Vedic mathematicss-R.SANKAR

VEDIC MATHEMATICSVEDIC MATHEMATICS

R.SANKARR.SANKARASSISTANT PROFESSOR,ASSISTANT PROFESSOR,

DEPARTMENT OF MATHEMATICS,DEPARTMENT OF MATHEMATICS,PROFESSONAL GROUP OF INSTITUTIONS,PROFESSONAL GROUP OF INSTITUTIONS,

PALLADAM-641662.PALLADAM-641662.

BYBY

INTRODUCTIONINTRODUCTION Vedic Mathematics is the ancient system of Vedic Mathematics is the ancient system of

Mathematics which was rediscovered early last Mathematics which was rediscovered early last century by “ century by “ Sri Bharati Krishna Tirtaji Sri Bharati Krishna Tirtaji (1884-1960)(1884-1960)”.”.

Vedic Mathematics is a new approach to Vedic Mathematics is a new approach to mathematics, direct, one-line and mental mathematics, direct, one-line and mental solutions to mathematical problem.solutions to mathematical problem.

The following chapters explains how easy the The following chapters explains how easy the mathematics.mathematics.

TOPICS TOPICS Left to Right Calculation:Left to Right Calculation:

1. Addition1. Addition2. Multiplication2. Multiplication3. Subtraction3. Subtraction

Digit Sum (Checking)Digit Sum (Checking)Special MethodsSpecial MethodsAll from 9 and Last from 10 All from 9 and Last from 10 Squaring Squaring DivisibilityDivisibilityRemaindersRemaindersSpecial NumbersSpecial Numbers

Left to Right CalculationLeft to Right Calculation

ADDITIONADDITION

Normal Form:Normal Form:58+77=?58+77=?5858

7777 135135

Vedic FormVedic Form

58+77=?58+77=?5858

7777 135135Sum of Sum of Ten-thTen-th place digits place digits 5+7=120 5+7=120Sum of Sum of UnitUnit place digits place digits 8+7= 15 8+7= 15

135135

Example : 2Example : 2

97+96=?97+96=?97979696 193193Sum of Sum of Ten-thTen-th place digits 9+9= 180 place digits 9+9= 180Sum of Sum of Unit Unit place digits 7+6= 13 place digits 7+6= 13 193193

3-digit and more….3-digit and more….

789+999=?789+999=?Sum of Sum of 100-th 100-th place digits 7+9=1600place digits 7+9=1600Sum of Sum of Ten-thTen-th place digits 8+9= 170 place digits 8+9= 170Sum of Sum of Unit Unit place digits 9+9= 18place digits 9+9= 18

17881788

We can continue this process for any digit We can continue this process for any digit valuevalue

Example : 2Example : 2578+764=?578+764=?Sum of Sum of 100-th100-th place digits 5+7=1200 place digits 5+7=1200Sum of Sum of Ten-th Ten-th place digits 7+6= 130place digits 7+6= 130Sum of Sum of UnitUnit place digits place digits 8+4= 12 8+4= 12

13421342We can continue this process for any digit We can continue this process for any digit

valuevalue

Practice 1Practice 1 875 + 746 875 + 746 = ?= ? 375 + 96375 + 96 = ?= ? 1565 + 17451565 + 1745 = ?= ? 4688 + 4651 4688 + 4651 = ?= ? 685 + 592685 + 592 = ?= ? 88525+ 47469 = ?88525+ 47469 = ? 87848+ 12345 = ?87848+ 12345 = ? 68598+ 99999 = ?68598+ 99999 = ? 9484899+9 9484899+9 = ?= ?

Ans:Ans: ??

MULTIPLICATIONMULTIPLICATIONFind 584 × 8 = ?Find 584 × 8 = ?Normal Form :Normal Form : 584 × 8584 × 8

46724672We can use Vedic method to solve the We can use Vedic method to solve the

above problem easily.above problem easily.

