Columns
Number of the operations. Cards of the
Variable cards.
Statement of results.
Number of the Nature of each Columns acted
Columns
Indication of
1
V
0
=
m
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{0~}=m}}
1
1
×
{\displaystyle \scriptstyle {\times }}
1
V
0
×
1
V
4
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{0~}\times ~^{1}\mathbf {V} _{4~}=}}
1
V
6
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{6~}\ldots \ldots }}
{
1
V
0
=
1
V
0
1
V
4
=
1
V
4
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{0~}=~^{1}\mathbf {V} _{0~}}\\&\scriptstyle {^{1}\mathbf {V} _{4~}=~^{1}\mathbf {V} _{4~}}\end{aligned}}\right\}}}
1
V
6
=
m
n
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{6~}=mn'}}
1
V
1
=
n
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{1~}=n}}
2
"
×
{\displaystyle \scriptstyle {\times }}
1
V
3
×
1
V
1
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{3~}\times ~^{1}\mathbf {V} _{1~}=}}
1
V
7
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{7~}\ldots \ldots }}
{
1
V
3
=
1
V
3
1
V
1
=
1
V
1
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{3~}=~^{1}\mathbf {V} _{3~}}\\&\scriptstyle {^{1}\mathbf {V} _{1~}=~^{1}\mathbf {V} _{1~}}\end{aligned}}\right\}}}
1
V
7
=
m
′
n
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{7~}=m'n}}
1
V
2
=
d
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{2~}=d}}
3
"
×
{\displaystyle \scriptstyle {\times }}
1
V
2
×
1
V
4
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{2~}\times ~^{1}\mathbf {V} _{4~}=}}
1
V
8
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{8~}\ldots \ldots }}
{
1
V
2
=
1
V
2
1
V
4
=
0
V
4
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{2~}=~^{1}\mathbf {V} _{2~}}\\&\scriptstyle {^{1}\mathbf {V} _{4~}=~^{0}\mathbf {V} _{4~}}\end{aligned}}\right\}}}
1
V
8
=
d
n
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{8~}=dn'}}
1
V
3
=
m
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{3~}=m'}}
4
"
×
{\displaystyle \scriptstyle {\times }}
1
V
5
×
1
V
1
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{5~}\times ~^{1}\mathbf {V} _{1~}=}}
1
V
9
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{9~}\ldots \ldots }}
{
1
V
5
=
1
V
5
1
V
1
=
1
V
1
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{5~}=~^{1}V_{5~}}\\&\scriptstyle {^{1}\mathbf {V} _{1~}=~^{1}\mathbf {V} _{1~}}\end{aligned}}\right\}}}
1
V
9
=
d
′
n
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{9~}=d'n}}
1
V
4
=
n
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{4~}=n'}}
5
"
×
{\displaystyle \scriptstyle {\times }}
1
V
0
×
1
V
5
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{0~}\times ~^{1}\mathbf {V} _{5~}=}}
1
V
10
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{10}\ldots \ldots }}
{
1
V
0
=
0
V
0
1
V
5
=
0
V
5
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{0~}=~^{0}\mathbf {V} _{0~}}\\&\scriptstyle {^{1}\mathbf {V} _{5~}=~^{0}\mathbf {V} _{5~}}\end{aligned}}\right\}}}
1
V
10
=
d
′
m
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{10}=d'm}}
1
V
5
=
d
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{5~}=d'}}
6
"
×
{\displaystyle \scriptstyle {\times }}
1
V
2
×
1
V
3
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{2~}\times ~^{1}\mathbf {V} _{3~}=}}
1
V
11
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{11}\ldots \ldots }}
{
1
V
2
=
0
V
2
1
V
3
=
0
V
3
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{2~}=~^{0}\mathbf {V} _{2~}}\\&\scriptstyle {^{1}\mathbf {V} _{3~}=~^{0}\mathbf {V} _{3~}}\end{aligned}}\right\}}}
1
V
11
=
d
m
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{11}=dm'}}
7
2
−
{\displaystyle \scriptstyle {-}}
1
V
6
−
1
V
7
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{6~}-~^{1}\mathbf {V} _{7~}=}}
1
V
12
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{12}\ldots \ldots }}
{
1
V
6
=
0
V
6
1
V
7
=
0
V
7
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{6~}=~^{0}\mathbf {V} _{6~}}\\&\scriptstyle {^{1}\mathbf {V} _{7~}=~^{0}\mathbf {V} _{7~}}\end{aligned}}\right\}}}
1
V
12
=
m
n
′
−
m
′
n
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{12}=mn'-m'n}}
8
"
−
{\displaystyle \scriptstyle {-}}
1
V
8
−
1
V
9
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{8~}-~^{1}\mathbf {V} _{9~}=}}
1
V
13
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{13}\ldots \ldots }}
{
1
V
8
=
0
V
8
1
V
9
=
0
V
9
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{8~}=~^{0}\mathbf {V} _{8~}}\\&\scriptstyle {^{1}\mathbf {V} _{9~}=~^{0}\mathbf {V} _{9~}}\end{aligned}}\right\}}}
1
V
13
=
d
n
′
−
d
′
n
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{13}=dn'-d'n}}
9
"
−
{\displaystyle \scriptstyle {-}}
1
V
10
−
1
V
11
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{10}-^{1}\mathbf {V} _{11}=}}
1
V
14
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{14}\ldots \ldots }}
{
1
V
10
=
0
V
10
1
V
11
=
0
V
11
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{10}=~^{0}\mathbf {V} _{10}}\\&\scriptstyle {^{1}\mathbf {V} _{11}=~^{0}\mathbf {V} _{11}}\end{aligned}}\right\}}}
1
V
14
=
d
′
m
−
d
m
′
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{14}=d'm-dm'}}
10
3
÷
{\displaystyle \scriptstyle {\div }}
1
V
13
÷
1
V
12
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{13}\div ~^{1}\mathbf {V} _{12}=}}
1
V
15
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{15}\ldots \ldots }}
{
1
V
13
=
0
V
13
1
V
12
=
1
V
12
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{13}=~^{0}\mathbf {V} _{13}}\\&\scriptstyle {^{1}\mathbf {V} _{12}=~^{1}\mathbf {V} _{12}}\end{aligned}}\right\}}}
1
V
15
=
d
n
′
−
d
′
n
m
n
′
−
m
′
n
=
x
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{15}={\frac {dn'-d'n}{mn'-m'n}}=x}}
11
"
÷
{\displaystyle \scriptstyle {\div }}
1
V
14
−
1
V
12
=
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{14}-~^{1}\mathbf {V} _{12}=}}
1
V
16
…
…
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{16}\ldots \ldots }}
{
1
V
14
=
0
V
14
1
V
12
=
0
V
12
}
{\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{14}=~^{0}\mathbf {V} _{14}}\\&\scriptstyle {^{1}\mathbf {V} _{12}=~^{0}\mathbf {V} _{12}}\end{aligned}}\right\}}}
1
V
16
=
d
′
m
−
d
m
′
m
n
′
−
m
′
n
=
y
{\displaystyle \scriptstyle {^{1}\mathbf {V} _{16}={\frac {d'm-dm'}{mn'-m'n}}=y}}
1
2
3
4
5
6
7
8
