VEDIC MATHS-17

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VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is our 17th blog from the series of "Vedic maths" blogs. Here in this blog we will learn about "Criss-Cross System of Multiplication".

Criss-Cross System of Multiplication :

               In Vedic Mathematics , we have similar system as like traditional way of multiplication it helps us to get the answer much faster. This system is also universal system and can be used for any combination of numbers of any length.
                     This system of Multiplication is given by the "Urdhva-Tiryak Sutra." It means ' vertically and cross-wise'. The application of this system are manifold, but in this blog we shall confine our study only to it's utility in multiplying numbers. We shall call it the criss-cross system of multiplication.

Reference:
We had already learn about "Criss-Cross System of Multiplication for 2-digit number" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-14".

We had already learn about "Criss-Cross System of Multiplication for 3-digit numbers where carry over is not involved" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-15".

We had also already learn about "Criss-Cross System of Multiplication for 3-digit numbers where carry over is involved" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-16".

 
Method:

Here in in this blog we will learn about "Criss-Cross System of Multiplication for 4-digit number". 
We have seen how to multiply 2-digit and 3-digit numbers. We can expand the same logic and multiply a bigger numbers. Let us have a look at how to Multiply 4-digits numbers.

The following are the steps involved in multiplying 4-digits numbers:

Steps involved in multiplying 4-digit numbers

Suppose we want to multiply  1111 by 1111. Then, there will be 7 steps involved in complete multiplication as suggested above from steps 'a' to 'g'.



Let us have a look at one more example:

                 2  1  0  4
             x  3  0  7  2 
    ----------------------------
     6  4  6  3  4  8  8


STEP-WISE ANSWERS

a) (4 x 2) = 8

b) (7 x 4) + (0 x 2) = 28 (2 carry-over)

c) (0 x 4) + (0 x 7) + (1 x 2) + (2 carried) = 4

d) (3 x 4) + (0 x 0) + (7 x 1) + (2 x 2) = 23 (2 carry over)

e) (3 x 0) + (0 x 1) +(7 x 2) + (2 carried)=16 (1 carry over)

f) (2 x 0) + (3 x 1) + (1 carried) = 4

g) (2 x 3) = 6

Answer:
2104 x 3072 = 6463488


            We have seen multiplication of 2-digit, 3-digit and 4-digit numbers. A question may arise regarding multiplication of numbers with an unequal number of digits.
              Let us suppose you want to multiply 342 by 2009. Here, we have one number that has three digits and another number that has four digits. Now, for such multiplication which technique will you use?
               Will you use the  technique used for multiplying numbers of 3-digits or the technique used for multiplying numbers of 4 digits?
            To multiply 342 by 2009, write the number 342 as 0342 and then multiply it by 2009. Use the technique used for multiplying four-digits numbers.

               3  4  2     ➡️            0  3  4  2
       x  2  0  0  9                 x  2  0  0  9
     --------------------              ---------------------

Thus, if we want to multiply 312 by 64, we will write 64 as 064 and then multiply it by 312 using the technique of 3-digits multiplication.

More examples:
  1. 1122x2323=2606406
  2. 1231x1253=1542443
  3. 2150x1271=2732650
  4. 1191x1235=1470885
  5. 1091x2031=2215821
                Thus, we see how to Criss-Cross system of multiplication helps us get our answer in just one line! And, the astonishing fact is that this same system can be expanded to multiplication of numbers of higher digits too.
                 And in every case, we will be able to get answer in single line.         
                The simplicity of this method can be vouched from examples given above.


You may try following example:
1) 2354 x 1191
2) 1531 x 1271
3) 1293 x 2010

You may answer this in comment box. You may ask your any query or doubt in comment box. I will try to resolve as early as possible.

In next blog we will discuss about "The characteristics Criss-Cross System of Multiplication".     

Are you excited for this?...
Then, please wait for it.
I will post my new blog in next week.

We will meet very soon through our next blog. Till that stay connected, stay healthy and stay safe.

Thanks

for giving your valuable time.

Good day😊.

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