लेखक
ॐ जितेन्द्र सिंह तोमर
(M.A., B. Ed., MASSCOM, DNYS )
(Specialist in Basic and Vedic Maths)
सूत्र: निखिलं नवतश्चरमं दशत: यह एक लोकप्रिय सूत्र है, इस सूत्र के अनुसार (सभी 9 से, और अंतिम 10 से) का उपयोग किसी संख्या को 10n से घटाने और 10n के करीब दो संख्याओं को गुणा करने के लिए किया जाता है।
यह वैदिक गणित के अभ्यासी इसे 10n के करीब की संख्या के लिए बहुत प्रभावी पाते हैं, यहां तक कि प्रसिद्ध सूत्र: ऊर्ध्व तिर्यगभ्यां से भी अधिक प्रभावी।
Subtraction from Base 10,000 or 100,000 or 10,00,000
निखिलं नवतश्चरमं दशत:
Nikhilaṃ navataścaramaṃ daśataḥ -
All from 9, and the last from 10.
Sutra: Nikhilam Navatashcharama Dashat: This is a popular formula, according to this formula (all from 9, and last from 10) is used to subtract a number from 10n and multiply two numbers close to 10n.
Practitioners of Vedic mathematics find it very effective for numbers close to 10n, even more effective than the famous sutra: Urdhva Tiryagbhyan.
Subtraction of number from 10n:
As an illustration, let us use this Sūtra for:
As an illustration, let us use this Sūtra for:
Subtraction using appropriate base
1. Five digit number (base 10,000)
For Practice
Practice Time (1)
(1) 10000 – 1473
(2) 10000 – 3224
(3) 10000 – 5265
(4) 10000 – 6267
(5) 10000 – 1136
(6) 10000 – 2326
(7) 10000 – 5487
(8) 10000 – 7468
(9) 100000 – 9249
(10) 10000 – 2390
(11) 10000 – 4312
(12) 10000 – 6543
(13) 10000 – 8564
(14) 10000 – 1375
(15) 10000 – 3336
Sol. (1) 10000 – 1473
1473
(All from 9, and the last from 10)
= (9–1)(9–4)/(9–7)/(10–3)
=8/5/2/7
= 8527
Thus, 10000 – 1473 = 8527
Sol. (2) 10000 – 3224
3224
(All from 9, and the last from 10)
= (9–3)(9–2)/(9–2)/(10–4)
=6/7/7/6
= 6776
Thus, 10000 – 3224 = 6776
2. Six digit number (base 100,000)
For Practice
Practice Time (2)
(1) 100000 – 19431
(2) 100000 – 38762
(3) 100000 – 57543
(4) 100000 – 75234
(5) 100000 – 83345
(6) 100000 – 32456
(7) 100000 – 25676
(8) 100000 – 14787
(9) 100000 – 13878
(10) 100000 – 24569
(11) 100000 – 85670
(12) 100000 – 66771
(13) 100000 – 47542
(14) 100000 – 61343
(15) 100000 – 69564
(16) 100000 – 43575
(17) 100000 – 44446
(18) 10,0000 – 67657
(19) 100000 – 36568
(20) 100000 – 57849
Sol. (1) 100000 – 19431
19431
(All from 9, and the last from 10)
= (9–1)(9–9)(9–4)/(9–3)/(10–1)
= 8/0/5/6/9
= 80569
Thus, 10000 – 19431 = 80569
Sol. (2) 100000 – 38762
38762
(All from 9, and the last from 10)
= (9–3)(9–8)/(9–7)/(9–6)/(10–2)
= 6/1/2/3/8
= 61238
Thus, 10000 – 38762 = 61238
3. Seven digit number (base 10,00,000)
For Practice
Practice Time (3)
(1) 1000000 – 194313
(2) 1000000 – 387624
(3) 1000000 – 575435
(4) 1000000 – 752346
(5) 1000000 – 833457
(6) 1000000 – 324568
(7) 1000000 – 256769
(8) 1000000 – 147870
(9) 1000000 – 138781
(10) 1000000 – 245692
(11) 1000000 – 856703
(12) 1000000 – 667714
(13) 1000000 – 475425
(14) 1000000 – 613436
(15) 1000000 – 695647
(16) 1000000 – 435758
(17) 1000000 – 444469
(18) 1000000 – 676570
(19) 1000000 – 365681
(20) 1000000 – 578492
Sol. (1) 1000000 – 194313
194313
(All from 9, and the last from 10)
= (9–1)(9–9)(9–4)/(9–3)/(9–1)/(10–3)
= 8/0/5/6/8/7
= 805687
Thus, 10000 – 194313 = 805687
Sol. (2) 1000000 – 387624
387624
(All from 9, and the last from 10)
= (9–3)(9–8)/(9–7)/(9–6)/(9–2) /(10–4)
= 6/1/2/3/7/6
= 612376
Thus, 10000 – 387624 = 612376
4. Eight digit number (base 1,00,00,000)
Practice Time (4)
(1) 1000000 – 1294547
(2) 1000000 – 3223456
(3) 1000000 – 5265678
(4) 1000000 – 6262345
(5) 1000000 – 1134534
(6) 1000000 – 2323456
(7) 1000000 – 5489023
(8) 1000000 – 7467890
(9) 1000000 – 9245678
(10) 1000000 – 2390123
(11) 10000000 – 4312345
(12) 10000000 – 6545678
(13) 10000000 – 8567890
(14) 10000000 – 1378901
(15) 10000000 – 3333333
(16) 10000000 – 4324444
(17) 10000000 – 4433232
(18) 10000000 – 6345678
(19) 10000000 – 3656789
(20) 10000000 – 5767890
Sol. (1) 10000000 – 1294547
1294547
(All from 9, and the last from 10)
= (9–1)(9–2)(9–9)/(9–4)/(9–5)/(9–4)/(10–7)
= 8/7/0/5/4/5/3
= 8705453
Thus, 10000000 – 1294547 = 8705453
Sol. (2) 10000000 – 3223456
3223456
(All from 9, and the last from 10)
= (9–3)(9–2)/(9–2)/(9–3)/(9–4) /(9–5)/(10–6)
= 6/7/7/6/5/4/4
= 6776544
Thus, 10000000 – 3223456 = 6776544
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