There are two common problems when designing and using artificial neural networks. The first is the need for better performance. The second is the need to combat the increasing complexity with enhancements. In this paper we design a way to do both.This is done in each iteration by calculating what weights would give the optimal answer for each input and output pair. The weights are then updated by the difference between the ideal weight and the current weights all of it times the learning rate.We find that this method not only converges much faster for an image classification problem but it also is much simpler to understand and does not rely on using calculus or derivatives. However the method only works for a shallow or single layer neural network.By using simple arithmetic, neural networks can be updated in a way that is both simpler and more efficient than back-propagation.