10-விதி: கடன் வாங்கி கழித்தல்
10-Rule: Subtracting with Borrow
When ones can't give enough beads, borrow 10 from the tens rod and add the complement to ones. Borrowing across rods, understood clearly.
Let's Learn
What you will learn today
Subtract numbers from a two-digit value by borrowing from the tens rod when ones can't give enough.
Recall: 10-rule for addition
Last lesson: when ones overflows → add 1 to tens, subtract 10-complement from ones. Now: what happens when the ones rod doesn't have enough to subtract from?
Your abacus shows 12 (tens: 1, ones: 2). You need to subtract 5. The ones rod only shows 2 — not enough! You need to borrow from the tens rod. This is the 10-complement rule for subtraction.
கழிக்கும்போது, ஒன்றுகள் தண்டு போதுமான இல்லாவிட்டால், பத்துகளிடம் கடன் வாங்குகிறோம்.
The 10-complement rule for subtraction (borrow)
When the ones rod can't give enough to subtract N:
- Remove 1 bead from the TENS rod (−10 from total value)
- Add the 10-complement of N to the ONES rod
- Net result: −10 + (10-complement of N) = −N
📐 Worked example: 12 − 5 = 7
Tens: 1, Ones: 2. Subtract 5.
- 1Can ones give 5? Ones only shows 2 — cannot subtract 5 directly.
- 2Borrow: remove 1 from tens (tens: 0), this gives us −10 to work with
- 310-complement of 5 is 5. Add 5 to ones: 2 + 5 = 7
- 4Tens: 0. Ones: 7. Read as: 7. And 12 − 5 = 7 ✓
📐 Worked example: 14 − 7 = 7
Tens: 1, Ones: 4. Subtract 7.
- 1Can ones give 7? Ones shows 4 — not enough.
- 2Borrow: remove 1 from tens (tens: 0)
- 310-complement of 7 is 3. Add 3 to ones: 4 + 3 = 7
- 4Tens: 0. Ones: 7. Answer: 7 ✓
The logic of borrowing
When you remove 1 from tens (−10) and add the 10-complement of N, you net exactly −N. Verify: −10 + (10-complement of 5) = −10 + 5 = −5. Yes! The borrow undoes itself except for the N part.
Forgetting to add the complement to ones
Students often remove 1 from tens but forget to add the complement to ones. This gives an answer that is too small by the complement amount. Both moves are always required.
- →Wrong: 12−5 → remove 1 from tens only → shows 02 = 2 (wrong!)
- →Right: 12−5 → remove 1 from tens, add complement(5)=5 to ones: 2+5=7 → shows 07 = 7 ✓
Try it: 13 − 6
Set up: tens=1, ones=3. Subtract 6 using the borrow rule. What should your abacus show? (Answer: 7)
🎯 Goal: Show the number 13
10-rule subtraction (borrow): when ones can't give enough, remove 1 from tens (−10), add 10-complement of N to ones. Net = −N.
↪ Next: Both Rules Together — when one problem needs both the 5-rule and 10-rule.
Key Points
முக்கிய குறிப்புகள்
- ✓10-rule subtraction: when ones can't give enough, borrow from tens
- ✓Remove 1 from tens (−10), add 10-complement of N to ones
- ✓Net result: −10 + complement = −N
- ✓Always do BOTH moves: remove from tens AND add to ones
Glossary
சொல் அகராதி
Borrow
கடன் வாங்கு
10-complement
10-நிரப்பு
Insufficient
போதுமான இல்லை
Add back
திரும்ப கூட்டு
Practice Activities
Speed Drill · விரைவு பயிற்சி
10-Rule Subtraction Drill
10-விதி கழித்தல் பயிற்சி
Quizவினாடி வினா
Answer each question to check your understanding.
Your abacus shows 11. You subtract 4. Why can't you subtract directly from ones?