இலக்கத்தொகை சரிபார்ப்பு
The Digit Sum Check
Before checking an answer with a calculator, check it with digit sums. This ancient technique instantly tells you if a calculation is correct — or has a hidden error.
Let's Learn
What you will learn today
Verify any arithmetic answer using digit sums — a fast self-checking tool that exposes hidden errors.
Add all the digits
Try: add all digits of 347. (3+4+7=14. Then 1+4=5.) Add all digits of 289. (2+8+9=19. Then 1+9=10. Then 1+0=1.) The final single digit is called the 'digital root.'
How do you know if your calculation is correct without a calculator? The digit sum check. It is fast, reliable, and teaches you something deep about how numbers work. Every time you solve a problem, spend 5 seconds checking it with digit sums.
இலக்கத்தொகை — உங்கள் கணக்கின் சரிபார்ப்பு கண்ணாடி.
What is a digital root?
The digital root of a number is found by adding all its digits together, repeatedly, until you reach a single digit. 347: 3+4+7=14 → 1+4=5. Digital root = 5. This is also called 'casting out nines.'
- Add all digits of the number
- If the result has more than one digit, add those digits too
- Repeat until you have one digit
- Special rule: if you ever reach 9, the digital root is 9 (not 0)
Using digital root to check addition
If A + B = C, then digital_root(A) + digital_root(B) should equal digital_root(C) (accounting for if the sum itself needs reducing).
- Example: 234 + 567 = 801. Checking:
- Digital root of 234: 2+3+4=9
- Digital root of 567: 5+6+7=18 → 1+8=9
- Digital root of 801: 8+0+1=9
- Check: 9+9=18 → 1+8=9 = digital root of 801 ✓
Using digital root to check multiplication
If A × B = C, then digital_root(A) × digital_root(B) = digital_root(C).
- Example: 24 × 11 = 264. Checking:
- Digital root of 24: 2+4=6
- Digital root of 11: 1+1=2
- 6 × 2 = 12 → 1+2=3
- Digital root of 264: 2+6+4=12 → 1+2=3 ✓
What the check tells you
A mismatch means your answer definitely has an error. A match means your answer is likely correct — but not guaranteed (because different wrong answers can have the same digital root). Think of it as a quick sanity check, not absolute proof.
பொருந்தவில்லை → நிச்சயமாக தவறு. பொருந்துகிறது → சாத்தியமான சரி.
Digital root of 9 stays as 9
If your digit sum reaches exactly 9, the digital root is 9, not 0. This is a common mistake. 9, 18, 27, 36... all have digital root 9, not 0.
Check this: 35² = 1225
Compute digital_root(35) and digital_root(1225). Do the squares match?
Digital root check: compute digital root of each input and the result. For addition: roots should sum to root of answer. For multiplication: roots should multiply to root of answer. Mismatch = definite error.
↪ Next: Doubling and Halving — the flexibility technique for any multiplication.
Key Points
முக்கிய குறிப்புகள்
- ✓Digital root: add digits repeatedly until single digit (9 stays as 9)
- ✓Addition check: dr(A) + dr(B) = dr(C)
- ✓Multiplication check: dr(A) × dr(B) = dr(C)
- ✓Mismatch = error. Match = likely correct (not guaranteed)
Glossary
சொல் அகராதி
Digit sum
இலக்கத்தொகை
Digital root
இலக்க மூலம்
Self-check
தன் சரிபார்ப்பு
Error detection
தவறு கண்டுபிடிப்பு
Practice Activities
Quizவினாடி வினா
Answer each question to check your understanding.
What is the digital root of 999?
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check.