mathematics with fun !!!…vedic maths

Hie frndz…

welcome to the world of vedic mathematics……Its a simple to understand……very interesting………..very helpful to school students……and most important…who are giving competative exams…….

I m very much thankful to my father’s friend…he…encouraged me to….learn this…..He  given me books…also……..

I came to know that….in the banks competative exams……people..finds short of time………so…this magical technique is the answer for…all problems……..

We will learn this technique……..

Are u  ready?????

Cheers!!!!

love to all

Shrimat Jagadguru Shankaracharya SwamiBharati Khushna Tirth

Born in 1884…..original name Venkatraman ….very intelligent….

In 1902 he graduated( B.A.)…in 1904..he graduated from  “”American institute of sciences” ….with M.A.and he stood first in all subjects like….Science, Histery, English, Maths, Sanscrit, Philosophy…which is.. a record..

He found 16 sutras and he says…with these only 16 sutras we can do any complex problem… in mathematics….

 

With Sanskrit he had command on 10 to 12 languages like English, French, Latin etc

 

This great man passed away on 2nd Feb.1960…..  

I m very thankful to you that u visited the BOLG ……

Here is a request…

start reading as sequense …I mentioned..below..

multiplication

1…..starting with multiplication

2…..Nikhilam and anurupyen

3…..subsutras of nikhilam

4…..subsutras of nikhilam…cont..

 Dont go reverse…..its like going in second standerd without passing first….hehehe

THank U!!

Ref books: वैदिक गणित  भाग  १ ते ४ ….ब.गं. बापट अणि दिलीप कुलकर्णी.

i.e vedic mathematics part 1 to 4….by B.G Bapat and Dilip Kulkarni.

3) अन्त्ययोदर्शकेsपि|  

Antyayodarshke S pi |

means…when thr is 10 at end then also….heheh word to word meaning……

i.e. This method is used when the last digits sum  is 10 and other digits are same……

like…

   32                                   24

x 38                                  26

————                —————-

3(3+1)/8×2             2(2+1)/ 6×4

 12/16= 1216                 6/32

note: here there should be two digits on RHS of slash

we seen that how to do when there is 5 on ones place…this is also same…..bcoz….5+5=10…..

I thinbk many of us known previouslyhow to do if there is 5 on….ones place…but this third sutra fould by Swami……this shows how intelligent he was!!!

Now some more points….

There is nothing hard and fast rule that…onlu last digits some dhould be 10…it can be 100 1000…and so on……….

e.g

197×103

1 97

1 03

————–

1×2/97×3

=2/0291

 

here remember on RHS thr should be 2 raise to 2 digits….i.e 4 digits…bcoz we taken 2 digits from multiplier…….and multiplicand

345                 45: 5

355                   55: 5

——–            ———-

12/2475          5(50)/    25    = 2500-25=2475

Here the multiplication of digits is tough……so we taken out and made them….

But Vedic mathematics…dont like that much complications….so there is different sutras for…these kind of examples…..

Think beforesolving examples…that which method is convinient….

Now the forth sunsutra……this is last one….

4)  एक्न्यूनेन  पूर्वेण |

Eknyunnen purven |

This is used when…there are all 9′s in the multiplier……like..9, 99, 999….and so on…….

now for multiplicand there are three parts…

a) multiplicand and multiplier have sme number of digits….i.e 8×9, 79×99

b) multiplicand have less number of digits than multiplier….i.e. 7×99, 28×999

3) multiplicand have more number of digits  than multiplier…..i.e. 87×9, 876×99 etc….

 oops….whats the problem is these methods are somewhat…..comlicated…..instead there is very……..simple…..method to deal with this..

and you all knows that…heeehe

30×9=30(10-1)=300-30=270….

we can do…any calculations which are where …multiplier..is nearer to 9, 99, 999 etc…

i e. we can do with 98, 101, 102, ..ets by spliting……the multiplier…

simple and sweet………………

thax for reading with patience………………more to come…enjoyyyyyyyyyy!!!!!!!!!

Let us move towards  subsutras of Nikhilam…..

