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Vedic Arithmetics - Coggle Diagram
Vedic Arithmetics
addition
End numbers
Addition table
non carry combination
carry combination
addition that needs digit change
double digit + single digit
remember second digit
determine addition between first digit
if carry combination
increment second digit by 1
put end number of carry combination at first digit
if non carry combination
preseve second digit
do addition with first digit
double digit + double digit
add second digit
three digit + three digit
add third digit
determine addition between second digit
if carry combination
increment third digit by 1
add second digit to get end number
if non carry combination
preserve third digit
addition of many digits
lipit the way learned at three digit addition
addition of list
single digit
down to up(not necessary can go opposite)
proceeding to find end numbers till you reach top
write down last end number at first digit
count how many carry combination we meet
write down number of carry combination at second digit
8. multiple digit
do down to up list addition per digit
write each answer for digit following balancing rules
add it with balancing rules
Balancing Rule
ex : $$ 35|37|38 = 3908 $$
consider digits and add it from right side
source of information
foundation IIT
IIT & Jee Foundation material
subtraction
9. fundamental
complements
number that forms 10 together
ex: 1 complement is 9
simple subtraction
10. match combination
minuend is bigger than subtrahend or minuend is equal to subtrahend
simply calculate left to right
11. mismatch combination
minuend is smaller than subtrahend
start calculation from left
observe next digit and notice if it's mismatch combination
subtract 1 at current digit
add complement of subtrahend and minuend
write down if it's last digit otherwise observe next digit
12. direct method
it was practice of previous substraction
13. double digit - double digit
applied this at double digit
14. tripple digit - triple digit
applied this at triple digit
15. Lengthy Substraction
if current and next digit is match combination combine calculation
if mismatch combination comes next, subtract 1 from combined calculation and carry on as before
16. special substraction
to subtract from big number(might be used to expand complement concept)
power of 10
turn minuend's each digit to all 9 till last 10
multiplication
basics
17. balancing rule/carryover rule
ex: $$ 23 | 14 | 35 $$ = 2475
from right to left
5, 3+4, 1+3, 2
other ex: $$ 63|21|05|31 $$ = 65181
$$ 36|29|47 $$ = 3937
18. single digit multiplication
ex: 32 * 4 = $$ 12|8 $$ = 128
other ex: 754683 * 6 = $$ 42|30|24|36|48|18 $$ = 4528098
vedic
simple misc
19. Multiplication with number 5
multiply 10 and divide with 2
easier for big number
20. Multiplication with Series of 9's
series of 9's
9, 99, 999, 9999, ...
key concept
9 = (10-1)
$$ x\cdot(10-1) = 10x-x $$
ex
$$ 5246 \cdot 99 = 524600 - 5246 = 519354 $$
$$ 5946 \cdot 9 = 59460 - 5946 = 53514 $$
21. Mulitiplication with 9's Special Type
key concept
Number of digits in LHS = Number of 9's in RHS
this only works for mulitiplication between same digits
subtract 1 from last digit and use complements of 9
in case number of digits in LHS are lesser than 9's in RHS than put 0 at left to make number of digit equal to number of 9's
ex
$$ 643 \cdot 999 = 642357 $$
method: 643(3-1)3(9-6=3)5(9-4=5)7(9-2=7)
$$ 643 \cdot 9999 = 6429357 $$
$$ 0643 \cdot 9999 = 6429357 $$
method: 642(3-1)9(9-0=9)3(9-6=3)5(9-4=5)7(9-2=7)
22. Multiplication with Series of 1's
series of 1's
1, 11, 111, 1111
ex
$$ 3152 \cdot 11 = 34672 $$
method: 3(0+3)4(3+1)6(1+5)7(5+2)2(2+0)
$$ 57486 \cdot 11 = 5|12|11|12|14|6 = 632346 $$
$$ 3152 \cdot 111 = 349872 $$
method: 3(0+0+3)4(0+3+1)9(3+1+5)8(1+5+2)7(5+2+0)2(0+0+2)
more than single digits
23. Multiplication within 12 to 19
ex
$$ 12 \cdot 13 = 156 $$
method: $$ 12 + 3(from 13) = 15, 2 \cdot 3(from 13) = 6 $$ and combine and become 156
$$ 16 \cdot 15 = 240 $$
24. Multiplication any with 12 to 19
ex
$$ 2132 \cdot 12 = 25584 $$
method:
0 2 1 3 2 and 2(from 12)
$$ (2(from 12) \cdot 2=4) $$
1 more item...
$$ ((2(from 12) \cdot 3) + 2 =8) $$
1 more item...
$$ ((2(from 12) \cdot 1) + 3 =5) $$
1 more item...
$$ ((2(from 12) \cdot 2) + 1 =5) $$
1 more item...
$$ ((2(from 12) \cdot 0) + 2 =2) $$
1 more item...
$$ 4628 \cdot 15 = 69420 $$
25. Multiplication any with 21 to 91
ex
$$ 3212 \cdot 21 = 67452 $$
method:
3 2 1 2 0 and 2(from 21)
$$ (2(from 21) \cdot 0) + 2 = 2 $$
1 more item...
$$ (2(from 21) \cdot 2) + 1 = 5 $$
1 more item...
$$ (1(from 21) \cdot 2) + 2 = 4 $$
1 more item...
$$ (2(from 21) \cdot 2) + 3 = 7 $$
1 more item...
