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Mathematics › 🎯 Grade 4 › Borrowing Next Door: Subtraction with Regrouping
🎯 Grade 4 · Lesson 7 of 9

Borrowing Next Door: Subtraction with Regrouping

When a column doesn't have enough, you borrow a bundle of ten from your neighbour.

Grade 4Elementary
Borrowing Next Door: Subtraction with Regrouping — illustration
💡
The big idea: Subtraction with regrouping (borrowing) is just the place-value system run in reverse: when one column can't subtract, you trade one unit of the next-higher place for ten of the current place. The tricky case — borrowing across zeros — requires a chain of trades, but every trade follows the same single rule.
🎯 By the end, you'll be able to
  • Perform multi-digit subtraction by regrouping (borrowing) across columns
  • Explain each regroup step using place-value language (tens, hundreds, thousands)
  • Regroup across zeros using a chain of trades
  • Check a subtraction answer using addition
📎 You should already know
  • Place value (ones, tens, hundreds)
  • Basic subtraction facts 0–18

The borrowing rule — one trade at a time

Imagine the digits in each column as a stack of coins. When the top stack (minuend digit) is too small to give away the bottom amount (subtrahend digit), you reach over to the next column, take one bundle (1 ten = 10 ones, 1 hundred = 10 tens, etc.) and break it open into ten individual coins of the current size.

Example: 53 − 28. In the ones column, 3 − 8 is impossible, so we borrow 1 ten from the tens column. That ten becomes 10 extra ones, making the ones digit 13. We subtract: 13 − 8 = 5. The tens column shrinks by 1 (5 becomes 4), then 4 − 2 = 2. Answer: 25.

⚠️ Borrowing across zeros — the chain trade

300 − 148 looks scary because there are nothing in the tens or ones columns to borrow from. The fix: work left until you find a non-zero digit. Borrow 1 hundred → it becomes 10 tens. Then borrow 1 of those tens → it becomes 10 ones. Now the ones column has 10, the tens column has 9, and hundreds has 2.

Chain: 300 → (borrow 1 hundred) → 2 hundreds, 10 tens → (borrow 1 ten) → 2 hundreds, 9 tens, 10 ones. Now subtract column by column.

🎮 Regrouping Step-by-Step LIVE
Set the minuend and subtrahend with the sliders, then press 'Next Step' to watch each trade happen one column at a time. Digits that are being traded show in amber; digits that grow show in green.
🔑 Always check with addition

After any subtraction, verify: answer + subtrahend = minuend. If 300 − 148 = 152, then 152 + 148 should equal 300. Addition and subtraction are inverse operations — this check costs 30 seconds and catches carry errors instantly.

📝 Worked example: Calculate 403 − 257.
  1. Ones: 3 − 7 is impossible. Need to borrow, but the tens digit is 0.
  2. Chain trade: borrow 1 hundred → 3 hundreds becomes 2 hundreds, 10 tens.
  3. Then borrow 1 ten → 10 tens becomes 9 tens, 10 ones.
  4. Now ones: 10 + 3 = 13 ones. 13 − 7 = 6.
  5. Tens: 9 − 5 = 4.
  6. Hundreds: 2 − 2 = 0.
  7. Answer: 146. Check: 146 + 257 = 403. ✓
✓ 403 − 257 = <strong>146</strong>.
📝 Worked example: Calculate 6,000 − 3,456.
  1. All lower columns are zero — chain trade from thousands.
  2. 6 thousands → 5 thousands, 10 hundreds → 5 thousands, 9 hundreds, 10 tens → 5 thousands, 9 hundreds, 9 tens, 10 ones.
  3. Ones: 10 − 6 = 4.
  4. Tens: 9 − 5 = 4.
  5. Hundreds: 9 − 4 = 5.
  6. Thousands: 5 − 3 = 2.
  7. Answer: 2,544. Check: 2,544 + 3,456 = 6,000. ✓
✓ 6,000 − 3,456 = <strong>2,544</strong>.

Check your understanding

1. What is 72 − 38?
Ones: 2 − 8 → borrow 1 ten. 12 − 8 = 4. Tens: 6 − 3 = 3. Answer: 34.
2. When subtracting 500 − 263, how many trades (regroups) are needed before you can start subtracting?
Two trades: borrow 1 hundred → get 10 tens, then borrow 1 ten → get 10 ones. Chain of 2.
3. A student calculates 805 − 347 and gets 568. How can they quickly check this?
Subtraction check: answer + subtrahend = minuend. 568 + 347 = 915 ≠ 805, so the answer is wrong. The correct answer is 458.
4. Calculate 1,003 − 456.
Chain trade: 1,003 → 0 thousands, 10 hundreds → 0 thousands, 9 hundreds, 10 tens → 0 thousands, 9 hundreds, 9 tens, 13 ones. 13 − 6 = 7, 9 − 5 = 4, 9 − 4 = 5, 0 − 0 = 0. Answer: 547.
5. In 346 − 178, which digit borrows in the tens column?
After ones borrows (6→16, so tens shrinks to 3), we need 3 − 7 in tens column — impossible, so tens borrows from hundreds. Hundreds shrinks from 3 to 2, tens becomes 13. 13 − 7 = 6.
✅ Key takeaways
  • Regrouping (borrowing) trades one unit of a higher place for ten units of the current place.
  • When a column has a zero, chain-trade leftward until you find a non-zero digit.
  • Always check subtraction by adding the answer and the subtrahend — the result should equal the minuend.
  • The number of ones/tens/hundreds does not change the total value — only how it's grouped.
  • Carry out one column at a time, right to left, and mark crossed-out digits clearly.