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1. Multiplication
of any two numbers, lies between 11 and 19
13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247
Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it.
Example : 18*14 = (18+4)*10 + (8*4) = 220 + 32 = 252

2. EXCLUSIVE
DIVISION RULE FOR 8
If a number is divisible by eight the
last three digits are divisible by 8
Example :
4857248
last three digits are 248 248/8 = 31 Then 4857248 is divisible by 8 
3. AWESOME DIVISION RULE FOR 11
If a number is divisible by eleven the difference between the sum of
the digits in the even places and the sum
of the digits in the odd places is 11 or 0.
23485 is shown to be divisible by 11 because 2 + 4 + 5 = 11 3 + 8 = 11 11  11 = 0 and and 60852 is shown to be divisible by 11 because 6 + 8 + 2 = 16 0 + 5 = 5 16  5 = 11 
4. Amazing number 4
With number 4 the secret steps in the multiplication tables become a
little more intricate.
4*1 = 4  4 4*2 = 8  8 4*3 = 12  1+2 =  3 4*4 = 16  1+6 =  7 4*5 = 20  2+0 =  2 4*6 = 24  2+4 =  6 4*7 = 28 2+8=10 1+0 =  1 4*8 = 32  3+2 =  5 4*9 = 36  3+6 =  9 4*10 = 40  4+0 =  4 4*11 = 44  4+4 =  8 4*12 = 48 4+8=12  1+2= 3 4*13 = 52  5+2 =  7 4*14 = 56 5+6=11 1+1= 2 4*15 = 60  6+0 =  6 4*16 = 64 6+4=10 1+0= 1
At first the sums of the digits look like a jumble of figure, but
choose at random any sequence of numbers and multiply them by 4 and you will
see the pattern emerge of two interlinked columns of digits in descending
order.
2160*4 = 8640  8+6+4+0 = 18  1+8 =  9 2161*4 = 8644  8+6+4+4 = 22  2+2 = 4 2162*4 = 8648  8+6+4+8 = 26  2+6 =  8 2163*5 = 8652  8+6+5+2 = 21  2+1 = 3 2164*4 = 8656  8+6+5+6 = 25  2+5 =  7 2165*4 = 8660  8+6+6+0 = 20  2+0 = 2 2166*4 = 8664  8+6+6+4 = 24  2+4 =  6 2167*4 = 8668  8+6+6+8 = 28  2+8=10  1+0 = 1 2168*4 = 8672  8+6+7+2 = 23  2+3 =  5 
5. Percentage computation
Calculate 65% of 460:

6. To
calculate reminder on dividing the number by 7 11 and 13
Let me explain this rule by taking examples consider number 34568276, we have to calculate the reminder on diving this number by 7 11 and 13 respectively. make triplets as written below starting from units place 34.........568..........276 now alternate sum = 34+276 = 310 and 568 and difference of these sums = 568310 = 258 divide it by 7 we get reminder as 6 divide it by 11 we get reminder as 5 divide it by 13 we get reminder as 11
Other Example :
consider the number 4523895099854
triplet pairs are 4...523...895...099...854 alternate sums are 4+895+854=1753 and 523+099=622 difference = 1131 revise the same tripling process 1......131 so difference = 1311 = 130 divide it by 7 we get reminder as 4 divide it by 11 we get reminder as 9 divide it by 13 we get reminder as 0 
7. Square a 2 Digit Number Ending in 5
For this example we will use 25
·
Take
the "tens" part of the number (the 2 and add 1)=3
·
Multiply
the original "tens" part of the number by the new number (2x3)
·
Take
the result (2x3=6) and put 25 behind it. Result the answer 625.
Try a few more 75
squared ... = 7x8=56 ... put 25 behind it is 5625.
55 squared = 5x6=30 ... put 25 behind it ... is 3025. Another easy one! Practice it on paper first! 
8. Square 2 Digit Number: UPDOWN Method
Square a 2 Digit
Number, for this example 37:
·
Look
for the nearest 10 boundary
·
In
this case up 3 from 37 to 40.
·
Since
you went UP 3 to 40 go DOWN 3 from 37 to 34.
·
Now
mentally multiply 34x40
·
The
way I do it is 34x10=340;
·
Double
it mentally to 680
·
Double
it again mentally to 1360
·
This
1360 is the FIRST interim answer.
·
37
is "3" away from the 10 boundary 40.
·
Square
this "3" distance from 10 boundary.
·
3x3=9
which is the SECOND interim answer.
·
Add
the two interim answers to get the final answer.
·
Answer:
1360 + 9 = 1369

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