1)यावदूनं  तवादुनिकृत्य  वर्ग  च  योजयेत |

Yavadunam tavadunikrutya varga cha yojayet|

Its all about doing squares…..varga means square…..

It means….Subtract the number (which comes by subtracting that no from base) from the number to be squared…..and take square of that number …….

OOps didnt get anything???…..its difficult to put in words actually….let us understand with examples…….

92 = (9-1) / 12

      = 8/1

9 is nearer to base 10…..and one less than so….1 is taken….as we done earlier….also..

Let us understand by solving some more….

62 = (6-4) / 42 = 2/16 = 2+1/6 = 36…..

Recall previous procedures……

72 = (7-3) / 32 = 49……right???? 

 Now some big ones….

982= (98-2)/ 22= 94/04=9404……

Why 0 ???

recall…base 100 so… two zeros..and therefore..2 digits on RHS….

912= (91-9)/92= 82/81=8281

 

9992= (999-2)/ 22 = 998001

 

9902= (990-10)/102=980/100=980/100

If u know squares upto 25…you can make squares easily….

or else you always can take….suares taking RHS saperately….

Next….if number is greater than the base…….

Its simple….do addition instead of subtraction….

132= (13+3)/32

now you do rest…no spoon feeding…..hehhe

Try some more yourself…

 

2) एकाधिकेन पुर्वेन|

Ekadhiken Purven|

means add one in rmaining number…by excluding ones place…

But this method is only for some numbers….where 5 comes at ones place..e.g.5, 25, 65, 225….etc

 252= 2(2+1)/52 =2×3=6

 9952=99×100/52= 9900/25=990025…

 

note….here that number of zeros= digits on RHS rule not applicable…

only write LHS and .RHS one after the other….

here u can make 11 x 12 seperate…

1152 = 11x(11+1)/52= 132/25 = 13225….

 11:1

12:2

—–

13/2

 

is it seems to be simple??………….

Now some more examples you practice…..

take suares of……..

85, 993, 14, 75, 91, 1008, 114, 1005, 9998

 Dont forget to write comment how was the lesson

 with luv…. 

 

Some more examples on sutra Nikhilam….

upto now we seen multiplicand and multiplier are less than the base…..

How to do if they are more than base???

Hmm…Let us start with example…12x 13…base 10

12: 2         …   12-10=2

13: 3        …    13-10=3..simply subtract base from number….

——

15/6        ……. i e 12+3=15….also 13+2+15…therefore left hand side 15……..and rHS is 3 into 2 i.e 6……..so answer is..156!!!…..simple….

some more…examples….to…get clear idea….

19: 9                                112: 12                            10009: 9

13: 3                                109:  9                              10002: 2

——–                                ————-                         ————

22/27                              121/108                           10011/18

22+2/7=247                 122/08                             10011/0018

remember….the zeros on base= digits on RHS…

if thr are less digits on RHS..then, .add zero..left to the number

and if more digits then, remove extreme left digit from RHS number and add to the LHS…….

Now, some more where.. one number is less than base and another more than it….

13: 3

8:  2
——–

11/6
problem???

kk….base 10

so the answer becomes…..11×10-6=110-6=104

corect??……..its simple….now u can do….the rest…no need to giv more example….try…with..more digits….

Lets see what we done….upto now…

In Nikhilam sutra we done…examples in which

multiplier and multiplicand both less than base……….both more than base…….one is less and another more than base….

Hre we used….numbers nearer to base.right????

Hmm, now we will see how to make with numbers very far to the base…

we will use sutra Anurupyen………

should we start??….kkk…lets take break….hhehe…

After the break………..

where we were????…mm…kkk

how to do if multiplicand and mltiplier far from base…….

sutra anurupyen….i.e adjust the  the base..as per the numbers..

we will take example…so it will be easy to understand….

44×48=?……..

In this 50 is near to both numbers……so….taking 100 basic base

we can solve like this..

