Vedic Maths for Kids· Lesson 2 of 10
9-லிருந்து அனைத்தும், 10-லிருந்து கடைசி
All From 9, Last From 10
~10 min
The fastest way to subtract from 1000, 10000, or any power of ten. Learn the Nikhilam sutra that turns hard subtraction into a 3-second exercise.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Apply 'All from 9, last from 10' to subtract from 1000
- Apply the same rule to subtract from 100 and 10000
- Explain why the rule works using place value
Let's Learn
What you will learn today
Subtract any number from 1000, 10000, or any power of ten using the Nikhilam sutra in seconds.
What is a complement of 10?
Quick: what do you add to 4 to get 10? To 7? To 3? (6, 3, 7.) If you can answer these instantly, the core of today's lesson is already in your head.
Today's sutra: 'Nikhilam Navatascaramam Dasatah' — which means 'All from 9 and the last from 10.' It sounds like poetry, but it is a precise instruction: subtract each digit from 9, except the last digit, which you subtract from 10. That's it. You can now do 1000 − 647 in your head.
The rule, step by step
To subtract a number from a power of 10 (100, 1000, 10000...):
- Take each digit of the number you are subtracting
- Subtract each digit from 9 — EXCEPT the last digit
- Subtract the last digit from 10
- The result is your answer
📐 Example: 1000 − 347
We subtract 347 from 1000. Digits: 3, 4, 7.
- 19 − 3 = 6
- 29 − 4 = 5
- 310 − 7 = 3 (last digit: subtract from 10, not 9)
- 4Answer: 653. Check: 653 + 347 = 1000 ✓
📐 Example: 10000 − 4382
Four-digit number, subtract from 10000:
- 19 − 4 = 5
- 29 − 3 = 6
- 39 − 8 = 1
- 410 − 2 = 8 (last digit from 10)
- 5Answer: 5618. Check: 5618 + 4382 = 10000 ✓
Why does this work?
This is not a trick — it is the definition of a 10s-complement. When you subtract N from 1000, you are finding the number that adds to N to make 1000. That number is exactly what 'all from 9, last from 10' computes: it gives you each digit of the 10s-complement position by position.
What about trailing zeros?
1000 − 400: digit is just 4, but we have three decimal positions. Treat 400 as 400: digits 4, 0, 0. Apply rule: 9−4=5, 9−0=9, 10−0=10 — but 10 makes the tens digit... Actually: for trailing zeros, keep them as zeros and the rule still works: 600. Better: recognise 1000−400 = 600 directly. The sutra works best for non-zero last digits.
Forgetting which digit to subtract from 10
Every digit is subtracted from 9 — except the LAST (rightmost) digit, which is subtracted from 10. Students often subtract all digits from 9. Check: if the last digit is 7, it becomes 10−7=3 (not 9−7=2).
Challenge Round
Challenge: 10000 − 6391
Apply the rule to this 4-digit subtraction. What are the four steps? What is the answer?
Nikhilam sutra: 'All from 9, last from 10' subtracts any number from a power of 10 in one pass. Each digit gets subtracted from 9, except the last which is subtracted from 10.
↪ Next: Multiplying by 11 — the elegant gap trick.
Key Points
- ✓Sutra: 'All from 9, last from 10' (Nikhilam)
- ✓Subtract each digit from 9, except the last digit which is subtracted from 10
- ✓Works for any subtraction from 100, 1000, 10000, etc.
- ✓This computes the 10s-complement digit by digit
Glossary
சொல் அகராதி
Nikhilam
நிகிலம்
Power of ten
பத்தின் அடுக்கு
Digit
இலக்கம்
10s-complement
10 நிரப்பு
Practice Activities
Speed Drill · விரைவு பயிற்சி
Nikhilam Speed Drill
Quizவினாடி வினா
Answer each question to check your understanding.
Using 'All from 9, last from 10', what is 1000 − 273?
Match the Termsபொருத்துக
Click a term on the left, then click its matching definition on the right.
Click a term, then click its matching definition.
Terms
Definitions
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check or press Enter.