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Multiply the numbers close to the power of 10s in just 5 seconds! - Part 2 and Part 3
In my last article "Multiply the numbers close to the power of 10s in just 5 seconds! - Part 1", I have mentioned a simple Vedic mathematics method of how to multiply numbers that are below to the power of 10. In this article, I would mention about - Part 2: Multiplying numbers greater than the power of 10s. and Part 3: Multiplying numbers of which one is greater than power of 10 and the other is less than power of 10.
As mentioned in previous article, in Vedic mathematics this method is known as "Nikhilam Navatashcaramam Dashatah - All from 9 and the last from 10"
Part 2: Multiplying numbers greater than power of 10s
Example 1: 12 X 15
Step 1: Identify the base (power of 10) to which the number is close. Here, 12 and 15 are close to 10. Therefore, base is 10
Step 2: Identify by how much both the numbers are greater than the base. Here, 12 is more by 2 and 15 is more by 5.
Step 3: Write the original numbers along with the number by which it is greater than 10 as below.
12 + 2
15 + 5
Step 4: Now, Cross add the original number and the surplus number. That is add 12 to 5 or add 15 to 2. So, we get
12 + 2
X
15 + 5
-----------
17
-----------
Step 5: Now, vertically multiply the two surplus numbers. Here, the surplus numbers are 2 and 5. Therefore, we have
12 + 2
X
15 + 5
-----------
17 / 0
1
-----------
Step 6: Now, since the base is 10, the right hand most digit is units and can have only one digit. Therefore, keep the 0 of the 10 on the right hand side and carry the 1 over the left and change the 17 into 18.
12 + 2
X
15 + 5
-----------
17 / 0 = 180
1
-----------
Note: If the number of digits are more than the number of zeroes in the base, the excess digit or digits are to be added to left hand side of the answer.
Therefore we have 12 X 15 = 180
Example 2: 101 X 109
Step 1: Identify the base (power of 10) to which the number is close. Here, 101 and 109 are close to 100. Therefore, base is 100
Step 2: Identify by how much both the numbers are greater than the base. Here, 101 is more by 1 and 109 is more by 9.
Step 3: Write the original numbers along with the number by which it is greater than 100 as below.
101 + 1
109 + 9
Step 4: Now, Cross add the original number and the surplus number. That is add 101 to 9 or add 109 to 1. So, we get
101 + 1
X
109 + 9
-----------
110
-----------
Step 5: Now, vertically multiply the two surplus numbers. Here, the surplus numbers are 9 and 1. Therefore, we have
101 + 1
X |
109 + 9
-----------
110 / 9
-----------
Step 6: Now, since the base is 100, the right hand most digit is tens and units and should have two digit. Therefore, fill the vacancies by adding zero. thus
101 + 1
X |
109 + 9
-----------
110 / 09 = 11009
-----------
Therefore we have 101 X 109 = 11009
Note: If the Right hand side contains less number of digits than the number of zeros in the base, the remaining digits are filled up by giving zero or zeroes on the left side of the right hand side digit.
Example 3: 125 X 101
Step 1: Identify the base (power of 10) to which the number is close. Here, 125 and 107 are close to 100. Therefore, base is 100
Step 2: Identify by how much both the numbers are greater than the base. Here, 125 is more by 25 and 101 is more by 1.
Step 3: Write the original numbers along with the number by which it is greater than 100 as below.
125 + 25
101 + 1
Step 4: Now, Cross add the original number and the surplus number. That is add 125 to 1 or add 101 to 25. So, we get
125 + 25
X
101 + 1
-----------
126
-----------
Step 5: Now, vertically multiply the two surplus numbers. Here, the surplus numbers are 25 and 1. Therefore, we have
125 + 25
X
101 + 1
-----------
126 / 25 = 12625
-----------
Therefore we have 125 X 101 = 12625
Part 3: Multiplying a number which is greater than power of 10, with a number which is less than power of 10
Example 1: 9 X 15
Step 1: Identify the base (power of 10) to which the number is close. Here, 9 and 15 are close to 10. Therefore, base is 10
Step 2: Identify by how much the numbers are greater than or less than the base. Here, 9 is less by 1 and 15 is more by 5.
Step 3: Write the original numbers along with the number by which it is greater / less than 10 as below.
15 + 5
9 - 1
Step 4: Now, based on the signs, cross add and cross subtract the numbers accordingly. That is add 9 to 5 or subtract 15 by 1. So, we get
15 + 5
X
9 - 1
-----------
14
-----------
Step 5: Now, vertically multiply the surplus and deficit numbers along with the signs. Here, the numbers are 1 and 5. Therefore, we have
15 + 5
X
9 - 1
-----------
14 / -5
-----------
Step 6: Now, to get rid of the minus sign, subtract the right hand side by the base and less the left hand side by 1. Here, we have base as 10 and right hand side number as 5. therefore we have 10 - 5 =5. Hence,
15 + 5
X
9 - 1
-----------
14 / -5 = 135
-----------
Therefore we have 9 X 15 = 135
Example 2: 101 X 97
Step 1: Identify the base (power of 10) to which the number is close. Here, 101 and 97 are close to 100. Therefore, base is 100
Step 2: Identify by how much both the numbers are greater than and less than the base. Here, 101 is more by 1 and 97 is less by 3.
Step 3: Write the original numbers along with the number by which it is greater than and less than 100 as below.
101 + 1
97 - 3
Step 4: Now, based on the signs, cross add and cross subtract the numbers accordingly. That is subtract 101 by 3 or add 97 to 1. So, we get
101 + 1
X
97 - 3
-----------
98
-----------
Step 5: Now, vertically multiply the surplus and deficit numbers along with the signs. Here, the numbers are 3 and 1. Therefore, we have
101 + 1
X |
97 - 3
-----------
98 / -3
-----------
Step 6: Now, to get rid of the minus sign, subtract the right hand side by the base and less the left hand side by 1. Here, we have base as 100 and right hand side number as 3. therefore we have 100 - 3 =97. Hence,
101 + 1
X |
97 - 3
-----------
98 / -3 = 9797
-----------
Therefore we have 101 X 97 = 9797
Example 3: 10006 X 9999
10006 + 6
X
9999 - 1
-----------
10005 / -6 = (10005 - 1) / (10000 - 6) = 100049994
-----------
Therefore we have 10006 X 9999 = 100049994
I am sure with little bit of practice, you can successfully perform multiplications very fast when compared to the traditional method. Also, please note that these methods should be applied accordingly for which it is designed. This method may not give an effective result, if you are trying to multiply 67 and 72. Vedic mathematics defines many methods by which calculations can be made simple, but you need to use them accordingly.
Hope this method was useful for you. If you have any other methods do share and let me know if you have any questions regarding these methods.
1 comments:
Thank you for sharing. It's a good resource for a student poor in math like me.
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