MULTIPLICATION

                                  Multiplication Trick

Method 1 :Multiplication of 2 Digit Numbers Where the first digit of both numbers is same and Last digit of the 2 Numbers sum to 10.
(1)56*54
First Digit of 56 is 5
First Digit of 54 is 5


Last Digit of 56 is 6
Last Digit Of 54 is 4
Sum of Last Two digit is 6+4=10



Multiply of 5 and (5+1)
5*(5+1)=5*6=30 Write Down 30
Multiply of Last Digit of Both Numbers
6*4=24 write Down 24
i.e
56*54=3024

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                                                                    OR

Multiplication of 2 Digit Number the Ten's Digit Add up to 10 and Unit digits Same

1.First Find the multiplication of last two digit of both the numbers

2.Multiply the Ten's Digits and Add the Common Digit to the multiplication

Ex:44 * 64

First Number is 44

First Digit of 44 is 4

Second Digit of 44 is 4

Second Number is 64

First Digit of 64 is 6

Second Digit of 64 is 4

Second Digit in Both Number is Same i.e 4

Sum of First Digit of Both Number is 4+6=10

Multiplying the unit Digit ,we get 4*4=16,Put it at right hand side.

Multiplying the Ten's Digits of Both Number and Adding Common Digit ,we get (4*6) + 4=24+4=28 ,Put it at the left hand side.

So,We get Answer is 2816

Method 2 :Multiplication of two digit number that differ by 6
(1)10*16
First Number =10
Second Number =16
Difference Between 10 & 16 is 16-10=6
If two number differ by 6 then their product is the square of  their average  minus 9 .
Average of 10 and 16 is (10+16)/2=26/2=13
Square of Average Number
13^2 =169
Minus 9 from Square of average
169-9=160
i.e
10*16=160



Method 3 :Multiplication of two digit number that differ by 4
(1)10*14
First Number =10
Second Number =14
Difference Between 10 & 14 is 14-10=4
If two number differ by 6 then their product is the square of  their average  minus 4 .
Average of 10 and 14 is (10+14)/2=24/2=12
Square of Average Number
12^2 =144
Minus 4 from Square of average
144-4=140
i.e
10*14=140

Method 4 :Multiplication of two digit number that differ by2
(1)10*12
First Number =10
Second Number =12
Difference Between 10 & 12 is 12-10=2
If two number differ by 6 then their product is the square of  their average  minus 1 .
Average of 10 and 12 is (10+12)/2=22/2=11
Square of Average Number
11^2 =121
Minus 1 from Square of average
121-1=120
i.e
10*12=120
Method 5 :Multiplication of 125 with Any Number.
(1)92*125
125=5^3=(10/2)^3=1000/8
Now,
92*125
92*(1000/8)
(92*1000)/8
92000/8
11500
i.e
92*125=11500

Method 6 :Multiplication of 25 with Any Number.
(1)92*25
25=5^2=(10/2)^2=100/4
Now,
92*25
92*(100/4)
(92*100)/4
9200/4
2300
i.e
92*25=2300

Method 7 :Multiplication of 5 with Any Number.
(1)92*5
5=5^1=(10/2)^1=10/2
Now,
92*5
92*(10/2)
(92*10)/2
920/2
460
i.e
92*5=460


Method 8 :Multiplication of 999 with Any Number.
(1)92*999
999=1000-1
Now,
92*999
92*(1000-1)
(92*1000)-(92*1)
92000-92
91908
i.e
92*999=91908

Method 9 :Multiplication of 99 with Any Number.
(1)92*99
99=100-1
Now,
92*99
92*(100-1)
(92*100)-(92*1)
9200-92
9108
i.e
92*99=9108


Method 10 :Multiplication of 9 with Any Number.
(1)92*99
9=10-1
Now,
92*9
92*(10-1)
(92*10)-(92*1)
920-92
828
i.e
92*9=828

Method 11 :Multiplication of 11 with Any Number.
(1)92*11
Write down 0 at the both end of Number(it is called Zero Sandwich )
0920
sum of the two successive number digit
0+9....9+2....2+0
9...11....2
10.....1(carry 1)....2

1012 
i.e92*11=1012
                                     OR
Insert the sum of 2 successive digits and to put 2 terminal digit in its place

456872*11
Put Two Terminal Digits in its place
4.........................................................................2

Insert the Sum of 2 Successive digit
4....(4+5).....(5+6)....(6+8)....(8+7).....(7+2).......2

4.....9......11.......14......15.....9.....2
 4.....9+1(Take Carry 1)......11-10(10 Carry Forwarded to left hand-side)+1(Carry take 1 from Right hand side).....14-10(10 Carry Forwarded to left hand-side)+1......15-10(10 Carry Forwarded to left hand-side).....9....2
4...........10.............2..............4+1...............5.........9...........2
4+1........10-10...........2...............5................5.........9..........2
 5..................0..............2...........5.......5...........9..........2
5025592
 i.e 
456872*11=5025592
Note: if sum of two digit is greater than 10 then add 1 to previous digit and subtract 10 to the associate digit



Method 12 :Multiplication of 12 with Any Number.
(1)65214*12
Write down 0 at the both end of Number(it is called Zero Sandwich )
0652140
The Ultimate Digit is 0 and the Penultimate digit is 4 .
Adding the ultimate digit and twice the penultimate digit we get 0+8=8

For the Ten's Column ,The ultimate digit is 4 and the Penultimate digit is 1 so 4+2=6

Like wise 1+4=5 and 2+10=12 ,with 12 We set down 2 and carry 1.
5+12+carry1=18 and again we carry 1.

The Final step is 6+0+carry 1=7

So ,the Answer is 782568

Method 13 :Multiplication of Any two Number, Both Ranging between 11 to 19.

(1)13*19
Add First Number and Last digit of second number Take 0 (Zero) in the third place of this number the add product of last digit of the two numbers in it.

First Number is 13
Second Number is 19

Add First Number and Last Digit of Second Number
First Number is 13
Second digit of second number is 9
13+9=22

Put 0 (Zero)
0

Product of Last Digit of two Number.
Last Digit of 13 is 3
Last digit of 19 is 9
3*9=27

Add Product of Last Digit of two Number in Number
22.....0 + 27
220+27
447
i.e.
13*19=447