Definitions from a mathematical mouse
division: the process of splitting a number or and amount into equal parts or equal groups (that is why it why it helps us understand fractions)
My Youtube videos below demonstrate how to understand formal methods for division. Hope you enjoy them and watch them as many times as you need until you become really confident that you fully understand them!
Of course, you as a great mathematician already know that sometimes using mental methods can be the best strategy and sometimes using formal methods is the best method. Don't always use the same approach - use the best approach!
TdM Brie-Anna de Mouse, creator and star of Maths with a Mouse