Vedic Math, Multiplication by Triplex Numbers

Multiplication by triplex numbers

After duplex numbers, let us learn multiplication by triplex numbers. As the name suggests, numbers like 111, 222, 333 are triplex numbers. The method is similar to that of multiplication by duplex numbers.

First let us see how to multiply any three-digit number by 111. The method is the same as for multiplication by 11. The only thing that is different is we added up to two digits at a time for multiplication by 11 and now we need to add the digits up to 3 at a time.

Let us see an example: 412  x 111

1. Put 2 as the units digit of the answer.
2.  Add 1 + 2 = 3, which gives you the next digit.
3.  Add 4 + 1 + 2 = 7, the hundreds digit of the answer.
4.  Add 4 + 1 = 5, which is the thousands digit.
5.  Then put down 4 as the first digit.

Answer: 45732

Let us see another example of triplex multiplication, where we get carry over numbers.

567 x 111

1. Put 7 as the units digit of the answer.
2.  Add 6 + 7 = 13, which gives you 3 as the next digit with 1 carried over.
3.  Add 5 + 6 + 7 = 18, which gives you 9 (8 + the carried over 1) as the hundreds digit of the answer.
4.  Add 5 + 6 = 11, which gives 2 as the thousands digit.
5.  Then put down 6 (5 + 1) as the first digit.

Answer: 62937

This method can be practised mentally to carry out very complex multiplications also.

But when we have to multiply a two-digit number by 111, it is better to put a 0 in front of the number and proceed in the same manner.

For example: 45 x 111 is done like this

Easy Method:

0 4 5

Conventional Method:

   4    5

   x    111

   4    5

   4    5    0

   4    5    0    0

   4    9    9    5

The answer is 4995. In this two-digit multiplication, we need to add the two digits twice so the zero included in the beginning helps us to get the correct answer. For us to understand, the reason for adding the digits 4 and 5 twice is shown in the conventional method.