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This PDF explain multiplication of numbers by anurupyena Sub Sutras and Vedic Mathematics.

1.
VEDAS TO

2.
JOURNEY THROUGH TEMPUS

Vedic Mathematics is

a book written by the Indian Hindu priest

jagadguru swami sri bharti krishna tirtha ji

(rediscovered from vedas between 1911 and

1918)

first published in 1965.

It contains a list of mental calulation

techniques based on the vedas.

The mental calculation system mentioned in

the book is also known by the same name or

as "Vedic Maths”

Vedic Mathematics is

a book written by the Indian Hindu priest

jagadguru swami sri bharti krishna tirtha ji

(rediscovered from vedas between 1911 and

1918)

first published in 1965.

It contains a list of mental calulation

techniques based on the vedas.

The mental calculation system mentioned in

the book is also known by the same name or

as "Vedic Maths”

3.
Vedicmathematics comprises “16

Sutras(formulae) & their

subsutras(corollaries)

At doer’s end:

doer has to identify and spot

certain characteristics , patterns

and then apply the sutra

( formula) which is applicable

there to

Sutras(formulae) & their

subsutras(corollaries)

At doer’s end:

doer has to identify and spot

certain characteristics , patterns

and then apply the sutra

( formula) which is applicable

there to

4.
MEMENTOES

Reduces silly mistakes

Fastens the calculations

Intelligent guessing

Reduces burden

Makes mathematics a bit of

fun game for pupils

Reduces silly mistakes

Fastens the calculations

Intelligent guessing

Reduces burden

Makes mathematics a bit of

fun game for pupils

5.
MULTIPLICATION BY 11 & ITS

MULTIPLES

(Sub sutra anurupyena)

Application of sutra is very

easy

Amazingly ; table of 11 is

not required

Just have to add digits in

pairs

MULTIPLES

(Sub sutra anurupyena)

Application of sutra is very

easy

Amazingly ; table of 11 is

not required

Just have to add digits in

pairs

6.
WORKING

2314× 11

Put single “0” in extreme left and

extreme right of the multiplicand

023140

(Single naught sandwich)

Add the digits in pair starting from

right to left

2314× 11

Put single “0” in extreme left and

extreme right of the multiplicand

023140

(Single naught sandwich)

Add the digits in pair starting from

right to left

7.
023140

02314+0 (4+0=4)

0231+40 (1+4=5)

023+140 (3+1=4)

02+3140 (2+3=5)

0+23140 (0+2=2)

2314×11 = 25454

02314+0 (4+0=4)

0231+40 (1+4=5)

023+140 (3+1=4)

02+3140 (2+3=5)

0+23140 (0+2=2)

2314×11 = 25454

8.
0 2314 0

˟11

2+0 3+2 1+3 4+1 0+4

25454

˟11

2+0 3+2 1+3 4+1 0+4

25454

9.
IF SUM OF 2 DIGITS OF

MULTIPLICAND EXCEEDS “9”

When the sum exceeds 9 then carry the tens place

digit & add to the preceding digit

2824×11

Single naught sandwich=028240

0+4=4

4+2=6

2+8=10=10

8+2=10=10+1=11=11

2+0=2=2+1=3

Product=31064

MULTIPLICAND EXCEEDS “9”

When the sum exceeds 9 then carry the tens place

digit & add to the preceding digit

2824×11

Single naught sandwich=028240

0+4=4

4+2=6

2+8=10=10

8+2=10=10+1=11=11

2+0=2=2+1=3

Product=31064

10.
MULTIPLICATION BY MULTIPLES

OF 11 (22,33,44.55.66…)

Multiply the multiplicand by the

number of rank of the multiple

(e.g. 44 is 4th and 99 is 9th multiple so

multiply the multiplicand by 4 or 9 in

case we are multiplying by 44 or 99)

Then apply the rule of multiplication

by 11 to the product obtained (single

naught sandwich)

OF 11 (22,33,44.55.66…)

Multiply the multiplicand by the

number of rank of the multiple

(e.g. 44 is 4th and 99 is 9th multiple so

multiply the multiplicand by 4 or 9 in

case we are multiplying by 44 or 99)

Then apply the rule of multiplication

by 11 to the product obtained (single

naught sandwich)

11.
245

×22 (2×11)

245×2= 490

04900

51390

×22 (2×11)

245×2= 490

04900

51390

12.
MULTIPLICATION BY 111

3496

×111

(Add 2 zeroes to the extreme right and

extreme left of the multiplicand)

Double Naught Sandwich

00 3496 00

Sandwiched Number=00349600

3496

×111

(Add 2 zeroes to the extreme right and

extreme left of the multiplicand)

