विनजीत वैदिक अंकगणित पुस्तक || 1 || अध्याय 13.02 || 9 सीरीज की गुणा (Type 2)
Vinjeet Vedic Arithmetic Book || 1 || Chapter 13.02 || Multiplication of 9 Series (Type 2)
Author
ॐ जितेन्द्र सिंह तोमर
(M.A., B. Ed., MASSCOM, DNYS )
(Specialist in Basic and Vedic Maths)
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Multiplication by 9's
द्वितीय प्रकार
गुणन –
– पूरक (निखिलम सूत्र द्वारा)
निखिलम नवत: चरमं दशत:
– 9 से 9 सीरीज की गुणा
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द्वितीय प्रकार
Second Type
When Number of the Multiplicand is less than multiplayer.
Counting Number of Multiplicand < Counting Number of Multiplier
दूसरे प्रकार में गुण्यांकों की संख्या कम तथा गुणकांकों की संख्या ज्यादा होती है। तो दोनों को बराबर करने के लिए गुणकांकों में शून्य लगा कर गुण्यांकों तथा गुणकांकों की संख्या बराबर कर लेते हैं।
In other types the number of Multiplicand is less and the number of multipliers. So to make both equal, we have to make the number of multiplier and coefficient equal by adding zero in the Multiplicand.
गुण्यांक संख्या कम = गुणकांक संख्या अधिक
Digits of Multiplicand < Digits of Multiplier
0B × 99
0AB × 999
0ABC × 99999
0ABCD × 999999
m × 9 = *(m)/(C of m)
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Multiplication by 9's
a) Any two digit numbers by 99
0a × 99
= *(0a)/(C of 0a)
b) Any three digit numbers by 999
0ab × 999
= *(0ab)/(C of 0ab)
c) Any four digit numbers by 9999
(i) 0abc × 9999
= *(0abc)/(C of 0abc)
(ii) 00ab × 9999
= *(00ab)/(C of 00ab)
d) Any five digit numbers by 99999
(i) 0abcd × 99999
= *(0abcd)/(C of 0abcd)
(ii) 00abc × 99999
= *(00abc)/(C of 00abc)
(iii) 000ab × 99999
= *(000ab)/(C of 000ab)
e) Any six digit numbers by 999999
(i) 0abcde × 999999
= *(0abcde)/(C of 0abcde)
(ii) 00abcd × 999999
= *(00abcd)/(C of 00abcd)
(iii) 000abc × 999999
= *(000abc)/(C of 000abc)
(iv) 0000ab × 999999
= *(0000ab)/(C of 0000ab)
So on ..... ..... .....
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Practice Time 01
2D × 99
(1) 2 × 99
(2) 9 × 99
(3) 3 × 99
(4) 7 × 99
(5) 4 × 99
(6) 5 × 99
(7) 1 × 99
(8) 6 × 99
(9) 9 × 99
(10) 46 × 999
(11) 32 × 999
(12) 79 × 999
(13) 63 × 999
(14) 84 × 999
(15) 74 × 999
(16) 73 × 999
(17) 58 × 999
(18) 96 × 999
(19) 36 × 999
(20) 86 × 999
Sol. (1)
2 × 99
= *02/(100–12)
= 1/88
= 188
Sol. (2)
99 × 999
= *099/(1000–099)
= 98/901
= 98901
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Practice Time 02
3D × 999
(1) 132 × 9999
(2) 909 × 9999
(3) 243 × 9999
(4) 867 × 9999
(5) 354 × 9999
(6) 796 × 9999
(7) 478 × 9999
(8) 676 × 9999
(9) 586 × 9999
(10) 476 × 9999
(11) 392 × 99999
(12) 719 × 99999
(13) 623 × 99999
(14) 834 × 99999
(15) 754 × 99999
(16) 743 × 99999
(17) 558 × 99999
(18) 976 × 99999
(19) 356 × 99999
(20) 896 × 99999
Sol. (1)
132 × 9999
= *0132/(10000–0132)
= 131/9868
= 1319868
Sol. (2)
392 × 99999
= *00392/(100000–00392)
= 391/99608
= 39199608
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Practice Time 03
4.D × 9999
(1) 1324 × 99999
(2) 9091 × 99999
(3) 2434 × 99999
(4) 8678 × 99999
(5) 3545 × 99999
(6) 7965 × 999999
(7) 4789 × 999999
(8) 6767 × 999999
(9) 5867 × 999999
(10) 4765 × 999999
(11) 3923 × 9999999
(12) 7191 × 9999999
(13) 6232 × 9999999
(14) 8343 × 9999999
(15) 7545 × 9999999
(16) 7434 × 99999999
(17) 5587 × 99999999
(18) 9767 × 99999999
(19) 3568 × 99999999
(20) 8967 × 99999999
Sol. (1)
1324 × 99999
= *01324/(100000–01324)
= 1323/98676
= 132398676
Sol. (2)
0009091 × 9999999
= *0009091/(10000000–0009091)
= 9090/9990909
= 90909990909
Practice Time 05
5.D × 5T9
(1) 13245 × 999999
(2) 90912 × 999999
(3) 24345 × 999999
(4) 86789 × 999999
(5) 35456 × 999999
6.D × 6T9
(6) 796578 × 99999999
(7) 478912 × 99999999
(8) 676781 × 99999999
(9) 586762 × 99999999
(10) 476563 × 99999999
7.D × 7T9
(11) 1796578 × 999999999
(12) 2478912 × 999999999
(13) 3676781 × 999999999
(14) 4586762 × 999999999
(15) 5476563 × 999999999
8.D × 8T9
(16) 39234565 × 9999999999
(17) 71912345 × 9999999999
(18) 62323456 × 9999999999
(19) 83434567 × 9999999999
(20) 75456789 × 9999999999
9.D × 9T9
(21) 743456789 × 9999999999
(22) 558789123 × 99999999999
(23) 976745678 × 999999999999
(24) 356891234 × 999999999999
(25) 896789234 × 9999999999999
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