**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

**Answer** 63 x 21= 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

**Find the following links to learn more:**

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.

Multiplication Criss Cross Method 6 Digits

Yes it is possible for 6 digits also, by similar way.

Excellent method.