vm4
TRANSCRIPT
Ved
ic M
athe
mat
ics
M. K
rish
nam
oort
hy (
moo
rthy
)
emai
l add
ress
: moo
rthy
@cs
.rpi
.edu
UR
L:
http
://w
ww
.cs.
rpi.e
du/~
moo
rthy
/vm
Out
line
of th
is c
lass
� Usi
ng U
rdhv
a-tr
iyag
bhya
m s
utra
(ve
rtic
ally
and
cros
swis
e) f
or d
ivis
ion
of la
rge
num
bers
.
� Div
isio
n us
ing
Dhv
ajan
ka s
utra
(on
top
ofth
e fl
ag).
Sut
ra
1.U
rdhv
a-T
irya
k Su
tra;
23
4 5
: 6
4
2
:1
----
----
----
--
8 2
: 12
Quo
tient
is 8
2
Rem
aind
er is
12
Ano
ther
Exa
mpl
e
3:
38
9 8
:2 d
ivid
end
row
7:
3
3
:1 r
emai
nder
row
----
----
----
----
----
----
-
5 3
4:0
quo
tient
row
Quo
tient
is 5
34
Rem
aind
er is
0.
How
doe
s th
e m
etho
d w
ork
� The
re a
re th
ree
row
s. T
he f
irst
row
is th
edi
vide
nd.
� The
sec
ond
row
is th
e re
mai
nder
row
.
� Thi
rd r
ow is
the
rem
aind
er r
ow.
� The
div
isor
is p
lace
d ac
cord
ing
to th
eD
hvaj
anka
Sut
ra.
Wha
t is
the
met
hod?
The
ent
ire
divi
sion
is to
be
by 7
(th
e le
adin
gdi
git)
.
We
allo
t one
pla
ce a
t the
rig
ht e
nd o
f th
edi
vide
nd f
or th
e re
mai
nder
por
tion
of th
ean
swer
.
1) W
e di
vide
38 b
y 7
and
we
get 5
as
the
quot
ient
and
3 a
s th
e re
mai
nder
.
Cru
cial
ste
ps!!
2)
We
put 5
as
the
firs
t quo
tient
and
pla
ce 3
on th
e to
p ro
w. (
note
trea
t the
nex
t tw
odi
gits
as
39 -
thre
e fr
om th
e re
mai
nder
and
9fr
om th
e ne
xt d
igit
in th
e di
vide
nd.)
3) F
rom
this
, we
dedu
ct 3
* 5
(th
e la
st d
igit
ofth
e di
viso
r an
d th
e qu
otie
nt).
39-1
5=24
isou
r ne
xt d
ivid
end.
Con
tinue
4) W
hen
we
divi
de 2
4 by
7 w
e ge
t 3 a
squ
otie
nt a
nd 3
as
the
rem
aind
er. A
s be
fore
,w
e pl
ace
quot
ient
3 in
the
quot
ient
row
and
rem
aind
er 3
in th
e re
mai
nder
row
.
5) N
ow th
e ne
w d
ivid
end
is 3
8-3*
3=29
(3 is
the
rem
aind
er a
nd 8
is th
e ne
xt d
igit
inth
e di
vide
nd -
so
38 a
nd th
en s
ubtr
act t
hepr
oduc
t of
3 an
d 3
(the
quo
tient
and
the
last
digi
t))
Con
td
6) D
ivid
ing
29 b
y 7,
we
get 4
as
the
quot
ient
and
1 as
the
rem
aind
er. P
lace
4 in
the
quot
ient
row
and
1 in
the
rem
aind
er r
ow.
7) 1
2 is
the
next
dig
it w
e ne
ed to
con
side
r.H
owev
er, s
ince
2 is
the
desi
gnat
edre
mai
nder
in th
e fi
rst r
ow, w
e w
ill s
ubtr
act
as u
sual
fro
m 1
2 , t
he n
umbe
r 4*
3 an
d w
ege
t the
rem
aind
er is
0.
Mor
e E
xam
ples
Div
ide
7632
by
94
476
3:2
9
4
:2
----
----
----
----
----
----
--
81
:18
Quo
tient
: 81
Rem
aind
er 1
8