Vinjit Vedic Arithmetic Book 00.01 || Chapter 01.01 || Vedic Maths A Grand Parable
Author
Om Jitendra Singh Tomar
M.A., B.Ed., MASSCOM, DNYS
Chapter 01.01 || Vedic maths a grand parable
(Part 1)
**Division by 9
**Simplify to 1/A9
– by ekadhik purvena multiplication method
– By ekadhik Purvena by division method
I . Multiplication :
(i) Multiply 265 by 327
2 6 5
×3 2 7
1 8 5 5
5 3 0 ×
7 9 5 × ×
8 6 6 5 5
By Vedic Mental (One-line Method)
The “ Sanskrit Sutra (Formula) is Urdhwa Tiryagabhyam
2 6 5
×3 2 7
8 6 6 5 5
Note: Only the answer is written automatically down by Urdhwa Tiryak Sutra (forwards or back-wards).
(ii) Multiply 87265 by 32117
87265
×32117
610855
87265×
87265××
174530×××
261795××××
2802690005
By Vedic mental (one-line method)
The “ Sanskrit Sutra (Formula) is Urdhwa Tiryagabhyam
87265
×32117
2802690005
Note: Only the answer is written automatically down by Urdhwa Tiryak Sutra (forwards or back-wards).
***********************************************
(iii) Multiply by a × 9 or ab × 99 or abc × 999
5
× 9
4 5
By Vedic Mental (One-line Method)
A × 9
Eknuna of A (A – 1) / Complement of A {base – No.}
5 × 9
= (5 – 1) / (10 – 5)
= 45
(B) By Current (Traditional) Method:
7 2
× 9 9
6 4 8
6 4 8 ×
7 1 2 8
By Vedic Mental (One-line Method)
Ab × 99
Eknuna of Ab (Ab – 1) / Complement of Ab {base – No.}
7 2 × 9 9
= (72 – 1) / (100 – 72)
= 71 / 28
(C) By Current (Traditional) Method:
8 2 7
× 9 9 9
7 4 4 3
7 4 4 3 ×
7 4 4 3 × ×
8 2 6 1 7 3
By Vedic Mental (One-line Method)
Abc × 999
Eknuna of Abc (Abc – 1) / Complement of Abc {base – No.}
8 2 7 × 9 9 9
= (827 – 1) / (1000 – 827)
= 826 / 173
***********************************************
(iv) Multiply by 11
4 2
× 1 1
4 2
4 2 ×
4 6 2
By Vedic mental (one-line method)
A B × 1 1
= A / (A+B) / B
4 2 × 1 1
= 4 / (4 + 2) / 2
= 462
4 2 × 1 1 = 4 / (4 + 2) / 2 = 462
***********************************************
(v) Multiply
By Current (Traditional) Method:
9 9
× 9 1
9 1
8 9 1 ×
9 0 0 1
By Vedic Mental (By Base Method)
9 9 × 9 1
9 9 – 01
× 9 1 – 09
(99 – 9) / – 01 × – 09 [Cross Addition / Multiplication of Complement]
OR
(91 – 1) / 09
90 /09
Squaring By Vedic mental (by Base Method)
1 0 1 × 1 0 1
1 0 1 + 01
× 1 0 1 + 01
(101 + 1) / + 01 × + 01 [Cross Addition / Multiplication of Complement]
(102) / 01
102 01
1 0 2
× 1 0 2
(102+2)/04
104 04
1 0 6
× 1 0 6
(106+6)/36
112 36
***********************************************
II. Division:
Division by 9
(i) 1 2 ÷ 9
1 | 2 ÷ 9
1 | 3 Q = 1 R = 3
(ii) 1 2 3 ÷ 9
1 2 | 3 ÷ 9
1 3 | 6 Q = 13 R = 6
(iii) 1 2 3 4 ÷ 9
1 2 3 | 4 ÷ 9
1 3 6 | 10 [Now 10 ÷ 9 in (a)]
+ 1 | 1 Q = 137 R = 3
1 3 7 | 1
(a) 1 0 ÷ 9
1 | 0 ÷ 9
1 | 1 Q = 1 R = 1
Division by 99
(iv) 1 2 3 4 ÷ 9 9
12 | 34 ÷ 99
12 | 46 Q = 12 R = 46
Division by 999
(iv) 1 2 3 4 ÷ 999
1 | 234 ÷ 999
1 | 235 Q = 1 R = 235
Simplify 1/A9
Express 1/19 in its full recurring decimal shape (18 digits) :
By The Current Method :
19) 1.00( 0.052631578947368421
95
50
38
120
114
60
57
30
19
110
95
150
133
170
152
180
171
90
76
140
133
70
57
130
114
160
152
80
76
40
38
20
19
1
**1/A9 को सरल करना
–एकाधिक पूर्वेण भाग विधि द्वारा
Forwards (Division) Method (by the Ekadhika-Purva Sutra)
**1/A9 को सरल करना
–एकाधिक पूर्वेण गुणन विधि द्वारा
By Vedic mental (one-line method)
The “ Sanskrit Sutra” (Formula) is Ekadhika Purva;
(by the Ekadhika-Purva Sutra)
Backwards (Multiplication) Method.
We merely write down the 18-digit answer:
1/19 = 0.052631578-947368421
0.052631578
947368421
1/19 = 0.052631578-947368421
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