In my thinking, for example, 97 x 16 became 100 x 16 (1600)
minus 3 x 16 (48). It was easier that way, and thinking this way
became almost automatic. As a result, I might just write down 1552
even though I couldn't explain very well how I arrived at the
answer. My teachers called that a problem, but many years later such
math shortcuts were being sold in seminars and books.
Making Your Own Math Shortcuts
You can make your own math shortcuts. The following may give you
some ideas on how to do that. Alternately, you can try any of the
shortcuts and algorithms you read about and adopt the ones that are
best suited to you. There are no perfect techniques for all people,
because our minds work in slightly different ways.
For example, suppose you want to multiply 68 x 6. My mind
immediately thinks "60 x 6 = 360 and 8 x 6 = 48, and 360 + 48 is
408." That is one way to quickly arrive at a solution without pen
and paper. It is essentially this: (60 x 6) + (8 x 6) = 408.
Want another way? Think of it as (70 x 6)  (2 x 6). The
"internal dialog" might be something like this: "70 x 6 = 420, but
that is two "sixes" too many, so take away two sixes (12) and I have
408." The point is that there is often more than one way, and you
can use whichever math shortcut is easier for you.
If the problem was 68 x 9, by the way, my mind immediately
focuses on the 9. Why? Because it is close to 10, and multiplying by
10 is easy. 68 x 10 is 680, from which I just have subtract the
extra 68 to arrive at the solution of 612. Always look for the
numbers that are close to 10 or 100 or 1000, and you'll find the
easier way to do the math, especially if you are trying to do it in
your head.
Percentages can be trickier to do as mental math, but there are
ways. Suppose, for example, that you want to figure what the 4.6%
sales tax will amount to on your $29 book. One quick way to estimate
it is to take 10%, or $2.90, cut that in half to arrive at 5%, or
$1.45, and then just guess at around $1.35, because you know 4.6% is
a little less than 5%. Alternately, you could think of 5% as a 20th
of the price  if this is easier  and then round that figure down a
bit.
What if you want a more precise solution? 1% of $29 is easy to
arrive at (.29), so multiply that by 4 to arrive at $1.16. (You
might think of this as (4 x 30)  4.) Now you just need to add .6%
to that. Think 6 x 29 = 174, and then put the decimal in the right
place: .174. Add that .18 (round it up as the store will likely do)
to the 1.16 and you have $1.34 in sale's tax, pretty close to our
quick estimate. This is not as difficult as it might seem once you
practice these shortcuts a bit.
