Vedic maths › All from 9, the last from 10
Subtracting from 100, 1000 or 10,000: all from 9 and the last from 10
Taking a number away from 1000 usually means borrowing across a row of zeros. The sutra Nikhilaṃ Navataścaramaṃ Daśataḥ, “all from 9 and the last from 10”, skips the borrowing: take every digit from 9, and the last one from 10.
The answer is the number’s complement: how far it is from the round number. You need it for change from a ₹1000 note, and it is the first step of the Vedic ways to multiply near a base.
The method
- Give the number as many digits as the round number has zeros: to take 57 from 1000, think of it as 057.
- Take each digit from 9, except the last.
- Take the last digit from 10.
- If the number ends in zeros, they stay zeros, and the last digit that isn’t 0 is the one you take from 10.
Worked examples
1000 − 357
- Take each digit from 9, except the last.9 − 3 = 6, 9 − 5 = 4
- Take the last digit from 10.10 − 7 = 3
1000 − 357 = 643
10,000 − 4086
- Take each digit from 9, except the last.9 − 4 = 5, 9 − 0 = 9, 9 − 8 = 1
- Take the last digit from 10.10 − 6 = 4
10,000 − 4086 = 5914
1000 − 270
- Take each digit from 9, except the last.9 − 2 = 7
- Take the last digit that isn't 0 from 10.10 − 7 = 3
- The zeros at the end stay zeros.0
1000 − 270 = 730
Why it works
Taking a number from 1000 is the same as taking it from 999 and adding 1. Taking digits from 9 never needs borrowing, because no digit is bigger than 9: 999 − 357 = 642. Adding the 1 back lands on the last digit, which is the same as taking that digit from 10: 643.
Watch out
- Short numbers need their zeros in front: 10,000 − 38 is 10,000 − 0038, so 9, 9, 6 and 2: 9962.
- The round number must be a 1 and zeros. For 5000 − 357, take 357 from 1000 (643) and add the other 4000: 4643.
Try these
Work each one out, then tap it to see the answer.
1000 − 463
9 − 4, 9 − 6, 10 − 3: 537
100 − 28
9 − 2, 10 − 8: 72
10,000 − 2718
9 − 2, 9 − 7, 9 − 1, 10 − 8: 7282
1000 − 509
9 − 5, 9 − 0, 10 − 9: 491
1000 − 680
9 − 6, 10 − 8, then 0: 320
Practise it in the game: Speed Tricks, 1.3 Take from 1,000. Free, with no sign-up.
Source: This method is from Bharati Krishna Tirtha’s Vedic Mathematics (1965). The explanation, examples and questions here are our own.
More Vedic maths
- Squares ending in 5: 75²: 7 × 8 = 56, then 25: 5625.
- Multiplying near 100: 97 × 96: 97 − 4 = 93, 3 × 4 = 12: 9312.
- Squaring near 100: 96²: 96 − 4 = 92, 4² = 16: 9216.
- Vertically and crosswise: 23 × 41: 2 × 4 | 2 × 1 + 3 × 4 | 3 × 1: 943.
- Multiplying by 9, 99, 999: 437 × 999: 436, then 999 − 436 = 563: 436563.
- Last digits adding to 10: 63 × 67: 6 × 7 = 42, 3 × 7 = 21: 4221.
- Multiplying by 11: 253 × 11: 2 | 2 + 5 | 5 + 3 | 3: 2783.
- Checking with digit sums: 437 × 26 = 11362? 5 × 8 → 4, and 11362 → 4: it passes.
- Dividing by 9: 2312 ÷ 9: 2, 2 + 3, 5 + 1: 256, remainder 6 + 2 = 8.
- Squaring with the duplex: 43²: 4² | 2 × 4 × 3 | 3² = 16 | 24 | 9: 1849.
Where Vedic maths comes from, all 16 sutras, and our sources: Vedic maths, explained.