Abacus for Children — Level 3· Lesson 6 of 10
10-விதி: தண்டுகளில் கடன்
10-Rule: Borrow Across Rods
~14 min
When a rod can't give enough beads to subtract, borrow from the rod to its left. Master borrowing across tens and hundreds rods in three-digit subtraction.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Borrow from tens to ones when ones rod has insufficient beads
- Borrow from hundreds to tens when tens rod has insufficient beads
- Execute a double borrow in one calculation
Let's Learn
What you will learn today
Apply the 10-complement rule to borrow from tens to ones, and from hundreds to tens.
Recall: 10-rule borrowing from Level 2
When ones rod can't subtract directly (current value < digit being subtracted): −1 from tens, +complement of N to ones. The rod you borrow from shrinks by 1. The rod you add to gains the complement.
In Level 3 you also borrow from the hundreds rod into the tens rod using the exact same rule. Tens can't subtract → borrow from hundreds. The rule never changes — only the rod pair changes.
📐 213 − 5 = 208
Ones: 3 − 5 → can't! Borrow from tens: −1 from tens (1→0), +complement of 5 (=5) to ones: 3+5=8. Hundreds: 2 unchanged. Result: 208.
- 1Show 213: hundreds=2, tens=1, ones=3
- 2Subtract 5 from ones: 3<5, can't! Borrow.
- 3Tens: −1 (1→0)
- 4Ones: +complement of 5 (=5): 3+5=8
- 5Hundreds: unchanged = 2
- 6Result: 208
📐 230 − 50 = 180
Tens: 3 − 5 → can't! Borrow from hundreds: −1 from hundreds (2→1), +complement of 5 (=5) to tens: 3+5=8. Ones: 0 unchanged. Result: 180.
- 1Show 230: hundreds=2, tens=3, ones=0
- 2Subtract 5 from tens (subtract 50): 3<5, can't! Borrow.
- 3Hundreds: −1 (2→1)
- 4Tens: +complement of 5 (=5): 3+5=8
- 5Ones: unchanged = 0
- 6Result: 180
The borrow direction is always right
Borrowing always goes one rod to the RIGHT (from higher to lower place value). Ones can't subtract → borrow from tens (one left). Tens can't subtract → borrow from hundreds (one left of tens). The borrowed rod loses 1.
Forgetting which rod gets the complement
The complement always goes to the rod that NEEDED the borrow — not the rod that gave it. In 213−5: ones needed the borrow, so ones gets the complement (+5). Tens gave the borrow, so tens loses 1.
352 − 6 = 346
Subtract 6 from 352. The ones rod (2) cannot subtract 6 directly.
🎯 Goal: Show the number 346
Challenge Round
341 − 70 = 271
Subtract 70 from 341. The tens rod (4) cannot subtract 7 directly.
🎯 Goal: Show the number 271
Borrowing in three-digit problems uses the same 10-rule from Level 2. Ones can't subtract → borrow from tens. Tens can't subtract → borrow from hundreds. Borrowed rod: −1. Borrowing rod: +complement.
↪ Next: Cascading Carries and Borrows — when the same problem needs both.
Key Points
- ✓Borrow = ones can't subtract → −1 from tens; tens can't subtract → −1 from hundreds
- ✓10-rule: −1 from next rod, +10-complement to current rod
- ✓213 − 5 = 208: ones 3<5 → borrow from tens, tens 1→0, ones +5 → 8
- ✓230 − 50 = 180: tens 3<5 → borrow from hundreds, hundreds 2→1, tens +5 → 8
- ✓Borrow always goes from left to right (higher to lower rod)
Glossary
சொல் அகராதி
Borrow
கடன் கொள்
Borrow from hundreds
நூறுகளிலிருந்து கடன்
Complement
நிரப்பு
Can't subtract
கழிக்க முடியாது
Decrease
குறை
Practice Activities
Speed Drill · விரைவு பயிற்சி
Borrow Drill — Three-Digit Subtraction
Quizவினாடி வினா
Answer each question to check your understanding.
413 − 8 = ? (Ones: 3 < 8, borrow from tens)
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