When doing a calculation like “196 / 4”, there are a few ways you can go about it. My nature, as in school, is to divide by 2 twice, starting from the right: so 196 / 2 = (6 / 2) + (90 / 2) + (100 / 2) = 3 + 45 + 50 = 98, and then halving that brings 49 out of the ether (presumably I have seen this calculation enough I no longer need to compute it). Sometimes I would try to cluster (190 / 2) together instead of splitting them, but it seems faster and easier to split.

Starting from the left forces you to do all the splits, so that can be convenient if you find yourself clumping together and slowing yourself down, and it’s also nice because if you’re telling someone the answer, you can start saying and forgetting numbers: after you solve the first two, you can say the first number knowing it won’t change. You could also split and divide by 4 directly: 100 / 4 = 25, 90 / 4 = (80 + 10) / 4 = 20 + 2.5 = 22.5, 6 / 4 = 3 / 2 = 1.5, but it’s easy to make mistakes when dealing with large numbers and fractions.

The easiest way is probably to observe that 196 is close to 200, and do it as (200 - 4) / 4 = 50 - 1 = 49. Even though this one comes out really nicely in one-shot, I would probably still default to two-shotting it: (200 - 4) / 2 = 100 - 2 = 98, and then (100 - 2) / 2 = 50 - 1 = 49.

This method of rearranging to involve a subtraction I had known as “Vedic mathematics”. I thought I got it from Wikipedia, but I can only find a page on a book about this, and the page has no details about the actual techniques. Over time, they seem to have deleted many articles and redirected to subsections: e.g. the article on the occupancy theorem now merely links to a subset of another page, instead of giving a nice summary.