Recall : ‘Ekadhiken Purvena’ means ‘One more than the previous one’
Usually we make mistakes in adding numbers which involve carrying. The problem increases when we add too many numbers containing large number of digits.
Study the following examples:
While adding if the addition is 10 or more, then the Ekadhik symbol (•) is placed for a group of 10 on the digit of the number with the next higher place value and continue adding with the balance of the sum. The same process is followed for tens , hundreds and thousands place respectively.
For example,
Question. Add 49 and 36.
Image by woodleywonderworks via Flickr
1 1
4 9
8 6
----- ----- ----
1 3 5
Usual method :
Step 1. 9 + 6 = 15
Step 2. Write 5 in the unit’s column and annex 1 to the ten’s column.
Step 3. Add ten’s column. 1 + 4 + 8 = 13
Step 4. Write 3 in the ten’s column and annex 1 in the hundred’s column.
Step 5. Write 1 as the sum of the hundred’s column.
The sum is 135.
Now with the method of ‘Ekadhiken Purvena’:
Question. Add 49 and 36.
4 9
8 6
Image via Wikipedia
----- ----- ----
5
Step 1.
9 + 6= 15 therefore Ekadhik symbol will be on 8 and the remainder 5 will be written at the units place in the sum.
4 9
0 8 6
----- ----- ----
3 5
Step 2.
Here, 4 + 8 = 13 ( 8 = 8+1=9)
i.e., 4 + 9 = 13 . (The Ekadhik of 8 is 9)
comes on 0 i.e., 0 . The remainder 3 will be
written at the tens place in the sum.
4 9
0 8 6
----- ----- ----
1 3 5
Step 3.
Since 0 = 1 (0+1=1)thus , 1 will be written at
the hundreds place in the sum.
Thus, the sum is 135.
Thus, in a single step the procedure will be as follows:
4 9
Image via Wikipedia
0 8 6
----- ----- ----
1 3 5
Example : Add using ‘Ekadhiken Purvena’
412, 635, 433,1275
Solution:
4 1 2
0 6 3 5
4 3 3
1 2 7 5
----- ----- ---- ----
Image via Wikipedia
2 7 5 5
------ ------ ---- ----
Example : Find the sum.
2356 + 136 + 6759 + 345 + 1289 + 2899
Solution:
2 3 5 6
1 3 6
6 7 5 9
3 4 5
0 1 2 8 9
Image via Wikipedia
2 8 9 9
---- ---- --- --- ----
1 3 7 8 4
---- ---- --- --- ----
PRACTICE EXERCISE
Add the following the Vedic Mathematics way (using Ekadhiken Purvena):
1. 48 + 67
2. 67 + 57 + 36
3. 9 + 15 + 125
4. 16 + 55 + 67 +234
5. 123 + 234 + 345 + 456
6. 654 + 543 + 432 + 321
7. 4563 + 234 + 1239 + 666 + 7777
8. 3567 + 5376 + 7356 + 3675 + 6753 + 7563
9. 1111 + 7898 + 34 + 635 + 90 + 9087 + 1378
10. 6666 + 5555 + 4444 + 3333 + 2222 + 1111
ANSWERS
1. . 115
2. . 160
3. . 149
4. . 372
5. . 1158
6. . 1950
7. . 14479
8. . 34290
9. . 20233
10. 23331
For example, for the number 68, the nearest base ten th
Image via Wikipedia
The last digit in 68 is 8 and the other digit is 6.
When we subtract “all from nine and the last from ten”,we get
6 from 9, that is 9 – 6 = 3 ( other than the last from nine)
8 from 10, that is 10 – 8 = 2 ( last from ten)
Thus, 100 – 68 = 32 can be obtained mentally by using Nikhilam that is “ all from nine and the last from ten”.
Examples:
a) Complement of 73 :
Think mentally - 7 from 9 (9 – 7 ) = 2
3 from 10 (10 – 3) = 7
Therefore, 100 – 73 = 27.
b) Complement of 43 : 4 from 9 = 5
3 from 10 = 7
Complement of 43 is 57 Answer
c) Complement of 88 :
8 8
9 – 8 10 – 8
1 2 Answer
d) Complement of 4 9
Image via Wikipedia
5 1 Answer
e) Complement of 7 0 = 30
f) Complement of 10 = 90
0 comments:
Post a Comment