For my kids, apparently some kind of number line nonsense, which is counting with extra steps.
I just memorize it. When the numbers get big, I do it like you did. For example, my kid and I were converting miles to feet (bad idea) in the car, and I needed to calculate 2/3 mile to feet. So I took 1760 yards -> 1800 yards, divided by three (600), doubled it (1200), and multiplied by 3 to get feet (3600). Then I handled the 40, but did yards -> feet -> 2/3 (40 yards -> 120 ft -> 80 ft). So the final answer is 3520 ft (3600 - 80). I know the factors of 18, and I know what 2/3 of 12 is, so I was able to do it quickly in my head, despite the imperial system's best efforts.
So yeah, cleaning up the numbers to make the calculation easier is absolutely the way to go.