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This PDF explain multiplication of numbers by anurupyena Sub Sutras and Vedic Mathematics.
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”
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
4.
MEMENTOES
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
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
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
8.
0 2314 0
˟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
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)
11.
245
×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
13.
3496
×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
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)
16.
WORKING
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
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
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
20.
SAME METHOD FOR 13 TO
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
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
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
24.
PRACTICE THE METHOD..
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
+1-315-636-4485
+91 98151-74050 
