10-விதி: கடந்து கூட்டல்
10-Rule: Adding with Carry
When the ones rod is full and you still need to add, carry one bead to the tens rod and remove the complement from ones. Numbers cross rods for the first time.
Let's Learn
What you will learn today
Add numbers that make the ones rod overflow by carrying 1 bead to the tens rod.
Recall: when do rods cross?
You learned in Level 1 that the abacus has a tens rod and a ones rod. Each rod can show 0–9. What happens when the ones rod shows 9 and you need to add 1 more? That's what this lesson answers.
Your abacus shows 7 on the ones rod. You need to add 5. The answer is 12 — but the ones rod can only hold 9! Numbers bigger than 9 need two rods. This is where the 10-complement rule for addition comes in: carry a bead to the tens rod.
10-க்கு மேல் போகும்போது, பத்துகள் தண்டுக்கு கொண்டு செல்கிறோம்.
When does the 10-rule for addition apply?
Use the 10-complement addition rule when:
- You need to add N to the ones rod
- The ones rod CANNOT hold (current value + N) — the result would exceed 9
- Solution: carry to the tens rod
The 10-complement rule for addition (carry)
When adding N would overflow the ones rod:
- Add 1 bead to the TENS rod (+10 to total value)
- Subtract the 10-complement of N from the ONES rod
- Net result: +10 − (10-complement of N) = +N
📐 Worked example: 7 + 5 = 12
Tens shows 0, ones shows 7. Add 5.
- 1Can ones rod hold 7+5=12? No — maximum is 9.
- 210-complement of 5 is 5. Add 1 to tens (+10). Subtract 5 from ones (7−5=2).
- 3Tens: 1. Ones: 2. Read as: 12. And 7 + 5 = 12 ✓
📐 Worked example: 6 + 8 = 14
Tens shows 0, ones shows 6. Add 8.
- 1Can ones hold 6+8=14? No.
- 210-complement of 8 is 2. Add 1 to tens (+10). Subtract 2 from ones (6−2=4).
- 3Tens: 1. Ones: 4. Read as: 14. And 6 + 8 = 14 ✓
How to check your work
After every 10-rule addition, check: (tens digit × 10) + ones digit = your expected answer. So 1 ten + 2 ones = 12. Always verify before moving on.
Forgetting to subtract from ones
The most common mistake: students add 1 to the tens rod but forget to subtract the complement from the ones rod. Both moves are essential — the add to tens AND the subtract from ones. One without the other gives the wrong answer.
- →Wrong: 7+5 → add 1 to tens only → shows 17 (too much!)
- →Right: 7+5 → add 1 to tens, subtract 5 from ones → 7−5=2 ones, 1 ten = 12 ✓
Try it: show 5+7
Set ones rod to 5, tens to 0. Now add 7 using the 10-rule. What should the abacus show? (Answer: 12)
🎯 Goal: Show the number 5
10-rule addition (carry): when ones overflows, add 1 to tens (+10), subtract the 10-complement of N from ones. Net = +N.
↪ Next: 10-Rule Subtracting — borrowing from the tens rod when ones can't give enough.
Key Points
முக்கிய குறிப்புகள்
- ✓10-rule addition: when ones rod can't hold the sum, carry to tens rod
- ✓Add 1 to tens (+10), subtract 10-complement of N from ones
- ✓Net result: +10 − complement = +N
- ✓Always do BOTH moves: add to tens AND subtract from ones
Glossary
சொல் அகராதி
Carry
கொண்டு செல்
Tens rod
பத்துகள் தண்டு
10-complement
10-நிரப்பு
Overflow
மிகுதி
Practice Activities
Speed Drill · விரைவு பயிற்சி
10-Rule Addition Drill
10-விதி கூட்டல் பயிற்சி
Quizவினாடி வினா
Answer each question to check your understanding.
You have 8 on the ones rod. You add 7. What is the 10-complement of 7?