def apply_solved_equivalent_fractions_to_fraction
      int = self.solve_equivalent_fractions
      answer = []
      @reduced_row_echelon_form.each do |row|
        answer << row.last * int
      end
      answer << int
      count = 0
      @balanced = Hash.new
      @left_system_of_equations.each do |x,v|
        answer[count]
        @left_system_of_equations[x] = answer[count].to_i.abs unless answer[count].nil?
        count += 1
      end
      @right_system_of_equations.each do |x,v|
        answer[count]
        @right_system_of_equations[x] = answer[count].to_i.abs unless answer[count].nil?
        count += 1
      end
      answer
      @balanced = {left:@left_system_of_equations,right:@right_system_of_equations}
      self.balanced_string.gsub(/([\D^])1([\D$])/, '\1\2')  # or (/1(?!\d)/,"")
    end
def apply_solved_equivalent_fractions_to_fraction
      int = self.solve_equivalent_fractions
      answer = []
      @reduced_row_echelon_form.each do |row|
        answer << row.last * int
      end
      answer << int
      count = 0
      @balanced = Hash.new
      @left_system_of_equations.each do |x,v|
        answer[count]
        @left_system_of_equations[x] = answer[count].to_i.abs unless answer[count].nil?
        count += 1
      end
      @right_system_of_equations.each do |x,v|
        answer[count]
        @right_system_of_equations[x] = answer[count].to_i.abs unless answer[count].nil?
        count += 1
      end
      answer
      @balanced = {left:@left_system_of_equations,right:@right_system_of_equations}
      self.balanced_string.gsub(/([\D^])1([\D$])/, '\1\2')  # or (/1(?!\d)/,"")
    end
Now that we have the whole number from solve_equivalent_fractions
 we must apply that to each of the fractions to solve for the
 balanced equation