Class 2
Class 3
Class 4
CBSE
UP Board
📘 What's inside:
Concept 1 — What is Borrowing / Regrouping?
```When we subtract using the column method, sometimes the digit on top in a column is smaller than the digit below it. We cannot subtract a bigger number from a smaller one directly. So we borrow 1 ten from the next column on the left, convert it into 10 ones, and add it to the current column. This is called borrowing or regrouping.
3 − 7
Problem
Top digit < bottom digit — cannot subtract directly!
borrow 1
Take 1 ten from next column
Cross out that digit, write one less above it
13 − 7
Now subtract
3 + 10 = 13. Now 13 − 7 = 6 ✓
Borrowing = Regrouping. When we borrow 1 ten from the Tens column, we regroup it as 10 ones. The Tens digit is reduced by 1 (cross it out, write one less). The Ones digit effectively becomes 10 more. Same idea applies when borrowing from Hundreds into Tens.
▶ Column Method — Steps (With Borrowing)
- Write minuend on top, subtrahend below, aligned H/T/O.
- Start at the Ones column. If top ≥ bottom — subtract directly. If top < bottom — borrow: cross out the Tens digit, write one less above it; add 10 to the Ones top digit, then subtract.
- Move to the Tens column. Use the reduced Tens digit (if you borrowed). Again, if top < bottom — borrow from Hundreds.
- Subtract the Hundreds column. Use the reduced Hundreds digit if borrowed.
- Draw the double line and read the difference.
⚠ Most Common Mistakes
```
1. Forgetting to reduce the digit you borrowed from — if you borrow from Tens, the Tens digit must become one less.
2. Borrowing from the wrong column — always borrow from the immediate next column to the left.
3. Subtracting the wrong way — always top minus bottom, never bottom minus top.
Concept 2 — Subtracting 2-Digit Numbers With Borrowing
```With 2-digit numbers, borrowing happens when the Ones top digit is smaller than the Ones bottom digit. We borrow 1 ten from the Tens column.
▶ Solved Example 1 — Borrow from Tens
Find 53 − 27 using the column method.
TO
5¹
̲543
−27
26
O
Ones: 3 < 7 — must borrow.
Borrow 1 ten from Tens: Tens 5 → 4.
Ones becomes 3 + 10 = 13.
13 − 7 = 6. Write 6.
Borrow 1 ten from Tens: Tens 5 → 4.
Ones becomes 3 + 10 = 13.
13 − 7 = 6. Write 6.
T
Tens (now reduced): 4 − 2 = 2. Write 2.
- 1Ones: 3 < 7. Cannot subtract. Borrow 1 ten from the Tens column.
- 2Cross out 5 in the Tens, write 4 above it. Ones becomes 13.
- 3Ones: 13 − 7 = 6. Write 6.
- 4Tens (reduced): 4 − 2 = 2. Write 2.
53 − 27 = 26
▶ Solved Example 2 — Tens Becomes 0 After Borrowing
Find 41 − 18 using the column method.
TO
4¹
̲431
−18
23
O
1 < 8. Borrow: Tens 4 → 3. Ones = 11.
11 − 8 = 3.
11 − 8 = 3.
T
Tens: 3 − 1 = 2. Write 2.
41 − 18 = 23
▶ Solved Example 3
Find 72 − 35 using the column method.
TO
7¹
̲762
−35
37
O
2 < 5. Borrow: Tens 7 → 6. Ones = 12.
12 − 5 = 7.
12 − 5 = 7.
T
Tens: 6 − 3 = 3. Write 3.
72 − 35 = 37
✍ Practice — Concept 2
Q1
Find using the column method: 62 − 35
▼
Answer
O: 2<5 → borrow. Ones=12. 12−5=7. T: 5−3=2. Answer: 27
TO
6¹
̲652
−35
27
Q2
Find using the column method: 84 − 47
▼
Answer
O: 4<7 → borrow. Ones=14. 14−7=7. T: 7−4=3. Answer: 37
TO
8¹
̲874
−47
37
Q3
True or False: In 35 − 18, we borrow from the Tens, so Tens becomes 2, and Ones becomes 15. Then 15−8=7 and 2−1=1. Answer = 17.
▼
Answer
True. Tens 3 → 2 (reduced by 1). Ones 5 + 10 = 15. 15−8=7. 2−1=1. 35−18=17 ✓
Q4
Drill: (a) 51−26 (b) 93−58 (c) 70−43 (d) 66−29
▼
Answer
(a) 25 (b) 35 (c) 27 (d) 37
(a)
TO
5¹
̲541
−26
25
(b)
TO
9¹
̲983
−58
35
(c)
TO
7¹
̲760
−43
27
(d)
TO
6¹
̲656
−29
37
Concept 3 — Subtracting 3-Digit Numbers With Borrowing
```With 3-digit numbers, borrowing can happen in the Ones column (borrow from Tens), the Tens column (borrow from Hundreds), or both. Each borrow is handled the same way — reduce the lender digit by 1, add 10 to the borrower digit.
▶ Solved Example 4 — Borrow in Ones Only
Find 435 − 218 using the column method.