Vedic FormVedic Form Find 584 × 8 = ? Find 584 × 8 = ? Multiplication of Multiplication of 100-th100-th place 5 × 8 = 4000 place 5 × 8 = 4000 Multiplication of Multiplication of Ten-thTen-th place 8 × 8 = 640 place 8 × 8 = 640 Multiplication of Multiplication of UnitUnit place 4 × 8 = 32 place 4 × 8 = 32

46724672

Practice 2Practice 2, , Try this: Try this: 989 × 9=?989 × 9=? 68778 × 5=?68778 × 5=?

Practice 2Practice 2 Try this: Try this: 989 × 9=?989 × 9=? 68778 × 5=?68778 × 5=? 899474 × 8 =?899474 × 8 =? Sometimes the Sometimes the

addition of the No’s is addition of the No’s is 10 r more, here we 10 r more, here we carry the one to the carry the one to the previous no and previous no and continue the process.continue the process.

989 × 9= 8100989 × 9= 8100 720720 81 81 89018901

989 × 9 = 8901 989 × 9 = 8901

SUBTRACTIONSUBTRACTIONFind 625 – 183 = ?Find 625 – 183 = ?Normal Form:Normal Form: 625 –625 –

183183 442442

Here in the unit digit 5-3=2 and in the 10Here in the unit digit 5-3=2 and in the 10 thth place borrow 10 from 6 and make 2 as 12 place borrow 10 from 6 and make 2 as 12 and then subtract 8 we get 4 and 100and then subtract 8 we get 4 and 100 thth place 5-1=4place 5-1=4

Vedic FormVedic Form Find 625 – 183 = ?Find 625 – 183 = ? We subtract in each column on the left, but before we put We subtract in each column on the left, but before we put

an answer down we look in the next column.an answer down we look in the next column. IfIf the top is greater than the bottom we put the figure down the top is greater than the bottom we put the figure down If not, If not, we reduce the figure by 1, put that down and give the other we reduce the figure by 1, put that down and give the other

1 to smaller number at the top of the next column1 to smaller number at the top of the next column If the figures are the same we look at the next column to decide If the figures are the same we look at the next column to decide

whether to reduce or notwhether to reduce or not

625 -625 -183183442442

Here in the unit digit 6-1=5. Now we look at the next Here in the unit digit 6-1=5. Now we look at the next column, here the top 2 is less than the bottom 8, so we column, here the top 2 is less than the bottom 8, so we put down 4 in the 1put down 4 in the 1stst column and carry 1 in the next column and carry 1 in the next column top so 12-8=4 in that column and look at the next column top so 12-8=4 in that column and look at the next column 5 is greater than 3 so 5-3=2column 5 is greater than 3 so 5-3=2

Practice 3Practice 3 68 – 25 = ?68 – 25 = ? 813 – 489 = ?813 – 489 = ? 986 – 584 = ?986 – 584 = ? 6226-2662= ?6226-2662= ? 5161-1838 = ?5161-1838 = ? 35567-12346=?35567-12346=? 486645 – 359 = ?486645 – 359 = ?

Ans:Ans: ??

DIGIT SUM (CHECKING)DIGIT SUM (CHECKING) This is an interesting and also very useful to check This is an interesting and also very useful to check

our answer.our answer. The The digit sumdigit sum of a number is found by adding the of a number is found by adding the

digits in a number and adding again if necessary digits in a number and adding again if necessary until a single figure is reached.until a single figure is reached.

Example:Example: consider the no:78158consider the no:78158 Sum of the digit is7+8+1+5+8=29Sum of the digit is7+8+1+5+8=29 =2+9=2+9 =11=11

=1+1 =1+1 =2=2

Any pair or group of digits which add up to 9 can be Any pair or group of digits which add up to 9 can be deleted.deleted.

