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VERTICALLY AND CROSSWIRE (Urdhva-Tiryagbyham)

Example 1


 22 x 31 = ?


Follow the general steps :
First part : 2 x 3 = 6 (multiplying the left side )
Last part : 2 x 1 = 2 (multiplying the right side)
Middle part :  (2 x 1)  + (2 x 3) =  2  +  6 = 8 (cross-multiplying both sides)
The answer is (first part | middle part  | last part ) = 682

Therefore 22 x 31 = 682




Example :2

68 x 35 = ?



First part | Middle part | Last part
(6 x 3) | ( 6 x 5 )+ (8 x 3)  | (8 x 5)
18 | (30 + 24 ) | 40
18 | 54 | 40
8 | 5 4 | 4 0 (carry over and add the left side of the digits)
 = 2380

Therefore 68 x 35 = 2380

There is yet another technique known as the Grid Method ,good for multiplication









GRID METHOD  or Sum of the Products

Example : 1
15 x 17 =?

For this method rewrite 15 as (10 + 5) and 17 as (10 + 7)  and then fill in the grid as shown
Finally add all the numbers inside the grid for the final answer ( 100 + 50 + 70 + 35) = 255

Therefore 15 x 17 = 255

Example 2:

78 x 25 = ?

Rewriting the numbers and forming the grid , we get
Again adding all the digits inside the grids ,(1400+160+350+40) =1950

Therefore 78 x 25 = 1950

You can try with different two digit numbers for both the above methods.In case of a single digit number, say 35 x 6 ,it becomes 35 x 06 and calculate using the same rules as described above.



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