to right, which makes it easier to understand its behaviour.

You've indicated that you prefer not to use regular expressions. In that case, you're still working too hard. In that case, you should look for a library function that does the job, such as the standard scanf library.

require 'scanf'

def eval_binary_expr(expr)
  l_operand, op, r_operand = expr.scanf('%f %c %f')
  if l_operand.nil?
    raise ArgumentError, "Missing or invalid left operand"
  end

  begin
    case op
      when '/' then l_operand / r_operand
      when '*' then l_operand * r_operand
      when '+' then l_operand + r_operand
      when '-' then l_operand - r_operand
      else raise ArgumentError, "Missing or invalid operator"
    end
  rescue TypeError
    raise ArgumentError, "Missing or invalid right operand"
  end
end

This implementation is better than the original, in that it can handle negative operands and explicitly positive operands. It also examines the string from left to right, which makes it easier to understand its behaviour.