जब गुणांक के सभी अंक 9 से बने हो।
या
9 की सीरीज से गुणा।
Multiplication of numbers with a series of 9’s
निखिलम उप प्रमेय एक न्यून पूर्वेण के द्वारा
(गुण्य) × (गुणक) = गुणनफल
(गुण्य) × (गुणक)
= (*गुण्य) / (गुणक – *गुण्य)
यहां स्टार (*) एक न्यून पूर्वेण का प्रतीक है
Stage 1
9 से (From 9)
1 × 9 = *1 / 9–*1 = 0/ 9–0 = 0/9
2 × 9 = *2 / 9–*2 = 1 / 9–1 = 1/8
3 × 9 = *3 / 9–*4 = 2 / 9–2 = 2/7
4 × 9 = *4 / 9–*5 = 3 / 9–3 = 3/6
5 × 9 = *5 / 9–*5 = 4 / 9–4 = 4/9
6 × 9 = *6 / 9–*6 = 5 / 9–5 = 5/4
7 × 9 = *7 / 9–*7 = 6 / 9–6 = 6/4
8 × 9 = *8 / 9–*8 = 7 / 9–7 = 7/2
9 × 9 = *9 / 9–*9 = 8 / 9–8 = 8/1
10 × 9 = *10 / 9–*10 = 9 / 9–9 = 9/0
Stage 2
99 से (From 99)
11 × 99 से 99 × 99
11 × 99
= *11 / 99–*11
= 10 / 99–10
= 10/89
12 × 99
= *12 / 99–*12
= 11 / 99–11
= 11/88
15 × 99
= *15 / 99–*15
= 14/ 99–14
= 14/85
19 × 99
= *19 / 99–*19
= 18 / 99–18
= 18/81
20 × 99
= *20 / 99–*20
= 19 / 99–19
= 19/80
99 × 99
= *99 / 99–*99
= 98 / 99–98
= 98/01
999 से (From 999)
111 × 999 से 999 × 999
101 × 999
= *101 / 999–*101
= 100 / 999–100
= 100/899
112 × 999
= *112 / 999–*112
= 111 / 999–111
= 111/888
999 × 999
= *999 / 999–*999
= 998 / 999–998
= 998/001
उधर त्रिगत सूत्र से
Udharv Tryagat Sutra se
Base 10
7 × 9 =
7 –3
× 9 –1
(7–1)/(–3 × –1)
or
(9–3)/(–3 × –1)
6 / 3
63
In Short
Base 10
7 × 9 =
7 –3
× 9 –1
6 / 3
Base 100
7 × 99 =
7 – 93
× 99 – 1
(7–1)/(–93 × –1)
or
(99–93)/(–93 × –1)
6 / 93
693
In Short
7 × 99 =
7 –93
× 99 –1
6 / 93
693
In Short
77 × 99 =
77 –23
× 99 –1
76 / 23
7623
In Short
79 × 99 =
79 –21
× 99 –1
78 / 21
7821
In Short
83 × 99 =
83 –17
× 99 –1
82 / 17
8217
Base 1000
7 × 999 =
7 – 993
× 999 – 1
(7–1)/(–993 × –1)
or
(99–93)/(–993 × –1)
6 / 993
6993
In Short
7 × 999 =
7 – 993
× 99 –1
6 / 993
693
In Short
77 × 999 =
77 – 923
× 999 –1
76 / 993
76993
In Short
877 × 999 =
877 – 123
× 999 –1
876 / 123
876123
In Short
979 × 999 =
979 – 21
× 999 –1
978 / 021
876123
In Short
789 × 9999 =
789 – 0211
× 999 –1
788 / 0211
7880221
इन सवालों को इस प्रकार देखिए
(गुण्य –1)/(आधार संख्या –गुण्य)
1* (गुण्य गुणक के शन्य के बराबर करके लिखें।)
2* / लिखें
3* (आधार संख्या –गुण्य)
आई अब इसी आधार पर कुछ उदाहरण करते हैं।
789 × 9999
आधार = 10000
(गुण्य –1)/(आधार संख्या –गुण्य)
= (789–1)/(10000 –0789)
= (788)/(0211)
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