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## Vedic Method for fast multiplication: criss-cross method or Bow method

Criss-cross method or bow method is the Vedic method for fast multiplication which is applicable to all type of multiplication.

Here Vedic sutra 3 Urdhva- Tiryagbhyham is useful. It means “vertically & crosswise”.

Case I: 2 Digit number multiplication

Ex. i) 22 x 13

Step 1: Do vertical multiplication of RHS digit i.e. 2 x 3 = 6

Step 2: Now we will do cross multiplication & add them

(2×3) +(2×1) = 8

Step 3: Do vertical multiplication of LHS digit i.e. 2 x 1 = 2

Answer 22 x 13 = 286.

We can represent this steps in general form as:

Ex. ii) 63 x 21

Note: If more than one digit will be there in first or second step of answer then right-hand side digit kept as it is & left digit to be carryover in LHS side.

As in middle digit we get 2-digit number so, we kept 2 & carryover 1 in Left side

Ans = 12+1:2:3

= 13:2:3=1323

Ex. iii) 21 x 42

Answer, 21 x 42 = 882.

Ex. iv) 88 x 24

From right side, we kept 2 as it is and carryover 3 in 48

Answer = 16: (48 +3): 2 = 16: 51: 2

Now we kept 1 as it is in middle digit & carryover 1 to left side,

Answer = (16 + 5): 1 :2 = 21:1:2

Answer 88 x 24 = 2112

#### Case 2: 3- digit number multiplication

As we see we get the answer in one line by using Criss-Cross method for 2- digit same method we can expand for more digits also.

Here we represent the steps in general form as

Now we will solve some examples to understand the steps-

Ex. v) 203 x 211

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Answer 203 x 211 = 42833

Ex. vi) 133 x 302

= 3:9:11:6:6 =3:10:1:6:6 (Middle part answer is 11 so we write 1 & carryover 1)

=4:0:1: 6:6 =40166 (From 10 we write 0 & carryover 1 so 3+1 =4)

Answer 133 x 302 = 40166

Once you understand the steps you can solve some in some seconds….

Ex. vii) 231 x 622 = (12:22:16:8:2)= 143682

Ex. viii) 432 x 151= (4:23:21:13:2)= 65232

By similar way multiplication of Higher digit is also possible.

Multiplication of number with unequal digits:

Till now we have seen all the sums having equal number of digits in both multiplier & multiplicand.  Now we will see the example having unequal digits.

e.g.) 87 X 432

Now here we have a question that which technique is need to use 2-digit or 3- digit, as one number have 2 – digits & other have 3- digits.

To convert both the number in equal digits write 87 as 087, then multiply it by 432.

Use the Technique used for 3- digit multiplication.

So, 87 x 432 = 087 x 432.

Similarly,   782 x 57 = 782 x 057

Try This:

i)  56 x 34   ii) 65 x 23   iii) 92 x 47    iv) 234 x 437

v) 67 x 419   vi) 453 x 271    vii) 78 x 234   viii) 435 x 232

i) Find the Square & Square-root of any number by simply observing the number

ii) Base Method of Multiplication

iii) Easiest way to find the cube & cube-root of any number.

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