WHY CASTING OUT NINES? - Ana Paula Garrão; Margarida Raposo Dias (European Scientific Journal, ESJ, 2014)
In this paper our purpose is to answer questions like: Why casting out nines works? Why it fails? Why casting out nines and not, for example, ―casting out elevens‖? The casting out nines method was used to ―check‖ the results of operations on positive integers. Although not currently taught in elementary school it hides mathematical concepts that will help to understand important current applications such as internet security. We present the mathematical concepts behind the casting out nines method: some tests for computing remainders and the congruence relation modulo n and its properties.