A faster way of doing math that I was not taught in school.
This trick is one of the most common tricks taught in UIL Number Sense (If you're interested)
Just thought I would tell you just in case you wanted to look up some more advanced Number Sense tricks.
Wrong 45x34 and all those inbetween numbers
Assuming You're talking about the near 100's trick, no it works by definition.
(100-x)(100-y), FOIL it out
10000-100x-100y-xy
10000-100(x+y)-xy (Association) This is what the trick does
So even though it is not efficient for 45x34 it still works
You get reference numbers of 55 and 66, their sum is 121
100-121=-21 (and we add two 0s since it is to go in the hundreds place), so -2100
55*66=3630
-2100+3630=1530 which is 45x34.
This trick is only beneficial when used in numbers 10+/- of 100, or else you start jumping into more 2 digit mult. Though it should work on any multiplication.