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
1 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.
