[NOTE: This is an entry in the 3Blue1Brown Summer of Math Exposition for 2021. Full disclosure: Originally, I wrote the multiplier and divider visuals without the detailed explanation as a project for a class this spring. Over the summer I’ve been extending it to the broader 3-part explanation that does addition and subtraction as well. I was already somewhat into the design when I heard about SoME, but apart from the original form, this has not been published previously.]