**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

**5**6 is

**5**

First Digit of

**5**4 is

**5**

Last Digit of 5

**6**is 6

Last Digit Of 5

**4**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**

**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**

__Multiplication of two digit number that__

**Method 2 :****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**

__Multiplication of two digit number that__

**Method 3 :****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**

__Multiplication of two digit number that__

**Method 4 :****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**

__Multiplication of__

**Method 5 :****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**

__Multiplication of__

**Method 6 :****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**

__Multiplication of__

**Method 7 :****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**

__Multiplication of__

**Method 8 :****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**

__Multiplication of__

**Method 9 :****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**

__Multiplication of__

**Method 10 :****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**

__Multiplication of__

**Method 11 :****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.e**

**92*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

__if sum of two digit is greater than 10 then add 1 to previous digit and subtract 10 to the associate digit__

**Note:**__Multiplication of__

**Method 12 :****12**with Any Number.

(1)65214*12

Write down 0 at the both end of Number(it is called

**Zero Sandwich**)

**0**65214

**0**

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**

__Multiplication of Any two Number, Both Ranging between 11 to 19.__

**Method 13 :****(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**

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