Unfortunately, this process isn’t easy to teach because it is mental math. It isn’t designed to be written down. It isn’t neat and tidy. It’s robust and practical.
Common Core Math is Not the Enemy
Brett Berry

How does mental math become mental math? In other words, how does it become embedded in your long term memory so that you can retrieve it mentally later on? I would argue that rote learning did play a role here, possibly not at this point, but more likely in your earlier days. This is a point that is largely ignored.