CHECKING THE ANSWERCHECKING THE ANSWER 58+77=?58+77=? 5858

7777 135135 The digit sum of 58=5+8=13=4The digit sum of 58=5+8=13=4 The digit sum of 77=7+7=14=5The digit sum of 77=7+7=14=5 Total digit sum is 4+5=9Total digit sum is 4+5=9 From the answer, From the answer,

The digit sum of 135=1+3+5=9The digit sum of 135=1+3+5=9 There fore from & , our answer is correct.There fore from & , our answer is correct. Check the answers from practice 1,2 and 3Check the answers from practice 1,2 and 3

1

2

1 2

Special MethodsSpecial Methods

MULTIPLICATION NEAR A MULTIPLICATION NEAR A BASEBASE

Numbers just below the baseNumbers just below the baseNumbers just above the baseNumbers just above the baseAbove and Below the baseAbove and Below the baseWith different baseWith different base

NUMBERS JUST BELOW THE NUMBERS JUST BELOW THE BASEBASE

Find 98 × 94 = ?Find 98 × 94 = ?Normal Form:Normal Form: 98 × 94 98 × 94

392392 882882 92129212

In Vedic form here we use In Vedic form here we use 100100 as a base as a base98 × 94 = ?98 × 94 = ?98 - 0298 - 02

94 - 0694 - 0692 / 1292 / 12

Subtract 98-06 or 94-02 we get 92Subtract 98-06 or 94-02 we get 92Multiply 02 × 06 we get 12Multiply 02 × 06 we get 1298 × 94 =921298 × 94 =9212


Example:2Example:2 88 × 89 = ?88 × 89 = ? 88 - 1288 - 12

89 - 1189 - 1177 / 13277 / 132

Subtract 88-11 or 89-12 we get Subtract 88-11 or 89-12 we get 7777

Multiply 12 × 11 we get 132Multiply 12 × 11 we get 132 We can’t put the answer like We can’t put the answer like

this 77132this 77132 Here from 132, 1 carry to 77 Here from 132, 1 carry to 77

and it becomes 78, thenand it becomes 78, then 88 × 89 = 783288 × 89 = 7832

To Multiply 12 and 11,we can To Multiply 12 and 11,we can use 10 as a base.use 10 as a base.

12 + 0212 + 0211 + 0111 + 0113/213/2

Practice 4Practice 4 91 × 89 = ? 91 × 89 = ? 92 × 92 = ? 92 × 92 = ? 88 × 85 = ? 88 × 85 = ? 86 × 97 = ?86 × 97 = ? 91 × 92 = ?91 × 92 = ? 94 × 97 = ?94 × 97 = ? 85 × 85 = ?85 × 85 = ? 98 × 98 = ?98 × 98 = ?

Ans:Ans: ??

NUMBERS JUST ABOVE THE BASENUMBERS JUST ABOVE THE BASE


412412 000000

10310310712 10712

Vedic FormVedic Form In Vedic form here we use In Vedic form here we use 100100 as a base as a base103 × 104 = ?103 × 104 = ?103 + 03103 + 03

104 + 04104 + 04107 / 12107 / 12

Add 103+04 or 104+03 we get 107Add 103+04 or 104+03 we get 107Multiply 03 × 04 we get 12Multiply 03 × 04 we get 12103 × 104 = 10712103 × 104 = 10712

125 × 105 = ?125 × 105 = ?125 + 025125 + 025

105 + 005105 + 005130 / 125130 / 125

Add 125+005 or 105+025 we get 130Add 125+005 or 105+025 we get 130Multiply 25 × 5 we get 125Multiply 25 × 5 we get 125We can’t put the answer like this 130125We can’t put the answer like this 130125Here from 125, 1 carry to 130 and it Here from 125, 1 carry to 130 and it

becomes 131, thenbecomes 131, then125 × 105 = 13125125 × 105 = 13125

Practice 5Practice 5 128 × 112 = ?128 × 112 = ? 109 × 105 = ?109 × 105 = ? 131 × 109 = ?131 × 109 = ? 125 × 125 = ?125 × 125 = ? 114 × 112 = ?114 × 112 = ? 107 × 108 = ?107 × 108 = ? 113 × 113 = ?113 × 113 = ? 102 × 125 = ?102 × 125 = ?

Ans :Ans : ??

