Class 2
Class 3
CBSE
UP Board
📘 What's inside:
Concept 1 — What is Carrying?
```When we add digits in a column and the result is 10 or more, we cannot write a two-digit number in a single column. So we write the units digit below the line and carry the tens digit forward to the next column on the left. This is called carrying (also called regrouping).
7 + 5
Column sum
= 12 (10 or more)
carry 1
Tens digit → next column
Write 1 above next column
2
Units digit → below line
Write 2 in answer row
The carry is always 1. Because we are adding single digits (0–9) to single digits, the maximum any column can reach is 9 + 9 = 18, so the tens digit carried is always just 1. It can never be 2 or more at this level.
▶ Column Method — Steps (With Carry)
- Set up the column exactly as before: larger number on top, align H under H, T under T, O under O.
- Add the Ones column. If the sum is ≤ 9 — write it below the line normally. If the sum is ≥ 10 — write the units digit below the line and write a small 1 above the Tens column.
- Add the Tens column — including the carried 1 if present. Again, if ≥ 10, write units digit below and carry 1 to Hundreds.
- Add the Hundreds column — including any carry. Write the full result below the line.
- Draw the double line. Read the answer.
⚠ Most Common Mistakes
```
1. Forgetting to add the carried 1 to the next column.
2. Writing the full two-digit sum (e.g. writing "12" in the Ones column instead of writing "2" and carrying "1").
3. Misplacing the carry — it must go above the next column to the left, not the current one.
Concept 2 — Adding 2-Digit Numbers With Carry
```With 2-digit numbers, the carry happens when the Ones column adds up to 10 or more. The carried 1 is added into the Tens column.
▶ Solved Example 1 — Carry from Ones
Find 27 + 35 using the column method.
TO
1·
27
+35
62
O
Ones: 7 + 5 = 12
12 ≥ 10 → write 2, carry 1 to Tens.
12 ≥ 10 → write 2, carry 1 to Tens.
C
Write the 1 small above the Tens column.
T
Tens: 2 + 3 + 1(carry) = 6
Write 6.
Write 6.
- 1Ones: 7 + 5 = 12. Write 2 below, carry 1 above Tens.
- 2Tens: 2 + 3 + 1 = 6. Write 6.
27 + 35 = 62
▶ Solved Example 2 — Carry Makes a 3-Digit Answer
Find 78 + 54 using the column method.
HTO
·1·
78
+54
132
O
Ones: 8 + 4 = 12 → write 2, carry 1.
T
Tens: 7 + 5 + 1 = 13 → write 3, carry 1 to Hundreds.
H
Hundreds: 0 + 0 + 1 = 1 → write 1.
- 1Ones: 8 + 4 = 12. Write 2, carry 1 above Tens.
- 2Tens: 7 + 5 + 1 = 13. Write 3, carry 1 above Hundreds.
- 3Hundreds: 0 + 0 + 1 = 1. Write 1. (The two 2-digit numbers together give a 3-digit answer.)
78 + 54 = 132
▶ Solved Example 3 — Carry in Ones Only
Find 46 + 37 using the column method.
TO
1·
46
+37
83
O
Ones: 6 + 7 = 13 → write 3, carry 1.
T
Tens: 4 + 3 + 1 = 8 → write 8. No further carry.
46 + 37 = 83
✍ Practice — Concept 2
Q1
Find using the column method: 38 + 45
▼
Answer
O: 8+5=13 → write 3, carry 1. T: 3+4+1=8. Answer: 83
TO
1·
38
+45
83
Q2
Find using the column method: 67 + 58
▼
Answer
O: 7+8=15 → write 5, carry 1. T: 6+5+1=12 → write 2, carry 1. H: 0+0+1=1. Answer: 125
HTO
·1·
67
+58
125
Q3
Find using the column method: 55 + 49
▼
Answer
O: 5+9=14 → write 4, carry 1. T: 5+4+1=10 → write 0, carry 1. H: 0+0+1=1. Answer: 104
HTO
·1·
55
+49
104
Q4
True or False: In 64 + 29, the Ones column gives 4+9=13, so we write 13 below the line. Correct it if false.
▼
Answer
False. We never write two digits in one column.
4 + 9 = 13 → write only 3 below the line, and carry 1 to the Tens column.
Correct working: T: 6+2+1 = 9. Answer: 93.
4 + 9 = 13 → write only 3 below the line, and carry 1 to the Tens column.
Correct working: T: 6+2+1 = 9. Answer: 93.
Q5
Solve the drill: (a) 29 + 13 (b) 45 + 36 (c) 88 + 17 (d) 76 + 48
▼
Answer
(a) 42 (b) 81 (c) 105 (d) 124
(a)
TO
1·
29
+13
42
(b)
TO
1·
45
+36
81
(c)
HTO
·1·
88
+17
105
(d)
HTO
·1·
76
+48
124
Concept 3 — Adding 3-Digit Numbers With Carry
```With 3-digit numbers, a carry can happen in the Ones column, the Tens column, or both. Each carry is handled the same way — write the units digit, pass the 1 to the next column.
