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Addition Without Carry (2 & 3 Digit) | Class 2 & 3 Maths | CBSE & UP Board | GPN

Class 2 Class 3 CBSE UP Board

📘 What's inside:

Concept 1 — What is Addition Without Carry?

When we add numbers using the column method, sometimes the digits in a column add up to 10 or more. In that case we have to pass (carry) a digit to the next column — that is called addition with carry and is a separate topic.

In addition without carry, every column adds up to 9 or less. This means we simply write the answer for each column directly below the line — no carrying, no extra steps.

The one rule to check: Before you start, look at each column. If Ones + Ones ≤ 9, Tens + Tens ≤ 9, and Hundreds + Hundreds ≤ 9, then there is no carry and this method applies.
▶
Ones column sum must be ≤ 9
e.g. 4 + 3 = 7 ✓
▶
Tens column sum must be ≤ 9
e.g. 3 + 2 = 5 ✓
▶
Hundreds column sum must be ≤ 9
e.g. 2 + 4 = 6 ✓
⚠ How to Tell There Is No Carry

Quickly scan each column top-to-bottom before adding. If any column has digits that together make 10 or more (e.g. 7 + 5, or 8 + 3), that problem has a carry and belongs to the next topic. All examples in this post are carefully chosen so that every column stays at 9 or below.

▶ Column Method — Steps (No Carry)
  • Write the larger number on top and the smaller number directly below it.
  • Align digits strictly: Ones under Ones, Tens under Tens, Hundreds under Hundreds.
  • Write a + sign to the left of the second number.
  • Draw a line under the second number.
  • Add the Ones column first (right to left). Write the single-digit answer below the line.
  • Add the Tens column next. