विनजीत वैदिक अंकगणित पुस्तक || 1 || अध्याय 13.01 || 9 सीरीज की गुणा (Type 1)
Vinjeet Vedic Arithmetic Book || 1 || Chapter 13.01 || Multiplication of 9 Series (Type 1)
Author
ॐ जितेन्द्र सिंह तोमर
(M.A., B. Ed., MASSCOM, DNYS )
(Specialist in Basic and Vedic Maths)
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गुणन –
– पूरक (निखिलम सूत्र द्वारा)
निखिलम नवत: चरमं दशत:
– 9 से 9 सीरीज की गुणा
* प्रथम प्रकार
गुण्यांक संख्या = गुणकांक संख्या
A × 9
AB × 99
ABC × 999
ABCD × 9999
ABCDE × 99999
m × 9 = *(m)/(C of m)
Multiplication – Multiplication of 9 Series
– Supplement (by Nikhilam Sutra)
Nikhilam Navatah Charam Dashat:
– Multiplication of 9 by 9 series
* First Type
When Number of the Multiplicand and multiplayer is same.
Counting Number of Multiplicand = Counting Number of Multiplier
A × 9
AB × 99
ABC × 999
ABCD × 9999
ABCDE × 99999
m × 9 = *(m)/(C of m)
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Multiplication by 9's
a) Any two digit numbers by 99
ab × 99
= *(ab)/(C of ab)
b) Any three digit numbers by 999
abc × 999
= *(abc)/(C of abc)
c) Any four digit numbers by 9999
abcd × 9999
= *(abcd)/(C of abcd)
d) Any five digit numbers by 99999
abcde × 99999
= *(abcde)/(C of abcde)
e) Any six digit numbers by 999999
abcdef × 999999
= *(abcdef)/(C of abcdef)
f) Any seven digit numbers by 9999999
abcdefg × 9999999
= *(abcdefg)/(C of abcdefg)
g) Any eight digit numbers by 99999999
abcdefgh × 99999999
= *(abcdefgh)/(C of abcdefgh)
h) Any nine digit numbers by 999999999 and so…on
abcdefghi.... × 999999999......
= *(abcdefghi....)/(C of abcdefghi....)
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Practice Time 01
1D × 9
(1) 1 × 9
(2) 9 × 9
(3) 2 × 9
(4) 8 × 9
(5) 3 × 9
(6) 7 × 9
(7) 4 × 9
(8) 6 × 9
(9) 5 × 9
Sol. (1)
1 × 9
= *0/(10–1)
= 9
Practice Time 02
2D × 99
(1) 12 × 99
(2) 99 × 99
(3) 23 × 99
(4) 87 × 99
(5) 34 × 99
(6) 76 × 99
(7) 48 × 99
(8) 66 × 99
(9) 56 × 99
(10) 46 × 99
(11) 32 × 99
(12) 79 × 99
(13) 63 × 99
(14) 84 × 99
(15) 74 × 99
(16) 73 × 99
(17) 58 × 99
(18) 96 × 99
(19) 36 × 99
(20) 86 × 99
Sol. (1)
12 × 99
= *12/(100–12)
= 11/88
= 1188
Sol. (2)
99 × 99
= *99/(100–99)
= 98/01
= 9801
Practice Time 03
3D × 999
(1) 132 × 999
(2) 909 × 999
(3) 243 × 999
(4) 867 × 999
(5) 354 × 999
(6) 796 × 999
(7) 478 × 999
(8) 676 × 999
(9) 586 × 999
(10) 476 × 999
(11) 392 × 999
(12) 719 × 999
(13) 623 × 999
(14) 834 × 999
(15) 754 × 999
(16) 743 × 999
(17) 558 × 999
(18) 976 × 999
(19) 356 × 999
(20) 896 × 999
Sol. (1)
132 × 999
= *132/(1000–868)
= 131/868
= 131868
Sol. (2)
909 × 999
= *909/(1000–909)
= 908/091
= 908091
Practice Time 04
4.D × 9999
(1) 1324 × 9999
(2) 9091 × 9999
(3) 2434 × 9999
(4) 8678 × 9999
(5) 3545 × 9999
(6) 7965 × 9999
(7) 4789 × 9999
(8) 6767 × 9999
(9) 5867 × 9999
(10) 4765 × 9999
(11) 3923 × 9999
(12) 7191 × 9999
(13) 6232 × 9999
(14) 8343 × 9999
(15) 7545 × 9999
(16) 7434 × 9999
(17) 5587 × 9999
(18) 9767 × 9999
(19) 3568 × 9999
(20) 8967 × 9999
Sol. (1)
1324 × 9999
= *1324/(10000–1324)
= 1323/8676
= 13238676
Sol. (2)
9091 × 9999
= *9091/(10000–9091)
= 9090/0909
= 90900909
Practice Time 05
5.D × 5T9
(1) 13245 × 99999
(2) 90912 × 99999
(3) 24345 × 99999
(4) 86789 × 99999
(5) 35456 × 99999
6.D × 6T9
(6) 796578 × 999999
(7) 478912 × 999999
(8) 676781 × 999999
(9) 586762 × 999999
(10) 476563 × 999999
7.D × 7T9
(11) 1796578 × 9999999
(12) 2478912 × 9999999
(13) 3676781 × 9999999
(14) 4586762 × 9999999
(15) 5476563 × 9999999
8.D × 8T9
(16) 39234565 × 99999999
(17) 71912345 × 99999999
(18) 62323456 × 99999999
(19) 83434567 × 99999999
(20) 75456789 × 99999999
9.D × 9T9
(21) 743456789 × 999999999
(22) 558789123 × 999999999
(23) 976745678 × 999999999
(24) 356891234 × 999999999
(25) 896789234 × 999999999
Sol. (1)
1324 × 9999
= *13245/(100000–13245)
= 13244/86755
= 1324586755
Sol. (6)
796578 × 999999
= *796578/(10000–796578)
= 796577/203422
= 796577203422
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