There we applied the "the Urdhva Tiryak Sutra" (meaning : Vertically and cross-wise) to perform multiplication of two digit numbers mentally, easily and speedily.

Here, we extend the method to perform multiplication of three digit numbers.

There and Here we deal with the principles appled to Multiplication. For the application to other topics of mental math, go to Vedic Maths eBook. for more details, see near the bottom of the page.

Multiply vertically and crosswise to get the digits of the product.

Examples will clarify the method.

Before seeing the examples, let us see the formula for finding the product of three digit numbers.

Let us say the three digits of the first number be 'a'(Hundreds' digit) and 'b'(tens' digit) and 'c'(units' digit)

And those of the second number be 'p'(Hundreds' digit) and 'q'(tens' digit) and 'r'(units' digit).

Write the digits of the two numbers one below the other as follows.

a b c
p q r

The product of these numbers has five parts which are given below seperated by '/'.

a b c
p q r
---------
ap/(aq+pb)/(ar+pc+bq)/(br+qc)/cr
---------

'ap' is the ten thousands' part which is the vertical product of the first column.

(aq+pb) is the Thousands' part which is the sum of the cross-wise products 'aq' and 'pb'.

(ar+pc+bq) is the Hundreds' part which is the sum of the cross-wise products 'ar' and 'pc' and the vertical product 'bq'.

(br+qc) is the Tens' part which is the sum of the cross-wise products 'br' and 'qc'.

'cr' is the units' part which is the vertical product of the last column.

Here, the five parts are obtained as in previous example. But some parts have more than one digit. In such cases, units's digit is retained and the other digits (shown in small letters) are carried over to the immediate left place as explained in the case of multiplication of two digit numbers in
Vedic mathematics.

To explain the procedure clearly, so many steps are shown.

In practice we can do the calculations mentally and write the answer in fewer steps as follows.

421
513
----
20/14/19/7/3
=21/5/9/7/3
(worked out from right)
421 x 513 = 215973

Here, obtaining the five parts and doing the carry over method is similar to the previous example. Here, the carry over is to be done in all the parts.

To explain the procedure clearly, so many steps are shown.

In practice we can do the calculations mentally and write the answer in fewer steps as follows.

456
789
----
28/67/118/93/54
=35/9/7/8/4
(worked out from right)
456 x 789 = 359,784.

Example 4 0f Mental Math

To find 567 x 89

567
089
----
0/40/93/110/63
=5/0/4/6/3
(worked out from right)
567 x 89 = 50463

Example 5 0f Mental Math

To find 987 x 21

987
021
----
0/18/25/22/7
=2/0/7/2/7 (worked out from right)
987 x 21 = 20,727

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