Vedic Math

Multiplication of Bigger Numbers by Duplex Numbers

For multiplication by duplex numbers we can follow the same method we saw earlier for any number of digits. The only thing that we have to keep in mind is to add every two neighbouring digits and multiply by the digit of the duplex number and get the answer in a single digit.

Let us start with a 4 digit number.

•  Put a zero at the beginning and end of the given number.
•  Starting from the last digit on the right, add every pair of digits and then multiply by the digit of the duplex number.
•  When the numbers obtained have two digits, carry the tens digits to the next higher place and put down the units digit in the answer.

Example: 1654 x 33

•  016540
•  (0 + 4) x 3 =12;  (4 + 5) x 3 = 27;

(5 + 6) x 3 = 33; (6 + 1) x 3 = 21;

(1+0) x 3 = 3

3   21   33   27   12 

•  2 in the units place, 1 carried over; 8 (7 + 1) in the tens place, 2 carried over; 5 (3 + 2) in the hundreds place, 3 carried over; 4 (1 + 3) in the thousands place, 2 carried over; 5 (3 + 2) in the ten thousands place

Answer: 54582

If we do not include the zeros at the two extremes, we may miss multiplying the last two digits and we will go wrong.

Let us try one more problem.

211365 x 55

•   02113650
•  (0 + 5) x 5 = 25; (5 + 6) x 5 = 55;

(6 + 3) x 5 = 45; (3 + 1) x 5 = 20;

(1 + 1) x 5 = 10; (1 + 2) x 5 = 15; (2

+ 0) x 5 = 10

10151020455525

•  5 in the units place, 2 carried over; 7 (5 + 2) in the tens place, 5 carried over; 0 (5 + 5) in the hundreds place, 5 (4+1) carried over; 5 (0 + 5) in the next place, 2 carried over; 2 (0 + 2) in the next place, 1 carried over; 6 in the next place, 1 carried over; 11 in the next two places.

Answer: 11625075

Practising this method makes multiplication real easy.

Now, how will you do this problem? 7986 x 99

Using the same duplex number method? No. If you are sharp you would remember the method we learned a few weeks back.

•  Multiply the number by 100.
•  As 99 is just 1 less than 100, subtract the number once from the answer.
•  7986 x 100 = 798600
•  798600 – 7986 = 790614

The key is to learn different methods, but remember to apply the easiest method to make your calculations simple.