2's, 3's, 5's, 10's, and struggled with our our 7's. If you do, you
are much younger than I, but then again, except for the baby–
boomers, everybody else is.
After memorizing everything from 1 x 1 = 1 to 12 x 12 = 144
we began to multiply things like
345 x 8 = 2760
Or did we think
(345 x 10) – (345 x 2) =
3450 – 690 = 2760
I know the second method was never mentioned, however I
thought it might be a good lead into what I am about to tell
you. That chart you memorized had a diagonal. These were
the perfect squares.
Why stop at 12 x 12 = 144. What if we could square any
2–digit number in your head. You might not think that it
would come in handy, but it gives you ideas about how you
can manipulate numbers to make what you are doing easier.
What is 93² or 93 x 93.
Well it is 8649, and I did not need a calculator to know it.
I simply added 8100 + 540 + 9 in my head.
Say what?
Well, you need to look at the problem as;
(90 + 3) (90 + 3)
and multiply every number in the 1st parenthesis by each
in the 2nd parenthesis.
90 x 90 = 8100
90 x 3 = 270 (twice) which makes 540
3 x 3 = 9
Thus, 8100 + 540 + 9 = 8649
You have to know how zeros work, but otherwise you are
just multiplying 9 x 9, 3 x 9, and 3 x 3.
It all comes from Algebra, and the F–O–I–L system.
Lets try 67 x 67, or (60 + 7)(60 + 7)
60 x 60 = 3600
60 x 7 = 420
7 x 60 = 420
7 x 7 = 49/ 3600 + 840 + 49 = 4449
With practice you can do these in your head.
No comments:
Post a Comment