ABOVE AND BELOW THE BASEABOVE AND BELOW THE BASE


510510 918918

96909690

Vedic FormVedic Form In Vedic form here we use In Vedic form here we use 100100 as a base as a base 102 × 95 = ?102 × 95 = ? 102 + 02102 + 02

95 - 0595 - 05 97 / 1097 / 10

Add 95 + 02 or Subtract 102-05 we get 97Add 95 + 02 or Subtract 102-05 we get 97 Multiply 97 with 100 =9700Multiply 97 with 100 =9700 Multiply 02 × 05 we get 10Multiply 02 × 05 we get 10 Finally we get the answer from 9700-10Finally we get the answer from 9700-10 102 × 95 = 9690102 × 95 = 9690

10

136 × 90 = ?136 × 90 = ? 136 + 36136 + 36

90 - 1090 - 10126 / 360126 / 360

Add 90+36 or Subtract 136-10 we get 126Add 90+36 or Subtract 136-10 we get 126 Multiply 126 with 100 =12600Multiply 126 with 100 =12600 Multiply 36 × 10 we get 360 Multiply 36 × 10 we get 360 Therefore 12600-360 we get the answer Therefore 12600-360 we get the answer 136 × 90 = 12240136 × 90 = 12240

Practice 6Practice 6 146 × 80 = ?146 × 80 = ? 97 × 145 = ?97 × 145 = ? 98 × 125 = ?98 × 125 = ? 139 × 95 = ?139 × 95 = ? 141 × 90 = ?141 × 90 = ? 128 × 96 = ?128 × 96 = ? 126 × 89 = ?126 × 89 = ? 130 × 99 = ?130 × 99 = ?

Ans:Ans: ??

WITH DIFFERENT BASEWITH DIFFERENT BASE

• 9997 ×9997 × 98 = ? 98 = ?• Here the numbers are Here the numbers are

close to different close to different bases:10,000 and 100bases:10,000 and 100

• The deficiencies areThe deficiencies are -3 and -2.-3 and -2.• Therefore: 9997 – 03Therefore: 9997 – 03 98 – 0298 – 02 9797/069797/06

• 02 is not subtracted from the 02 is not subtracted from the last two digit (97) of 9997, last two digit (97) of 9997, but from 99 of 9997.but from 99 of 9997.

• And 03 is a deficiency from And 03 is a deficiency from 10,000 so we can’t subtract it 10,000 so we can’t subtract it from 98,because it’s a base from 98,because it’s a base of 100of 100

• Mulply 98 by 100 and Mulply 98 by 100 and subtract 3 also give the anssubtract 3 also give the ans

• 9997 ×9997 × 98 = 979706 98 = 979706

Practice 7Practice 7999 × 80999 × 80= ?= ?9987 × 989987 × 98 = ?= ?99995 × 99899995 × 998 = ?= ?96 × 896 × 8 = ?= ?10004 × 10810004 × 108 = ?= ?9985 × 9969985 × 996 = ?= ?98889 × 99 98889 × 99 = ?= ?

Ans :Ans : ??

10,20,… As a Base10,20,… As a Base We can use 10 as a base We can use 10 as a base

for single digit numbers.for single digit numbers. Ex: 7 Ex: 7 × 8=?× 8=? 7-37-3 8-28-2

5/65/6 7 7 × 8=56× 8=56

We can use 20 as a base We can use 20 as a base for single digit numbers.for single digit numbers.

Ex: 25 × 24=?Ex: 25 × 24=? 25 + 0525 + 05

24 + 0424 + 0429/2029/20

Now Multiply 29 by 2, we Now Multiply 29 by 2, we get 58 again multiply by get 58 again multiply by 10,we get 580.10,we get 580.

Add 580 with (5 × 4)=20Add 580 with (5 × 4)=20 25 × 24=60025 × 24=600

Practice 8Practice 8 8 8 × 9 × 9 =?=? 22 22 × 23 =?× 23 =? 18 18 × 24 =?× 24 =? 29 29 × 34 =?× 34 =? 54 54 × 56 =?× 56 =? 38 38 × 39 =?× 39 =? 45 45 × 42 =?× 42 =? 9 9 × 5× 5 =?=?

Ans:Ans: ??

ALL FROM 9 AND LAST FROM ALL FROM 9 AND LAST FROM 1010

Subtraction From a Subtraction From a Base:Base: If we apply the formula If we apply the formula

to 854 we get 146 to 854 we get 146 because 8 and 5 are because 8 and 5 are taken from 9 and 4 is taken from 9 and 4 is taken from 10.taken from 10.