HTO
·3¹
4̲325
−218
217
O
5 < 8. Borrow from Tens: Tens 3 → 2. Ones = 15.
15 − 8 = 7.
15 − 8 = 7.
T
Tens (reduced): 2 − 1 = 1. No further borrow.
H
Hundreds: 4 − 2 = 2.
- 1Ones: 5 < 8. Borrow from Tens. Tens 3 → 2. Ones = 15.
- 2Ones: 15 − 8 = 7.
- 3Tens (now 2): 2 − 1 = 1. No borrow needed.
- 4Hundreds: 4 − 2 = 2.
435 − 218 = 217
▶ Solved Example 5 — Borrow in Tens Only
Find 652 − 381 using the column method.
HTO
6¹·
̲6552
−381
271
O
2 ≥ 1 ✓. 2 − 1 = 1. No borrow.
T
5 < 8. Borrow from Hundreds: H 6 → 5. Tens = 15.
15 − 8 = 7.
15 − 8 = 7.
H
Hundreds (reduced): 5 − 3 = 2.
- 1Ones: 2 ≥ 1. Subtract directly: 2 − 1 = 1.
- 2Tens: 5 < 8. Borrow from Hundreds. H 6 → 5. Tens = 15.
- 3Tens: 15 − 8 = 7.
- 4Hundreds (now 5): 5 − 3 = 2.
652 − 381 = 271
▶ Solved Example 6 — Borrow in Both Ones and Tens
Find 724 − 358 using the column method.
HTO
72¹
̲76̲214
−358
366
O
4 < 8. Borrow from Tens: T 2 → 1. Ones = 14.
14 − 8 = 6.
14 − 8 = 6.
T
Now Tens = 1. 1 < 5. Borrow from H: H 7 → 6. Tens = 11.
11 − 5 = 6.
11 − 5 = 6.
H
Hundreds (now 6): 6 − 3 = 3.
- 1Ones: 4 < 8. Borrow from Tens. T 2 → 1. Ones = 14. 14 − 8 = 6.
- 2Tens (now 1): 1 < 5. Borrow from Hundreds. H 7 → 6. Tens = 11. 11 − 5 = 6.
- 3Hundreds (now 6): 6 − 3 = 3.
724 − 358 = 366
▶ Solved Example 7 — Borrowing Across a Zero
Find 502 − 247 using the column method.
The Ones column needs to borrow, but the Tens digit is 0 — there is nothing to borrow from. So we must first borrow from Hundreds into Tens, then borrow from the now-replenished Tens into Ones.
HTO
50→9¹
̲5492
−247
255
!
Tens is 0 — can't borrow from 0 directly.
Borrow from Hundreds first: H 5 → 4. Tens becomes 10.
Borrow from Hundreds first: H 5 → 4. Tens becomes 10.
O
Now borrow from Tens: T 10 → 9. Ones = 12.
12 − 7 = 5.
12 − 7 = 5.
T
Tens (now 9): 9 − 4 = 5.
H
Hundreds (now 4): 4 − 2 = 2.
- 1Ones: 2 < 7. Tens is 0. Cannot borrow from 0.
- 2Go to Hundreds: H 5 → 4. Tens becomes 10.
- 3Now borrow from Tens: T 10 → 9. Ones = 12. 12 − 7 = 5.
- 4Tens (now 9): 9 − 4 = 5.
- 5Hundreds (now 4): 4 − 2 = 2.
502 − 247 = 255
✍ Practice — Concept 3
Q5
Find: 563 − 228
▼
Answer
O: 3<8 → borrow T. T:6→5. Ones=13. 13−8=5. T: 5−2=3. H: 5−2=3. Answer: 335
HTO
·6¹
5̲653
−228
335
Q6
Find: 831 − 564
▼
Answer
O:1<4→borrow T:3→2. Ones=11. 11−4=7. T:2<6→borrow H:8→7. Tens=12. 12−6=6. H:7−5=2. Answer: 267
HTO
83¹
̲87̲321
−564
267
Q7
Find: 600 − 358
▼
Answer
Both Tens and Ones are 0 — borrow from H into T, then T into O.
H:6→5. T:0→10, then T:10→9. O=10. O:10−8=2. T:9−5=4. H:5−3=2.
600 − 358 = 242
H:6→5. T:0→10, then T:10→9. O=10. O:10−8=2. T:9−5=4. H:5−3=2.
600 − 358 = 242
Q8
Asha says 912 − 476 = 436. Check her answer.
▼
Answer
O:2<6→borrow T:1→0. Ones=12. 12−6=6. T:0<7→borrow H:9→8. Tens=10. 10−7=3. H:8−4=4.
Correct answer = 436. Yes, Asha is correct.
HTO
91¹
̲98̲102
−476
436
Correct answer = 436. Yes, Asha is correct.
Concept 4 — Word Problems
```Word problems with borrowing are solved exactly as before — identify the numbers, set up the column, borrow wherever needed, and write the answer as a sentence.
▶ Solved Example 8 — 2-Digit
A bag had 73 sweets. 46 were eaten. How many sweets are left?
