Consider this idiotic exercise I'd never heard of lattice multiplication despite having been a math major in school and something like 70 semester hours of math courses. Assuming a need to multiply 14 by 56 as per the problem, I'd multiply 10 by 56 and get 560 in my head and then 4 x 56 (112 twice) for 224 and add the 560 and 224 to 784, again without having touched a pen or pencil, and generally thus feel no need for implements in multiplying two digit numbers. Anything much worse than that and I'd do the normal multiplication with a pen and paper.
Same here, math minor, CS major, UoA. Lots of Calculus, no lattice multiplication.
As I walk through the exercise I see no logical difference between your method and the lattice. What is different is the mechanics - you broke 14 into 10 and left the 56 intact. The lattice method breaks both numbers into single digits. The diagonals just establish the thousands, hundreds, tens, and ones positions. In any large number multiplication the result can have no more positions than the total of the positions of the two numbers being multiplied. Any lattice problem sets up with that number of diagonals.
When I was in school things like the lattice might have been shown as parlor tricks after teaching us traditional arithmetic. I grew up learning why arithmetic worked as it did. I wish more kids could have that.
” I’d multiply 10 by 56 and get 560 in my head and then 4 x 56 (112 twice) for 224 and add the 560 and 224 to 784, again without having touched a pen or pencil”
I feel a tad vindicated to learn that a math major does it that way. I’m a total math wimp, but I’ve been doing it that way for decades because it seems easier.