SHORTCUTS FOR MULTIPLICATION

TRICK1: 3-digit number multiplication:

x	5	4	1
	1	2	1
=   6     5     4     6     1    5   1 (1st column) 5    4   1    2 (first two columns) 5     4    1   1     2    1 (all columns) 4    1   2    1 (last two columns) 1   1 (3rd column) (5x1) = 5   (5x2)+(4x1) = 10+4 = 14 (5x1)+(1x1)+(4x2) = 5+1+8 =14 (4x1)+(2x1) = 4+2 = 6 (1x1) =1 = 5+1 = 6 = 14 +1 = 15 = 14 =6 =1

              

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

 

x	2	3	5
	4	6	7
=   1   0   9   7   4   5   2   4 (1st column) 2     3   4     6 (first two columns) 2     3    5   4     6    7 (all columns) 3    5   6    7 (last two columns) 5   7 (3rd column) (2x4) = 8   (2x6)+(4x3) = 12+12 =24 (2x7)+(4x5)+(3x6) = 14+20+18 =52   (3x7)+(6x5) = 21+30 =51   (5x7) =35 =8+2 = 1 0 =24+5 = 29 =52+5 = 57 = 51+ 3 = 54 =35

 

 

 

 

 

 

 

 

 

TRICK2: 2-digit number multiplication:

x	1	2
	2	4
=   2  8   8

1   2 (1st column)	1    2   2    4 (All columns)	2   4 (3rd  column)
(1x2) =2	(1x4)+(2x2) = 4+4 =8	(2x4) = 8

x	2	9
	5	4
=   1   5   6   6

2   5 (1st column)	2    9   5    4 (All columns)	9   4 (3rd  column)
(2x5) =10	(2x4)+(9x5) = 8+45 =53	(9x4) = 36
= 10 +5 =15	=53+3 =56	=36

x	8	4
	6	5
=   5   4   6   0

8   6 (1st column)	8    4   6    5 (All columns)	4   5 (3rd  column)
(8x6) =48	(8x5)+(6x4) = 40+24 =64	(4x5) = 20
= 48 +6 =54	=64+2 =66	=20

TRICK3:  numbers nearer to 10:

1 2 x 1 4 =

STEP 1			STEP 2
1 2 x 1 4			1 2 x 1 4
1 2	+2		1 2	+2
1 4	+4		1 4	+4
= 1 6  (12+4 or 14+2)			= 16	+8(2x4)
=  1 6 8

 

1 7 x 1 8 =

STEP 1			STEP 2
1 7 x 1 8			1 7 x 1 8
1 7	+7		1 7	+7
1 8	+8		1 8	+8
= 2 5 (17+8 or 18+7)			= 2 5	+56(8x7)
			= 2 5+5 = 30	56
=  3 0 6

 

Numbers nearer to 100:

9 6 x 9 4 =

STEP 1			STEP 2
9 6 x 9 4			9 6 x 9 4
9 6	- 4		9 6	- 4
9 4	- 6		9 4	- 6
= 9 0  (90-6 or 94-4)			= 9 0	+ 2 4(-4 x -6)
=  9 0 2 4

 

9 6 x 1 0 4 =

STEP 1			STEP 2
9 6 x 1 0 4			9 6 x 1 0 4
9 6	- 4		9 6	- 4
1 0 4	+4		1 0 4	+4
= 1 0 0  (96+4 or 104-4)			= 1 0 0	-1 6(-4 x 4)
			= 1 0 0    0 0                     - 1 6
=  9 9 8 4

 

1 0 6 x 1 0 4 =

STEP 1			STEP 2
1 0 6 x 1 0 4			1 0 6 x 1 0 4
1 0 6	+6		1 0 6	+6
1 0 4	+4		1 0 4	+4
= 1 1 0(106+4 or 104+6)			= 1 1 0	+ 2 4(6 x 4)
=  1 1 0 2 4

 

Numbers nearer to 1000:

1 0 0 5 x 1 0 0 3 =

STEP 1			STEP 2
1 0 0 5 x 1 0 0 3			1 0 0 5 x 1 0 0 3
1 0 0 5	+5		1 0 0 5	+5
1 0 0 3	+3		1 0 0 3	+3
= 1 0 0 8(1005+3 or 1003+5)			= 1 0 0 8	+015(5 x 3)
=  1 0 0 8 0 1 5

 

9 9 5 x 1 0 0 4 =

STEP 1			STEP 2
9 9 5 x 1 0 0 4			9 9 5 x 1 0 0 4
9 9 5	-5		9 9 5	-5
1 0 0 4	+4		1 0 0 4	+4
= 9 9 9(995+4 or 1004-5)			= 9 9 9	-020(-5 x 4)
			= 9 9 9 0 0 0           - 0 2 0
=9 9 8 9 8 0

 

9 9 2 x 9 9 6 =

STEP 1			STEP 2
9 9 2 x 9 9 6			9 9 2 x 9 9 6
9 9 2	-8		9 9 2	-8
9 9 6	-4		9 9 6	-4
= 9 8 8(992-4 or 996-8)			= 9 8 8	+032(-8 x -4)
=  9 8 8 0 3 2

 

TRICK4: 2-digit number multiplication:

Conditions to apply this trick:

1.     10’s place digits should be same

2.     Sum of unit place digits are equal to 10

64  x  66	6x7 (10’s place digit * after that)	6x4 (product of unit place digits)
	42	24
= 4 2 2 4
57  x  53	5x6 (10’s place digit * after that)	7x3 (product of unit place digits)
	30	21
= 3 0 2 1
10 6 x 10 4	10x11 (10’s place digit * after that)	6x4 (product of unit place digits)
	110	24
= 1 1 0 2 4

   

TRICK5: Shortcut to 11^th tables:

51  x  11	5          6(5+1)       1
72  x  11	7          9(7+2)     2
34  x  11	3          7(3+4)     4
42  x  11	4          6(4+2)     2
74  x  11	7         11(7+4)    4  7+1     11(7+4)    4  8          1           4
87  x  11	8         15(7+4)    7  8+1     15(7+4)    7  9          5           7

TRICK6: Lattice Multiplication:

4 3 2  x  3 3 4  = 

                       

 = 1 4 4 2 8 8

TRICK7: Crossing sticks method:

 1 4 2 x 4 3 = 

= 6 1 0 6