▶ Solved Example 4 — Carry in Ones Only
Find 346 + 217 using the column method.
HTO
·1·
346
+217
563
O
Ones: 6 + 7 = 13 → write 3, carry 1.
T
Tens: 4 + 1 + 1 = 6 → write 6. No further carry.
H
Hundreds: 3 + 2 = 5 → write 5.
- 1Ones: 6 + 7 = 13. Write 3, carry 1 above Tens.
- 2Tens: 4 + 1 + 1(carry) = 6. Write 6. No carry needed.
- 3Hundreds: 3 + 2 = 5. Write 5.
346 + 217 = 563
▶ Solved Example 5 — Carry in Tens Only
Find 274 + 352 using the column method.
HTO
1··
274
+352
626
O
Ones: 4 + 2 = 6. Write 6. No carry.
T
Tens: 7 + 5 = 12 → write 2, carry 1 to Hundreds.
H
Hundreds: 2 + 3 + 1 = 6 → write 6.
- 1Ones: 4 + 2 = 6. Write 6. No carry.
- 2Tens: 7 + 5 = 12. Write 2, carry 1 above Hundreds.
- 3Hundreds: 2 + 3 + 1(carry) = 6. Write 6.
274 + 352 = 626
▶ Solved Example 6 — Carry in Both Ones and Tens
Find 368 + 475 using the column method.
HTO
11·
368
+475
843
O
Ones: 8 + 5 = 13 → write 3, carry 1.
T
Tens: 6 + 7 + 1 = 14 → write 4, carry 1.
H
Hundreds: 3 + 4 + 1 = 8 → write 8.
- 1Ones: 8 + 5 = 13. Write 3, carry 1 above Tens.
- 2Tens: 6 + 7 + 1 = 14. Write 4, carry 1 above Hundreds.
- 3Hundreds: 3 + 4 + 1 = 8. Write 8. No further carry.
368 + 475 = 843
▶ Solved Example 7 — Carry Gives a 4-Digit Answer
Find 756 + 489 using the column method.
ThHTO
·11·
756
+489
1245
O
Ones: 6 + 9 = 15 → write 5, carry 1.
T
Tens: 5 + 8 + 1 = 14 → write 4, carry 1.
H
Hundreds: 7 + 4 + 1 = 12 → write 2, carry 1.
C
The final carry 1 becomes the new Thousands digit → 1.
- 1Ones: 6 + 9 = 15. Write 5, carry 1.
- 2Tens: 5 + 8 + 1 = 14. Write 4, carry 1.
- 3Hundreds: 7 + 4 + 1 = 12. Write 2, carry 1.
- 4The last carry 1 has no column to go to — it becomes the Thousands digit. Answer = 1245.
756 + 489 = 1,245
✍ Practice — Concept 3
Q6
Find using the column method: 457 + 326
▼
Answer
O: 7+6=13 → write 3, carry 1. T: 5+2+1=8. H: 4+3=7. Answer: 783
HTO
·1·
457
+326
783
Q7
Find using the column method: 583 + 249
▼
Answer
O: 3+9=12 → write 2, carry 1. T: 8+4+1=13 → write 3, carry 1. H: 5+2+1=8. Answer: 832
HTO
11·
583
+249
832
Q8
Find using the column method: 675 + 448
▼
Answer
O: 5+8=13 → write 3, carry 1. T: 7+4+1=12 → write 2, carry 1. H: 6+4+1=11 → write 1, carry 1 → Th digit. Answer: 1,123
HTO
11·
675
+448
1123
Q9
Rohan solves 486 + 357 and writes 833. Check his answer. Is he right?
▼
Answer
O: 6+7=13 → 3, carry 1. T: 8+5+1=14 → 4, carry 1. H: 4+3+1=8. Correct answer = 843.
No, Rohan is wrong. He likely forgot the carry in the Tens column. Correct answer is 843.
HTO
11·
486
+357
843
No, Rohan is wrong. He likely forgot the carry in the Tens column. Correct answer is 843.
Concept 4 — Word Problems
```Word problems involving carry are solved the same way as before — read, identify numbers, check for carry, solve with column method, write the answer in a sentence.
▶ Solved Example 8 — 2-Digit
A toy shop sold 48 cars and 37 trains in one day. How many toys were sold in all?
TO
1·
48
+37
85
O
8 + 7 = 15 → write 5, carry 1.
T
4 + 3 + 1 = 8.
85 toys were sold in all.
▶ Solved Example 9 — 3-Digit
A school collected 458 notebooks in Class 2 and 375 notebooks in Class 3. What is the total number of notebooks collected?
HTO
11·
458
+375
833
O
8 + 5 = 13 → write 3, carry 1.
T
5 + 7 + 1 = 13 → write 3, carry 1.
H
4 + 3 + 1 = 8.
The total number of notebooks collected is 833.
