Abacus for Children — Level 3· Lesson 5 of 10
10-விதி: தண்டுகளில் கேரி
10-Rule: Carry Across Rods
~14 min
When ones overflow 9, carry 1 to tens. When tens overflow 9, carry 1 to hundreds. Learn to cascade carries cleanly across all three rods.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Carry from ones to tens when ones rod overflows
- Carry from tens to hundreds when tens rod overflows
- Execute a double carry (ones → tens → hundreds) in one calculation
Let's Learn
What you will learn today
Apply the 10-complement rule to carry from ones to tens, and from tens to hundreds.
Recall: 10-rule from Level 2
When adding N to a rod and the result would overflow (> 9 on ones, or > 9 on tens), the 10-rule says: add 1 to the NEXT rod (to the left), and subtract the 10-complement of N from the current rod.
In Level 2, you used the 10-rule to carry from the ones rod to the tens rod. In Level 3, you also carry from the tens rod to the hundreds rod. The rule is exactly the same — just on a different pair of rods.
Carry from ones to tens
When ones rod overflows (adding N to ones gives > 9):
- +1 to the tens rod (that is +10 total)
- −(10-complement of N) from the ones rod
- Net effect: exactly +N on the whole number
📐 148 + 5 = 153
Ones: 8 + 5 = 13 → overflow! 10-rule: +1 to tens, subtract complement of 5 (=5) from ones: 8−5=3. Tens: 4+1=5. Hundreds: 1 unchanged. Result: 153.
- 1Show 148: hundreds=1, tens=4, ones=8
- 2Add 5 to ones: 8+5=13 → overflow → 10-rule
- 3Ones: subtract complement of 5 (=5): 8−5=3
- 4Tens: add 1: 4+1=5
- 5Hundreds: unchanged = 1
- 6Result: 153
Carry from tens to hundreds
When tens rod overflows (adding N to tens gives result > 9 for that rod):
- +1 to the hundreds rod (that is +100 total)
- −(10-complement of N) from the tens rod
- Net effect: exactly +N×10 on the whole number
📐 162 + 50 = 212
Tens: 6 + 5 = 11 → overflow! 10-rule on tens: +1 to hundreds, subtract complement of 5 (=5) from tens: 6−5=1. Hundreds: 1+1=2. Ones: 2 unchanged. Result: 212.
- 1Show 162: hundreds=1, tens=6, ones=2
- 2Add 50 (that's 5 to the tens rod)
- 3Tens: 6+5=11 → overflow → 10-rule on tens
- 4Tens: subtract complement of 5 (=5): 6−5=1
- 5Hundreds: add 1: 1+1=2
- 6Ones: unchanged = 2
- 7Result: 212
The carry direction is always left
When a rod overflows, the carry always goes one rod to the LEFT (to the higher place value). Ones overflow → carry to tens. Tens overflow → carry to hundreds. The rod receiving the carry gets +1 (which represents +10 or +100 in the actual value).
Adding 1 to the wrong rod
When ones overflows, add 1 to the TENS rod — NOT the hundreds rod. When tens overflows, add 1 to the HUNDREDS rod. The carry goes exactly one rod to the left.
245 + 8 = 253
Add 8 to 245. The ones rod (5) will overflow.
🎯 Goal: Show the number 253
Challenge Round
172 + 60 = 232
Add 60 to 172. The tens rod will overflow.
🎯 Goal: Show the number 232
The 10-rule carry works the same way at any rod boundary. Ones overflow → +1 on tens. Tens overflow → +1 on hundreds. The receiving rod gets exactly 1 bead added. The overflowing rod loses its complement beads.
↪ Next: 10-Rule Borrow in Three-Digit Subtraction.
Key Points
- ✓Carry = ones overflow → +1 to tens; tens overflow → +1 to hundreds
- ✓10-rule: add 1 to next rod, subtract complement from current rod
- ✓148 + 5 = 153: ones 8+5→carry, tens 4+1=5
- ✓162 + 50 = 212: tens 6+5→carry to hundreds, hundreds 1+1=2
- ✓The carry always goes one rod to the LEFT
Glossary
சொல் அகராதி
Carry
கொண்டுசெல்
Overflow
மிகிவிடுதல்
10-complement
10-நிரப்பு
Next rod
அடுத்த தண்டு
Tens overflow
பத்துகள் மிகிவிடுதல்
Practice Activities
Speed Drill · விரைவு பயிற்சி
Carry Drill — Three-Digit Addition
Quizவினாடி வினா
Answer each question to check your understanding.
6 உள்ள ஒன்றுகள் தண்டில் 7 கூட்டுகிறீர்கள். 13 — மிகிவிடுகிறது. என்ன செய்வீர்கள்?
You are adding 7 to the ones rod which shows 6. The result (13) overflows. What do you do?
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