Subtraction - Base method 5C
Subtract from numbers such as 1000, 2000, 3000 and more quickly
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:
1.Subtraction - Base method 5A Subtraction using appropriate base
1. Five digit number (base 10,000)
For Practice
Practice Time (1)
(1) 70000 – 51473
(2) 80000 – 63224
(3) 90000 – 75265
(4) 30000 – 16267
(5) 50000 – 31136
(6) 40000 – 42326
(7) 40000 – 25487
(8) 80000 – 37468
(9) 70000 – 49249
(10) 60000 – 32390
(11) 50000 – 14312
(12) 40000 – 26543
(13) 90000 – 38564
(14) 80000 – 41375
(15) 70000 – 53336
Sol. (1) 70000 – 51473
51473
(All from 9, and the last from 10)
= (*7–5)/(9–1)(9–4)/(9–7)/(10–3)
=1/8/5/2/7
= 18527
Thus, 70000 – 51473 = 18527
Sol. (2) 80000 – 63224
3224
(All from 9, and the last from 10)
= (*8–6)/(9–3)(9–2)/(9–2)/(10–4)
=1/6/7/7/6
= 16776
Thus, 80000 – 63224 = 16776
2. Six digit number (base 100,000)
For Practice
Practice Time (2)
(1) 500000 – 219431
(2) 600000 – 438762
(3) 800000 – 657543
(4) 900000 – 875234
(5) 300000 – 183345
(6) 500000 – 232456
(7) 600000 – 325676
(8) 700000 – 414787
(9) 800000 – 513878
(10) 900000 – 624569
(11) 800000 – 785670
(12) 300000 – 166771
(13) 400000 – 247542
(14) 500000 – 361343
(15) 600000 – 469564
(16) 700000 – 543575
(17) 900000 – 644446
(18) 90,0000 – 767657
(19) 500000 – 436568
(20) 900000 – 657849
Sol. (1) 500000 – 219431
219431
(All from 9, and the last from 10)
= (*5–2)) (9–1)(9–9)(9–4)/(9–3)/(10–1)
= 2/8/0/5/6/9
= 280569
Thus, 500000 – 219431 = 280569
Sol. (2) 600000 – 438762
438762
(All from 9, and the last from 10)
= (*6–4)/(9–3)(9–8)/(9–7)/(9–6)/(10–2)
= 1/6/1/2/3/8
= 161238
Thus, 600000 – 438762 = 161238
3. Seven digit and Eight digit number (base 10,00,000 and 1,00,00,000)
For Practice
Practice Time (3)
(1) 3000000 – 1294313
(2) 5000000 – 3387624
(3) 7000000 – 5475435
(4) 9000000 – 7552346
(5) 9000000 – 8633457
(6) 5000000 – 3724568
(7) 4000000 – 2856769
(8) 6000000 – 1947870
(9) 7000000 – 1038781
(10) 8000000 – 2145692
(11) 50000000 – 38256703
(12) 70000000 – 46367714
(13) 60000000 – 54475425
(14) 50000000 – 36513436
(15) 70000000 – 46695647
(16) 70000000 – 54735758
(17) 80000000 – 64844469
(18) 90000000 – 76976570
(19) 90000000 – 83065681
(20) 60000000 – 45178492
Sol. (1) 3000000 – 1294313
1294313
(All from 9, and the last from 10)
= (*3–1)/(9–2)(9–9)(9–4)/(9–3)/(9–1)/(10–3)
= 1/7/0/5/6/8/7
= 1705687
Thus, 3000000 – 1294313 = 1705687
Sol. (2) 5000000 – 3387624
3387624
(All from 9, and the last from 10)
= (*5–3)/(9–3)(9–8)/(9–7)/(9–6)/(9–2) /(10–4)
= 1/6/1/2/3/7/6
= 1612376
Thus, 5000000 – 3387624 = 1612376
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