In 1901, when I was drawing up notes on Mental Arithmetic, I looked into many text-books in search of a simple method for dividing by such numbers as 19, 29, 99, 87, etc., but found none. The following method, viz., that of using a multiple of ten as divisor instead of a given divisor, was then discovered by me, and I think it simple enough to be learned and practised by any one.
If it be required to divide A by D, let the quotient at any step be Q, then the product at that step will be DQ, and the remainder, R = A - DQ, where R cannot exceed D nor be less than zero.