vm3
TRANSCRIPT
Ved
ic M
athe
mat
ics
M. K
rish
nam
oor
thy
(moo
rthy
)
emai
l ad
dres
s: m
oort
hy@
cs.r
pi.e
du
UR
L:
http
://w
ww
.cs.
rpi.e
du/~
mo
orth
y/vm
Last
Tw
o C
lass
es
� We
lear
nt h
ow to
mul
tipl
y us
ing
two
sut
ras
nam
ely
ekha
dhik
ena
Purv
ena
an
d N
ikhi
lam
In p
artic
ular
, yo
u k
now
wha
t the
ans
wer
s fo
r
39 *
31,
48
* 4
2, 7
8 *
82,
6 4
5 *
6 55
(usi
ng e
kadh
iken
a su
tra)
and
53 *
52
, 89
* 9
2, 1
04
* 1
22 (u
sin
g n
ikhi
lam
met
hod)
.
Out
line
of th
is c
lass
� How
to c
omp
ute
deci
mal
exp
ansi
ons
of1/
19, 1
/29,
…1/
89
etc
usi
ng E
kadh
iken
aPu
rven
a
� Div
isio
n U
sing
two
sut
ras
usin
g n
ikhi
lam
and
urd
hva-
tirya
gbhy
am .
How
to d
ivid
e 1
11 b
y 8
9 1
234
by
888,
163
84 b
y 1
28.
Sut
ra
1. E
kadh
iken
a Pu
rven
a
By
one
mor
e th
an th
e p
revi
ous
one.
The
pre
posi
tio
n “
by”
mea
ns th
e o
pera
tions
this
sutr
a co
ncer
ns a
re e
ither
mul
tipl
icat
ion
or d
ivis
ion
( In
the
case
of
addi
tion
/sub
trac
tion
pre
pos
ition
to/fr
om is
used
.). I
n th
is c
ase
it i
s us
eful
for
bot
h of
them
.
Exa
mpl
es
1/ 1
9 =
1/29
=
Wha
t is
the
met
hod?
Tw
o m
etho
ds: d
ivis
ion
and
mul
tipl
icat
ion:
Mul
tipl
icat
ion:
Sta
rt w
ith 1
as
the
last
dig
it.
1
Mul
tipl
y th
e la
st d
igit
by 2
(I.e
., on
e m
ore
than
1 (1
bei
ng
the
firs
t dig
it in
19)
and
that
is th
e pr
evio
us d
igit.
21
Rep
eat t
he p
revi
ous
step
:42
1
Con
tinui
ng
68
421
1
Cru
cial
ste
ps!!
6
8 4
21
1
Mul
tipl
y 6
by
2 an
d ad
d 1.
3 6
8 4
2 1
1 1
Con
tinui
ng w
e ge
t
4 7
3 6
8 4
2 1
1
1 1
Con
tinue
1/1
9=.
0 5
2 6
3 1
5 7
8 9
4 7
3 6
8 4
2 1
1/29
=
.0
3 4
4 8
2 7
5 8
6 2
0 6
8
9
6 5
5 1
7 2
4 1
3 7
9 3
1
1/39
=
Met
hod
2
Div
isio
n M
etho
d fo
r co
mpu
ting
1/1
9
Div
ide
1 b
y 2
( on
e m
ore
than
1 in
1 in
19)
.Pl
ace
the
quot
ient
in li
ne 1
and
rem
inde
r in
line
2
0 5
2
1
1
Tre
at th
e la
st r
emin
der
quo
tient
as
one
num
ber
and
divi
de b
y 2
and
repe
at.
Con
tinui
ng
1/19
=
.0 5
2 6
3 1
5 7
8 9
4 7
3 6
8 4
2 1
1/29
=
. 0
3 4
4 8
2 7
5 8
6 2
0 6
8 9
6 5
5 1
7 2
4 1
3
7 9
3 1
Div
isio
ns
Nik
hila
m M
etho
d:
Exa
mpl
es:
12
/ 9
=
1 2
1
1
| 3
Quo
tient
: 1
Rem
inde
r: 3
53
/9
=
5
3
5
Quo
tient
: 5 R
emin
der
8
Mor
e E
xam
ples
Wha
t is
the
quo
tient
and
rem
inde
r w
hen
120
31 is
div
ided
by
9?
1 2
0 3
1
1
3 3
6
Qu
otie
nt is
1 3
3 6
Rem
inde
r 7
Mor
e E
xam
ples
1 8
ove
r 9
225
ove
r 9
136
ove
r 9
237
ove
r 9
Exa
mpl
es
101
164
9 d
ivid
ed b
y 9
111/
89
123
4 /
888
111/
73