This system is called as base method because in this system we use a certain number as a base.This base can be any numbers like 10, 100, 1000, 10000 etc. W select a particular base depending upon the numbers given in the question.
Suppose we are asked to multiply 95 X 97, these numbers are closer to 100, so we take the base as 100. Secondly, we will find answer in two parts, the left hand side (LHS) and right hand side (RHS).
Let us look at the procedure involved:
a. Find the base and the difference with the number.
b. RHS = Number of zeros in the base
c. Multiply the differncees on RHS.
d. Put the cross answer on LHS.
Qestion is multiply 95 X 97
a. Base number is 100, both numbers are near to 100. Difference between base and numbers 100-95=5 and 100-97=3. Now write 95-5 X 97- 3
b. Number of zeros in 100 are two so on RHS you need two digits.
c. Multiply 5X 3=15 here you have two digits so write 15 if it come belos ten then write 0 before the digit.
d. Subtact 3 from 95 = 92 and subtract 5 from 97, the answer is 92. write on LHS
Final Answer 9215
Multiply 9989 X 9995
a. Base number is 10000, both numbers are near to 10000. Difference between base and numbers 10000-9989=11 and 10000-9995=5. Now write 9989-11 X 9995- 5
b. Number of zeros in 10000 are four so on RHS you need four digits.
c. Multiply 11X 5=55 here you have two digits but you are to write four digits so write two zeros before 55 it come as 0055 .
d. Subtact 5 from 9989 = 9984 and subtract 11 from 9995 = 9984, the answer is 9984 for LHS. write on LHS
Final Answer 99840055
Multiply 1005 X 1013
a. Base number is 1000, both numbers are near to 1000. Difference between base and numbers 1005-1000=5 and 1013-1000=13. Now write 1005+5 X 1013+ 13, here we are wrting + 5 and + 13 because the multipliers exceed the base number.
b. Number of zeros in 1000 are three so on RHS you need three digits.
c. Multiply 13X 5=65 here you have two digits but you are to write four digits so write one zero before 65 it come as 065 .
d. Now weare to croo add. Add 5 to 1013 = 1018 and add 11 from 13 to 1005 = 1018, the answer is 1018 for LHS. write on LHS
Final Answer 1018065
667 X 995 =Answer
9985 X 9998=Answer
9500 X 9992=Answer
805 X 997=Answer
978 X 979=Answer
The above technique works where the numbers are near the base, it may be below or above. Otherwise it will become difficult to calculate if the numbers are 47, 57, 72 ets whose diggerence is double digit and it is a cumbersome task to do big multiplications.
Now we will study various combinations and the different teqniques to calculate easily.
When the number of digits in RHS exeeds number of zeros in the base.
We have studied as on now is that the RHS number is below the number of zeros in the base and we fill the gap by adding zeroes on left side of RHS.An opposite case may also arose when the number of digits on the RHS is more than the number of zeros in the base.
When the number of dogits in RHS exceeds number of zeros in the base.
We have studied the four steps used in the bese method of multiplication. It says that the RHS should be filled by as many digits as the number of zeros in the base. In some cases the answer on the RHS was small and so filled the remaining places by inserting zeros. An opposite situation may also arise when the number of dogits on the RHS is more than the number of zeros in the base. In that case, we will have to carry over as we do in normal multiplication. Have a look at the following Examples:
Q. Multiply 950 by 950
base is 1000
950 - 50 X 950 - 50
= 900 | 500
2 to be carried over to LHS
1. Base is 1000 and the difference is -50. The number of zeros in 1000 is 3 and so the RHS will be filled in by a three dogit answer.
2. The vertical multiplication (-50 X -50) gives 2500 and the cross answer gives 900. They are filled in as shown above.
3. Note that RHS can be filled by a three-digit answer only but we have a four- digit number - 2500.
4. We will carry over the extra 2 to LHS and add it to number 900 and write as 902.
5. The final answer is 920500
Q. Multiply 1200 by 1020
base is 1000
1200 + 200 X 1020 + 20
= 1220 | 000
4 to be carried over to LHS
1. Base is 1000 and the difference is +200 and +20 respectively. The number of zeros in 1000 is 3 and so the RHS will be filled in by a three digit answer.
2. The vertical multiplication (200 X 20) gives 4000. We will write 000 on RHS and carry extra 4 to LHS.
3. Add 4 to 1220 it becomes 1224
5. The final answer is 1224000
"Vandana Sachar, M.A. Eco, teaching Vedic Maths for the last 15 years"
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