विनजीत वैदिक अंकगणित पुस्तक || 1 || अध्याय 14.01 || 1 सीरीज की गुणा (Type 1A)
Vinjeet Vedic Arithmetic Book || 1 || Chapter 14.01 || Multiplication of 1 Series (Type 1A)
Author
ॐ जितेन्द्र सिंह तोमर
(M.A., B. Ed., MASSCOM, DNYS )
(Specialist in Basic and Vedic Maths)
अध्याय 14.01
गुणन
– 1 सीरीज की गुणा
Multiply ocean of 1 series
* प्रथम प्रकार
Type 1
गुण्यांक संख्या = गुणकांक 1 की संख्या
Digit Of Multiplicand = Digit Of Multiplier
01. शून्य प्रयोग द्वारा
By using zeros
A × 1
0AB0 × 11
00ABC00 × 111
000ABCD000 × 1111
(i) any two digit numbers by 11
m × 1 = 0 m 0
Add 2 – 2 digits pairs till the end.
(i) 11 तक कोई भी दो अंकीय संख्या
m × 1 = 0 m 0
अंत तक 2–2 अंकों के जोड़े जोड़ें।
0AB0 × 11
0ABC0 × 11
0ABCD0 × 11
(ii) any three digit numbers by 111
m × 1 1 1 = 0 0 m 0 0
Add 3 – 3 digits pairs till the end.
(ii) 11 तक कोई भी तीन अंकीय संख्या
m × 111 = 00 m 00
अंत तक 3–3 अंकों के जोड़े जोड़ें।
00AB00 × 111
00ABC00 × 111
00ABCD00 × 111
(iii) any four digit numbers by 1111
m × 1 1 1 1 = 0 0 0 m 0 0 0
Add 4 – 4 digits pairs till the end.
(iii) 1111 तक कोई भी 4 अंकीय संख्या
m × 1111 = 000 m 0000
अंत तक 4–4 अंकों के जोड़े जोड़ें।
000AB000 × 1111
000ABC000 × 1111
000ABCD000 × 1111
000ABCDE000 × 1111
(iv) any five digit numbers by 11111
m × 1 1 1 1 1 = 0 0 0 0 m 0 0 0 0
Add 5 – 5 digits pairs till the end.
(iv) 11111 तक कोई भी 5 अंकीय संख्या
m × 11111 = 0000 m 0000
अंत तक 5–5 अंकों के जोड़े जोड़ें।
0000AB0000 × 11111
0000ABC0000 × 11111
0000ABCD0000 × 11111
0000ABCDE0000 × 11111
(v) any six digit numbers by 111111
00000ABCD00000 × 111111
So on .......
(i) any two digit numbers by 11
0AB0 × 11
45 × 11
(i) 0450 × 11 = 495
U 0450 0+5 = 5
T 0450 4+5 = 9
H 0450 0+4 = 4
(ii) 04350 × 11 = 4983
U 04530 3+0 = 3
T 04530 5+3 = 8
H 04530 4+5 = 9
Th 04530 0+4 = 4
Practice Time 01
2D × 11
(1) 12 × 11
(2) 99 × 11
(3) 23 × 11
(4) 87 × 11
(5) 34 × 11
(6) 76 × 11
(7) 48 × 11
(8) 167 × 11
(9) 256 × 11
(10) 346 × 11
(11) 432 × 11
(12) 579 × 11
(13) 663 × 11
(14) 784 × 11
(15) 1274 × 11
(16) 3473 × 11
(17) 4558 × 11
(18) 7896 × 11
(19) 9236 × 11
(20) 2386 × 11
Sol. (1) 12 × 11 = 132
U 0120 2+0 = 2
T 0120 1+2 = 3
H 0120 0+1 = 1
Sol. (8) 1275 × 11
U 012750 5+0 = 5
T 012750 7+5 = 12
H 012750 2+7 = 9
Th 012750 1+2 = 3
TTh 012750 1+0 = 1
1275 × 11 = 139¹25 => 14025
Sol. (15) 167 × 11
U 01670 7+0 = 7
T 01670 6+7 = 13
H 01670 1+6 = 7
Th 01670 1+0 = 4
167 × 11 = 47¹37 => 4837
Practice Time 02
3D × 111
(1) 32 × 111
(2) 99 × 111
(3) 43 × 111
(4) 87 × 111
(5) 54 × 111
(6) 796 × 111
(7) 478 × 111
(8) 676 × 111
(9) 586 × 111
(10) 476 × 111
(11) 4392 × 111
(12) 5719 × 111
(13) 7623 × 111
(14) 6834 × 111
(15) 8754 × 111
(16) 12743 × 111
(17) 23558 × 111
(18) 34976 × 111
(19) 45356 × 111
(20) 56896 × 111
Sol. (1) 32 × 111
U 003200 2+0+0 = 2
T 003200 3+2+0 = 5
H 003200 0+3+2 = 5
Th 003200 0+0+1 = 3
32 × 111 = 3552
Sol. (8) 796 × 111
U 0079600 6+0+0 = 6
T 0079600 9+6+0 = 15
H 0079600 7+9+6 = 22
T 0079600 0+7+9 = 16
Th 0079600 0+0+7 = 7
796 × 111 = 7¹6²2¹56 => 88356
Sol. (8) 4392 × 111
U 00439200 2+0+0 = 2
T 00439200 9+2+0 = 11
H 00439200 3+9+2 = 14
H 00439200 4+3+9 = 16
T 00439200 0+4+3 = 7
Th 00439200 0+0+4 = 4
4392 × 111 = 47¹6¹4¹12 => 487512
Practice Time 03
4.D × 1111
(1) 324 × 1111
(2) 991 × 1111
(3) 434 × 1111
(4) 878 × 1111
(5) 545 × 1111
(6) 7965 × 1111
(7) 4789 × 1111
(8) 6767 × 1111
(9) 5867 × 1111
(10) 4765 × 1111
(11) 23923 × 1111
(12) 37191 × 1111
(13) 46232 × 1111
(14) 58343 × 1111
(15) 67545 × 1111
(16) 127434 × 1111
(17) 235587 × 1111
(18) 349767 × 1111
(19) 453568 × 1111
(20) 568967 × 1111
Sol. (1) 324 × 1111
U 000324000 4+0+0+0 = 4
T 000324000 3+4+0+0 = 7
H 000324000 3+2+4+0 = 9
Th 000324000 0+3+2+4 = 9
TTh 000324000 0+0+3+2 = 5
L 000324000 0+0+0+3 = 3
324 × 1111 = 359974
Sol. (11) 23923 × 1111
U 00023923000 3+0+0+0 = 3
T 00023923000 2+3+0+0 = 5
H 00023923000 9+2+3+0 = 14
Th 00023923000 3+9+2+3 = 17
TTh 00023923000 2+3+9+2 = 16
L 00023923000 0+2+3+9 = 14
TL 00023923000 0+0+2+3 = 5
C 00023923000 0+0+0+2 = 2
23923 × 1111 = 25¹4¹6¹7¹453
= 26578453
Sol. (16) 127434 × 1111
U 000127434000 4+0+0+0 = 4
T 000127434000 3+4+0+0 = 7
H 000127434000 4+3+4+0 = 11
Th 000127434000 7+4+3+4 = 18
TTh 000127434000 2+7+4+3 = 16
L 000127434000 1+2+7+4 = 14
TL 000127434000 0+1+2+7 = 10
C 000127434000 0+0+1+2 = 3
TC 000127434000 0+0+0+1 = 1
127434 × 1111 = 13¹0¹4¹6¹8¹174
= 141579174
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