TO
7¹
̲763
−46
27
O
3<6 → borrow. T:7→6. Ones=13. 13−6=7.
T
6−4=2.
There are 27 sweets left.
▶ Solved Example 9 — 3-Digit
A school had 845 students. 378 went on a trip. How many students remained at school?
HTO
84¹
̲87̲435
−378
467
O
5<8 → borrow T:4→3. Ones=15. 15−8=7.
T
3<7 → borrow H:8→7. Tens=13. 13−7=6.
H
7−3=4.
467 students remained at school.
✍ Practice — Concept 4
Q9
Meena had ₹82. She spent ₹47 at the market. How much money does she have left?
▼
Answer
Meena has ₹35 left.
TO
8¹
̲872
−47
35
Q10
A warehouse had 923 boxes. 547 were dispatched. How many boxes remain?
▼
Answer
O:3<7→borrow T:2→1. Ones=13. 13−7=6. T:1<4→borrow H:9→8. Tens=11. 11−4=7. H:8−5=3. 376 boxes remain.
HTO
92¹
̲98̲213
−547
376
Q11
A football stadium has 754 seats. 468 people are seated. How many seats are empty?
▼
Answer
O:4<8→borrow T:5→4. Ones=14. 14−8=6. T:4<6→borrow H:7→6. Tens=14. 14−6=8. H:6−4=2. 286 seats are empty.
HTO
75¹
̲76̲544
−468
286
★ Key Points to Remember
- When the top digit < bottom digit in a column, we must borrow from the next column to the left.
- Borrowing = Regrouping: 1 ten = 10 ones, 1 hundred = 10 tens.
- When you borrow, cross out the lender digit and write one less above it. The borrower digit gains +10.
- Always use the reduced (crossed-out) digit when subtracting in the lender's column.
- If the column you want to borrow from is 0, go one column further left, borrow there first, then borrow again.
- Always subtract right to left: Ones → Tens → Hundreds.
Exam Style — Class 2, 3 & 4
5 Questions on Subtraction With Borrowing
Q1
In 64 − 38, which column needs borrowing and why? Solve it completely.
▼
Answer
Ones column: top 4 < bottom 8 → borrowing needed here.
Borrow from Tens: T 6 → 5. Ones = 14.
O: 14−8=6. T: 5−3=2. 64 − 38 = 26
Borrow from Tens: T 6 → 5. Ones = 14.
TO
6¹
̲654
−38
26
Q2
Solve showing all borrowing clearly: 732 − 458
▼
Answer
732 − 458 = 274
HTO
73¹
̲76̲322
−458
274
O
2<8 → borrow T:3→2. Ones=12. 12−8=4.
T
2<5 → borrow H:7→6. Tens=12. 12−5=7.
H
6−4=2.
Q3
A student solves 614 − 257 = 367. Find the correct answer. What mistake did the student make?
▼
Answer
Correct answer = 357.
The student wrote 367 — the Tens digit is wrong. They likely forgot to reduce the Tens digit after borrowing (used 1 instead of 0 in the Tens column). 10−5=5, not 6. Correct: 614 − 257 = 357.
HTO
61¹
̲65̲104
−257
357
The student wrote 367 — the Tens digit is wrong. They likely forgot to reduce the Tens digit after borrowing (used 1 instead of 0 in the Tens column). 10−5=5, not 6. Correct: 614 − 257 = 357.
Q4
A city had 900 trees. A storm uprooted 364. How many trees are still standing? Show all borrowing.
▼
Answer
Subtraction: 900 − 364. Both Ones and Tens of minuend are 0.
O:0<4. T=0, so borrow from H: H:9→8, T becomes 10. Then borrow T for O: T:10→9, O=10. 10−4=6. T:9−6=3. H:8−3=5.
536 trees are still standing.
HTO
99→8¹
̲9890
−364
536
536 trees are still standing.
Q5
Find the missing digit: 7_3 − 248 = 5_5. What are the two missing digits?
▼
Answer
Let the missing Tens digit of minuend = a, difference Tens digit = b.
O: 3<8 → borrow. a → (a−1). Ones = 13. 13−8=5 ✓ (matches answer O=5).
T: (a−1) − 4 = b. H: 7−2=5 ✓ (matches answer H=5). No borrow from H, so (a−1)≥4 → a≥5.
Try a=6: (6−1)−4 = 5−4 = 1. So b=1.
Missing digits: minuend Tens = 6, difference Tens = 1. Full problem: 763 − 248 = 515.
O: 3<8 → borrow. a → (a−1). Ones = 13. 13−8=5 ✓ (matches answer O=5).
T: (a−1) − 4 = b. H: 7−2=5 ✓ (matches answer H=5). No borrow from H, so (a−1)≥4 → a≥5.
Try a=6: (6−1)−4 = 5−4 = 1. So b=1.
HTO
·6¹
7̲653
−248
515
📄 Free Worksheet
Practise 2-digit and 3-digit subtraction with borrowing/regrouping, including zero-in-minuend problems, word problems and error-checking. No login required.
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