1000 – 46 = ?1000 – 46 = ? 1000 -1000 - 046046

954954

Subtract the units Subtract the units digit from 10, then digit from 10, then each successive digit each successive digit from 9, then subtract from 9, then subtract 1 from the digit on the 1 from the digit on the left.left. 60000 – 34843 = ?60000 – 34843 = ? 60000 -60000 - 3484334843

2515725157

SQUARINGSQUARING

Digits ends with five and zeroDigits ends with five and zeroTwo digit numbers (aTwo digit numbers (a22+2ab+b+2ab+b22) form) form

DIGITS ENDS WITH DIGITS ENDS WITH FIVEFIVE AND AND ZEROZERO

75 × 75 =?75 × 75 =?Normal FormNormal Form 75 × 7575 × 75 375375 52552556255625


75 × 75 =?75 × 75 =?Here we use n(n+1)/25 formulaHere we use n(n+1)/25 formulaLet n= 7Let n= 7 n+1= 8n+1= 8 n(n+1) = 7 n(n+1) = 7 × 8 = 56× 8 = 56Therefore 75 × 75 =5625Therefore 75 × 75 =5625

3,4,… digits ends with 53,4,… digits ends with 5

135 × 135 = ?135 × 135 = ?Let n=13Let n=13n(n+1)=13(14)n(n+1)=13(14)169+13=182169+13=182135 × 135 =18225135 × 135 =18225Practice Practice

151522,25,2522,etc..,etc..

169+13=?169+13=? 169169 1313 11 0 70 7 1212 182182

DIGITS ENDS WITH DIGITS ENDS WITH ZEROZERO 10102 2 =?, 100=?, 100 202022

=?=?22 × 2 = 4 and put 00× 2 = 4 and put 00We get 400We get 400

125012502 2 =?=? 125/0125/0 125=12/5125=12/5 12*13/5*5=156/2512*13/5*5=156/25

125012502 2 = 1562500= 1562500

TWO DIGIT NUMBERS TWO DIGIT NUMBERS (A(A22+2AB+B+2AB+B22)) FORMFORM

36 × 36 =?36 × 36 =? A=3 & B=6A=3 & B=6 332 2 = 9= 9 2*3*6 = 362*3*6 = 36 662 2 = 36= 36 Therefore 9,36,36Therefore 9,36,36 1296 1296

Left to Right Left to Right Calculation:Calculation:

9+3=129+3=12 6+3= 096+3= 09 66 = 06 = 06

12961296

Practice 9Practice 9 89 × 89 89 × 89 =?=? 26 × 26 26 × 26 =?=? 93 × 93 93 × 93 =?=? 78 × 7878 × 78 =?=? 61 × 6161 × 61 =?=? 92 × 92 92 × 92 =?=? 44 × 4444 × 44 =?=? 55 × 5555 × 55 =?=?

Ans:Ans: ??

Left Side Same Digit and Addition of Left Side Same Digit and Addition of Right Digit is 10Right Digit is 10

82 × 88 =?82 × 88 =?Normal FormNormal Form 88 × 82 88 × 82

176176 704704 72167216


Here we are going to use n(n+1) formulaHere we are going to use n(n+1) formulai.e, we take n=8 and get 8(8+1)=8(9)=72i.e, we take n=8 and get 8(8+1)=8(9)=72and 2 × 8=16and 2 × 8=16

Therefore 82 × 88 = 7216Therefore 82 × 88 = 7216

Practice 10Practice 10 89 × 81 =?89 × 81 =? 26 × 24 =?26 × 24 =? 93 × 97 =?93 × 97 =? 78 × 72 =?78 × 72 =? 61 × 69 =?61 × 69 =? 92 × 98 =?92 × 98 =? 44 × 46 =?44 × 46 =?

Ans:Ans:

Doubt?Doubt?Keep Practice you will clear yourselfKeep Practice you will clear yourselfContact:Contact:R.SankarR.Sankar

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Vedic mathematicss-R.SANKAR