$$ (2(from 21) \cdot 3) + 0 = 6 $$
1 more item...
$$ 4536 \cdot 41 = 185976 $$
$$ 3764 \cdot 71 = 260854 $$
larger number
26. Multiplication with 25
multiply with 100 and divide with 4
27. Multiplication with 125
multiply 1000 and divide with 8
28. Multiplication with tens place same and ones place's sum is ten
ex
$$ 42 \cdot 48 = 2016 $$
method: $$ 4 \cdot 5= 20 $$(equal_second_digit 4) (next _number_from_equal_second_digit_4) , $$ 2 \cdot 8 = 16 $$ (multiplication_of_first_digit)
combine 20 and 16
$$ 57 \cdot 53 = 3021 $$
$$ 71 \cdot 79 = 5609 $$
29. multiplication with units place same and ten's place's sum is ten
ex
$$ 68 \cdot 48 = 3264 $$
method: $$ 6 \cdot 4 + 8 = 32 $$
(multiplcation of tensplace) + 8(from equal unit's place)
$$ 8 \cdot 8 = 64 $$
(power of equal unit's place)
combine 32 and 64
$$ 23 \cdot 83 = 1909 $$
$$ 74 \cdot 34 = 2516 $$
30. Multiplication with Base
Base
10, 100, 1000, 10,000, ...
any number near Base is easy. such as 99, 102, 98, 108, 89, 998, 1021, ...
ex
$$ 93 \cdot 98 = 9114 $$
method: $$ (93-100) = -7,
(98-100) = -2,
93-2 = 98-7 = 91, -7 \cdot -2 = 14 $$
combine 91 and 14
$$ 95\cdot 91 = 8645 $$
$$ 98 \cdot 103 = 10094 $$
method: $$ -2, +3, 98+3=103 -2 = 101, -2 \cdot +3 = -6 $$
because -6 comdination needs calculation
1 more item...
$$ 996 \cdot 992 = 988032 $$
method: because we used 1000 as Base 32 needs 0 at front to keep digits
31. Multiplication with Sub-Base
Sub-base
not near to power of ten
such as 20, 30, 40, ...
ex
$$ 24 \cdot 28 = 672 $$
method: MainBase 10, Subbase 20
$$ 20 = 2 \cdot 10 $$
$$ 24 - 20 = 4, 28 - 20 = 8, 24 + 8 = 28 + 4 = 32, 4 \cdot 8 = 32 $$
1 more item...
$$ 67 \cdot 73 = 4891 $$
method:
$$ 490 | -9 = 4900 - 9 = 4891 $$
Double digits
32. Multiplication within Double Digits
ex
$$ 22 \cdot 31 = 682 $$
method: $$ 2(from tens place) \cdot 3(from tens place) = 6, (2(from tens place) \cdot 1(from ones place)) + (3(from tens place) \cdot 2(from ones place)) = 8, 2(from ones place \cdot 1(from ones place) = 2 $$
1 more item...
$$ 32 \cdot 24 = 768 $$
$$ 56 \cdot 34 =15|38|24=1904 $$
$$ 79 \cdot 86 = 56|114|54 = 6794 $$
33. Multiplication with Double Digits
ex
$$ 4235 \cdot 32 = 135520 $$
method: $$ 4(from thousands place) \cdot 3(from tens place) = 12, (2(from hundreds place) \cdot 3(from tens place)) + (4(from thousands place) \cdot 2(from ones place)) = 14, (3(from tens place) \cdot 3(from tens place)) + (2(from hundreds place) \cdot 2(from ones place)) = 13, (5(from ones place) \cdot 3(from tens place)) + (3(from tens place) \cdot 2(from ones place)) = 21, 5(from ones place) \cdot 2(from ones place) = 10 $$
1 more item...
$$ 5643 \cdot 45 = 20 | 49 | 46 | 32 | 15 = 253935 $$
Triple digits
34. Multiplication with Triple Digits
ex
$$ 241 \cdot 324 = 78084 $$
method
1 more item...
$$ 352 \cdot 426 = 12|26|36|34|12 = 149952 $$
35. Multiplication by Factors
Factors
ex: $$ 36 = 4 \cdot 9 = 6 \cdot 6 $$
ex
$$ 5468 \cdot 36 = 5468 \cdot 4 \cdot 6 =196848 $$
method: $$ 5468 \cdot 4 = 20|16|24|32 = 21872 , 21872 \cdot 9 = 18|09|72|63|18 = 196848 $$
36. Multiplication Using Vilokanam
Vilokanam(Observation in indian)
ex
$$ 324 \cdot 500 = 162000 $$
method: $$ 324 \cdot 5 = 1620 $$ and put 00(from 500) behind 1620
division
simple
37. divisions with single digit
ex
$$ 4659 \div 3 = 1553 $$
method: seperate each digit number 4, 6, 5, 9 and divide with 3 from left, write quotient under digit number and carry remainder to next digit
4/1 , 16/5, 15/5, 9/3
and than combine shares together. so 1553
$$ 7351 \div 4 = 1837 ... 3 \ or 1837.75 $$
$$ 6572 \div 6 = 1095...2 $$
38. division with 5
method: multipy 2 at dividend and divide with 10
ex
$$ 4132423 \div 5 = 826484.6 $$
$$ 87659 \div 5 = 16|14|12|10|18 =17531.8 $$
$$ 96785 \div 5 = 18|12|14|16|10 = 19357 $$
39. Division with 9, 99, 999...