Double Naught Sandwich

00 3496 00

Sandwiched Number=00349600

13.
3496

×111

00349600

(Double naught sandwich)

Add 3 digits at a time

starting from right

to left

×111

00349600

(Double naught sandwich)

Add 3 digits at a time

starting from right

to left

14.
3 8 1 8 0

2 5

1 6

388056

2 5

1 6

388056

15.
MULTIPLICATION BY MULTIPLES

OF 111

(222 TO 999)

Find the rank of the multiple

(for 555 the rank is 5, for 777 the

rank is 7 and so on)

Multiply the multiplicand by the

number of rank

Apply the multiplication of 111 the

product obtained

(Double Naught Sandwich

Method)

OF 111

(222 TO 999)

Find the rank of the multiple

(for 555 the rank is 5, for 777 the

rank is 7 and so on)

Multiply the multiplicand by the

number of rank

Apply the multiplication of 111 the

product obtained

(Double Naught Sandwich

Method)

16.
WORKING

1348

(2 × 111) × 222

(2 ×1348) 00 2696 00

00269600

(Double Naught Sandwich)

1348

(2 × 111) × 222

(2 ×1348) 00 2696 00

00269600

(Double Naught Sandwich)

17.
00269600

2+0+0 6+2+0 9+6+2 0+0+6

6+9+6 0+6+9

6

8 17

21

5

8+1 17+2 21+1

9 19 22 1

299256

2+0+0 6+2+0 9+6+2 0+0+6

6+9+6 0+6+9

6

8 17

21

5

8+1 17+2 21+1

9 19 22 1

299256

18.
19

(sutra sopantyadvayamantyam)

sandwich the multiplicand

between single zero

Multiply each digit of the

multiplicand by first digit of the

multiplier from right to left and

add to the immediate right digit

following it one by one

(sutra sopantyadvayamantyam)

sandwich the multiplicand

between single zero

Multiply each digit of the

multiplicand by first digit of the

multiplier from right to left and

add to the immediate right digit

following it one by one

19.
WORKING

0 1235 0

× 12

(2 ×0)+1=1 (2 ×2)+3=7 (2 ×3)+5=11 (2 ×5)+0=10

(2 ×1)+2=4

7+1 11+1

1 4 8 12 10

14820

0 1235 0

× 12

(2 ×0)+1=1 (2 ×2)+3=7 (2 ×3)+5=11 (2 ×5)+0=10

(2 ×1)+2=4

7+1 11+1

1 4 8 12 10

14820

20.
SAME METHOD FOR 13 TO

19….

Practice the method

for

2356 ×15

2123 ×16

19….

Practice the method

for

2356 ×15

2123 ×16

21.
MULTIPLICATION OF SPECIAL NUMBERS

“Antyayordasake’pi”

Sum of unit digits are ten & rest

place digits are same

67

×63

Sum of ten’s place digits is ten

& unit digits are same

22

×82

“Antyayordasake’pi”

Sum of unit digits are ten & rest

place digits are same

67

×63

Sum of ten’s place digits is ten

& unit digits are same

22

×82

22.
WORKING 67 ×63

Multiply the unit digit & write the product in two digits

on one’s & ten’s place

Multiply the ten’s place digit with its successor

67

×63

(7 ×3=21)

(6 × 7=42)

4221

Multiply the unit digit & write the product in two digits

on one’s & ten’s place

Multiply the ten’s place digit with its successor

67

×63

(7 ×3=21)

(6 × 7=42)

4221

23.
22

× 82

Multiply the unit digits & write the product in two digits,

one’s & ten’s place

Multiply the ten’s place digits & add one “unit digit” then

put in hundred's & thousand’s place

22

× 82

(2 ×2=04)

[(8 ×2)+2]

1804

× 82

Multiply the unit digits & write the product in two digits,

one’s & ten’s place

Multiply the ten’s place digits & add one “unit digit” then

put in hundred's & thousand’s place

22

× 82

(2 ×2=04)

[(8 ×2)+2]

1804

24.
PRACTICE THE METHOD..

58

× 52

75

× 35

58

× 52

75

× 35

25.
Gaurav Raj (TGT N/M)

GHS Dakahal Edu. Block: Kotkhai

Distt. Shimla

Yogesh Kumar (TGT N/M)

GHS Samleu Edu. Block Banikhet

Distt. Chamba

Sunita Bindra (TGT N/M)

GSSS Tutu Distt Shimla

GHS Dakahal Edu. Block: Kotkhai

Distt. Shimla

Yogesh Kumar (TGT N/M)

GHS Samleu Edu. Block Banikhet

Distt. Chamba

Sunita Bindra (TGT N/M)

GSSS Tutu Distt Shimla

26.