Latest Articles

# Vertically and Cross wise

Info Post
Vertically and cross wise Sutra : It is also called as  Urdhva – tiryagbhyam  which is the general formula applicable to all cases of multiplication and also in the division of a large number by another large number.

(a) Multiplication of two 2 small digit numbers.

Lets take two  numbers,say 15 x 23
Here start the multiplication from Right to Left
Step :1
1   5
|
2   3
------
5 x 3 =15 ......keep the last digit  '5' and carry over '1'

Step 2:
1  5
\/
/\
2  3
-------
(1 x 3 ) + (2x5) = 3+10 =13

With carry over '1' from step 1 ,we get 13+1 =14.....keep the last digit '4' and carry over '1'

Step 3:
1  5
|
2  3
--------
1 x 2=2

With carry over '1' from step 2, we get 2+1=3

So our result from step 1 to step 3 = 345
Therefore, 15 x 23 =345

(b) Multiplication of two 2  large digit numbers

With the number 72 x 88 ,We do all the above three steps from (a)

7  2
| \/ |
| /\ |
8  8
-------------
7x8 / ( (7x8)+(2x8)) / 2x8

56 / ( 56 +16) /16
56 / 72 / 16
=  6336   , by keeping the last digits and carrying over the rest
Therefore, 72 x 88 = 6336

Algebric Proof :
(ax + b) (cx + d)  =  ac.x2 + adx + bcx + b.d
=  ac.x2 + (ad + bc)x + b.d

where in our example  15 x 23 , a=1 ,b=5 ,c=2,d=3
and so ac.x2 + (ad + bc)x + b.d = 2 x2  +13 x +15  where x=10 meaning the place value
=   345
by  keeping the last digits and carrying over the rest.

Now consider the multiplication of two 3 digit numbers.
Let the two numbers be (ax2 + bx + c) and (dx2 + ex + f). Note that x=10
Now the product is
ax2 + bx + c    multiply
dx2 + ex + f

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

=       ad.x4 + (bd + ae). x3 + (cd + be + af).x2 + (ce + bf)x + cf

From the above expression,  we see that we multiply from left to right as per the expression

Example :
Find the result of  234 x 615 ?

ad.x4 + (bd + ae). x3 + (cd + be + af).x2 + (ce + bf)x + cf  where  a= 2,b=3,c=4 and d=6 ,e=1,f=5

=2x6 +( 3x6 +2x1 ) +(4x6+3x1 +2x5) +(4x1+3x5)+ 4x5...lets keep X's outside
=12 +(18+2) +(24+3+10)+(4+15)+20
=12x4+20x3+ 37x2 +19x+20  ..inserting X's now

And so keeping the last digits and carrying over the rest, we get   143910

Therefore,  234 x 615 =143910

Nice ,as the proverb "Practicing keeps a Man perfect " ,practicing the above sutras makes your multiplication easier .Keep practicing..that's the Veda of Vedic Maths

Share:

1. Interesting!GOOD WORK UMA

2. good , informative post

Thank You for visiting Momscribe.com !