I find this is NOT a very helpful method. I have a bit of an issue with the term 'correct estimate', but the process that 'transforms' advocates is FAR more useful & memorable than remembering YET ANOTHER formula that you're advocating here. The method you show invariably leads to confused students because they confuse and/or misremember the fraction in the formula you show here.
I'm not sure I understand you. I HAVE shown a transformation here. You seem to suggest I'm advocating some formula, but I cannot see that I do use a formula. Please elucidate. And maybe suggest an alternate method that uses Fred's result (as the question demands)