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A few methods for speed:

When performing any
of these multiplication algorithms, the multiplier should have as many zeroes prepended(prefixed) to it as there are digits in the multiplicand. This will provide room for any carrying operations. For instance, when multiplying 366 × 7, add one zero to the front of 366 (write it "0366"); when multiplying 985 × 12, prepend two zeroes to 985 ("00985").

Each digit but the last, including the prepended zeroes, has a neighbor, i.e., the digit on its right.

To multiply by 12:
Starting from the rightmost digit, double each digit and add the neighbor. This gives one digit of the result. If the answer is greater than 1 digit simply carry over the 1 or 2 to the next operation. Example: 316 × 12 = 3,792:
In this example:

the last digit 6 has no neighbor.
the 6 is neighbor to the 1.
the 1 is neighbor to the 3.
the 3 is neighbor to the second prefixed zero.
the second prefixed zero is neighbor to the first.

6 × 2 = 12 (2 carry 1)
1 × 2 + 6 + 1 = 9
3 × 2 + 1 = 7
0 × 2 + 3 = 3
0 × 2 + 0 = 0

To multiply by 11:

0 3 4 2 5 x 11=37,675

  3     7     6     7     5

(0+3) (3+4) (4+2) (2+5) (5+0)

To multiply by 6:

Add half of the neighbor to each digit.
If the starting digit is odd, add 5.

6 × 357 = 2142

Working right to left,
7 has no neighbor, add 5 (since 7 is odd) = 12. Write 2, carry the 1.

5 + half of 7 (3) + 5 (since the starting digit 5 is odd) + 1 (carried) = 14. Write 4, carry the 1.

3 + half of 5 (2) + 5 (since 3 is odd) + 1 (carried) = 11. Write 1, carry 1.

0 + half of 3 (1) + 1 (carried) = 2. Write 2.

Multiplying by 7:

Double each digit.
Add half of its neighbor.
If the digit is odd, add 5

Multiply by 8:

Subtract last digit from 10 and double
Subtract the other digits from 9 and double
Add result to the neighboring digit on the right.
For the last calculation (The leading Zero), subtract 2 from the neighbour.

Multiply by 9:

subtract the last digit from 10 (Ex.: 10 - 3 = 7)
Subtract the middle numbers from 9, and add to the number to the right.
Take away 1 from the first number.

NOTE: these things take some time to learn (and read) but are quite helpful.

this system of mathematics was formulated by a person called Jakow Trachtenberg(Ukranian in a Nazi concentration camp)

check out this software:

http://www.shermankeene.com/powmath.zip

HOPE THIS HELPS A BIT!
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