Special multiplication methods
We know the normal method to multiply any two numbers using our tables. But is it necessary to stick to the same method always? Not at all. Just by looking at the numbers we must try to multiply them in our mind. That is the objective of vedic maths. Let us look at a special method of multiplication.
Today we look at a method to find the product of two-digit numbers with the same first digit and the sum of the second digits is 10. Number pairs like 11 and 19, 12 and 18, 23 and 27 are examples of numbers which have the same tens digit and whose units digits add up to 10.
Let us break down this method into the following steps.
Multiply the tens digit (same for both) by the next consecutive number. That will be the first part of our answer.
Multiply the units digits of the two numbers. That will be the second part of the answer.
We have to remember that it is similar to the Nikhilam method, which has a base number and where the number of digits in the answer is decided by the number of zeros in the base.
For two-digit numbers we take 100 as the base, so the number of digits should be two. In particular we have to stick to the number of digits in the second part of the answer. Otherwise the answer may go wrong.
Example: 33 X 37
The tens digit of both numbers is 3 and the sum of the units digits is 10.
Multiply 3 (the tens digit) by the next number 4.
3 x 4 = 12. This is the first part of the answer.
Multiply the units digits.
3 x 7 = 21. This is the second part of the answer.
Therefore, 33 x 37 = 1221
Let us look at some more examples.
22 x 28
Multiply 2 (the tens digit) by the next number 3.
2 x 3 = 6. This is the first part of the answer.
Multiply the units digits.
2 x 8 = 16. This is the second part of the answer.
Therefore, 22 x 28 = 616
81 x 89
Multiply 8 (the tens digit) by the next number 9.
8 x 9 = 72. This is the first part of the answer.
Multiply the units digits.
1 x 9 = 09. This is the second part of the answer.
Therefore, 81 x 89 = 7209
Remember that the product of the units digits, 9, has to be written as 09 to maintain the number of digits in the answer.
Now problems for you to try:
12 x 18
43 X 47
76 X 74
98 X 92
67 X 63