100/2=50

44:   6                       44-50=-6…so 6

48:   2                      48-50==2 so 2
———–

42/12  its like as we done preveously..

now divide 45 by 2…becoz we taken 50 base…..

therefore 1/2 (42)=21….now the ans is  21/12….so the ans is….. 21 x 100+12=2112……

some more methods…..in prev example..we can take 10 base..so it willl be solved like….

10×4=40 base..

44: 4

48: 8

———–

52/32………now what to do..simple!!!

52 x 4/32

208/32………here on RHS only one digit should be thr becoz……basic base is 10..only one zero on that

so…    208+3/2….i.e 211/2…..same  answer with both methods……hehehe

sounds to be simple na???? ..

now….we van do with big numbers….Enjoy….!!!

83×77

base: 10×8                base 100×9                          base100x8

83: 3                               893 :  7                                  375: 425

77:  3                             905 :   5                                  799:1

———                                   ————-                          ————-

8(80)/ 9                           9 (898)/  35                                 8(374)/425

640×10-9                      8082×100-35                              (2992+4)10+25

6391                                808165                                            299625

some more….examples……solved differently……using same sutra….

by changing multiplier…..as follows……

we wanted to do 999×249….now..in this…we can multiply249..to get some closer value to base….

249×4=996

999: 1

996:  4                     here base 1000

————-

995/004…..this is not the answer….now what to do??

divide whole answer by 4    i .e.  995004/4= 248751

Here  remember…..when we change the multiplier……by multiplying……then we should divide the whole answer by that number as we done now…..

and when we change the base….we should only work on LHS…..of slash….

Now we can do most of the examples on multiplication……but some more….remaining…..let us……do in next lesson….

till the time cyah…

Let us know basic….

multiplicand..multiplier…..terms used in..making multiplications…

and in the number from right side…to left….places defined..one..tens…100th….and so on…

rules…..

+x+=+      -x-=+     -x+=-   

e.g. -5 x 4=-20 ,   -2 x -1=2

we will use bar instead of negative sign….

—————————————-

Now, let us start with sutras………

1…..NIkhilam Navataha charamam dashataha….

we will take example……

9 x 8 = ?

take 10 as a base ..becoz….10 is nearer base of both numbers….

ok!  now,  base =10

9:    1            9-10=-1  therefore  is written

8:    2             8-10=-2   so  in front of 8  2 is written

now….do  addition in cross i>e.9-2 or 8-1 comes to 7 write on LHS…..simple..

and-1 into -2 =2….write on the right side of slash….

  9:    1

  8:    2
 ————–

  7 /   2

answer is 72…….right???      how it came??…..      7  x 10+2=72

seemes to be simple???

now……sm more examples….

9 :  1                   7:  3                      7: 3

9:                    8:   2                   4 : 6

——-                 ————-            —————

8/ 1                      5/ 6                        1/ 18     answer is 1x 10+ 18=28

                                                          1+1/8        simply

we considered..10 as a base…there is one zero on 10 so keep one number on RHS of slash and take second one left and add….simple…..

 now one more example….. 97 X 88

consider base  100..for this……………

now..meaning of sutra …..nikhilam navataha charamam dashataha…….i.e subtract ones place from 10 and other places from 9….

base 100

97 :  3                  use sutra….10-7=3 and 9-9=0

88:  12                  10-8 =2 and  9-8=1…simple na???

 ————-

85/ 36                answer is 8536….see how simple it is

clarify??? kkk….  97+88=185 and base 100 so ….185-100=85..right??…..or one more…..do addition in cross like…88-3 or …97-12 that comes to 85…….sounds to be simple???……

 some more examples….

88: 12

88: -12
———–

76/ 144…….take 1 LHS and add….ie answer is 77/44 i.e 7744         ……….wow…….too much simple!!!!…

now….this one..somthing different………

99 :1

98:2

———

97/2…ooops  some gadbad……..one rule hav to remember…

the no zeros in base should be equal to no of dogits on RHS of slash

so modified answer is 97/02..got it???..i e.9702……

 

base 1000

998:    2               988:  12                999:1
892:  108           899:  101            997: 3
—————–             —————-       —————–

810/216                 887/1212            996/003

                                =  888/212

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