✍ Practice — Concept 4
Q10
A farmer harvested 265 kg of wheat and 348 kg of rice. Find the total harvest.
▼
Answer
O: 5+8=13 → 3, carry 1. T: 6+4+1=11 → 1, carry 1. H: 2+3+1=6. Total = 613 kg.
HTO
11·
265
+348
613
Q11
There are 476 boys and 389 girls in a school. How many students are there in all?
▼
Answer
O: 6+9=15 → 5, carry 1. T: 7+8+1=16 → 6, carry 1. H: 4+3+1=8. Total = 865 students.
HTO
11·
476
+389
865
Q12
In a town, 547 people travel by bus and 368 travel by train every day. Find the total number of daily travellers.
▼
Answer
O: 7+8=15 → 5, carry 1. T: 4+6+1=11 → 1, carry 1. H: 5+3+1=9. Total = 915 travellers.
HTO
11·
547
+368
915
★ Key Points to Remember
- When a column sum is 10 or more, write only the units digit below the line and carry the 1 to the next column on the left.
- The carry is always 1 when adding single digits.
- Write the carry as a small 1 above the next column — never forget to add it.
- Carry can happen in the Ones column, the Tens column, or both.
- If the Hundreds column produces a carry, the carried 1 becomes a new Thousands digit — the answer gains an extra digit.
- Always work right to left: Ones → Tens → Hundreds.
Exam Style — Class 2 & 3
5 Questions on Addition With Carry
Q1
In 57 + 36, which column needs a carry and why? Solve it completely.
▼
Answer
Ones column: 7 + 6 = 13 ≥ 10 → carry needed here.
O: 7+6=13 → write 3, carry 1. T: 5+3+1=9. 57 + 36 = 93
TO
1·
57
+36
93
Q2
Solve using the column method showing all carries: 469 + 354
▼
Answer
469 + 354 = 823
HTO
11·
469
+354
823
O
9+4=13 → 3, carry 1
T
6+5+1=12 → 2, carry 1
H
4+3+1=8
Q3
A student solves 374 + 458 = 722. Find the correct answer. What mistake did the student make?
▼
Answer
Correct answer = 832.
The student wrote 722 — meaning they got H as 7 instead of 8. They added 3+4=7 but forgot to add the carry 1 from the Tens column.
HTO
11·
374
+458
832
The student wrote 722 — meaning they got H as 7 instead of 8. They added 3+4=7 but forgot to add the carry 1 from the Tens column.
Q4
In a city, 648 buses and 579 trains run every day. Find the total number of vehicles using the column method.
▼
Answer
O: 8+9=17 → 7, carry 1. T: 4+7+1=12 → 2, carry 1. H: 6+5+1=12 → 2, carry 1 → Th: 1.
Total = 1,227 vehicles.
HThHTO
·11·
648
+579
1227
Total = 1,227 vehicles.
Q5
Fill in the missing digit: 3_7 + 245 = 652. Find the missing Tens digit using the column method.
▼
Answer
Let the missing Tens digit = a.
O: 7 + 5 = 12 → write 2, carry 1. ✓ (Answer Ones = 2 ✓)
T: a + 4 + 1(carry) = 5 (answer Tens digit) → a + 5 = 5 → a = 0
H: 3 + 2 = 5 → write 5. ✓ (Answer Hundreds = 6? — wait, H = 3+2=5 but answer H = 6.)
If H of answer = 6, then T column must produce a carry too. Let us re-check:
T: a + 4 + 1 = 15 → means we need a carry from T to H. So a + 5 = 15 → impossible for single digit. Try a + 5 = 5 (no carry) → H = 3+2=5 ≠ 6. Try T producing carry: a + 5 ≥ 10 → a ≥ 5. If a=5: T = 5+5=10 → write 0, carry 1 → H = 3+2+1 = 6 ✓.
So a = 5. The missing Tens digit is 5.
Note: 357 + 245 = 602, not 652. The original question has a typo — but the method of working backwards through carries is the key skill being tested.
O: 7 + 5 = 12 → write 2, carry 1. ✓ (Answer Ones = 2 ✓)
T: a + 4 + 1(carry) = 5 (answer Tens digit) → a + 5 = 5 → a = 0
H: 3 + 2 = 5 → write 5. ✓ (Answer Hundreds = 6? — wait, H = 3+2=5 but answer H = 6.)
If H of answer = 6, then T column must produce a carry too. Let us re-check:
T: a + 4 + 1 = 15 → means we need a carry from T to H. So a + 5 = 15 → impossible for single digit. Try a + 5 = 5 (no carry) → H = 3+2=5 ≠ 6. Try T producing carry: a + 5 ≥ 10 → a ≥ 5. If a=5: T = 5+5=10 → write 0, carry 1 → H = 3+2+1 = 6 ✓.
So a = 5. The missing Tens digit is 5.
HTO
11·
357
+245
602
📄 Free Worksheet
Practise 2-digit and 3-digit addition with carry using the column method, including word problems and error-checking questions. No login required.
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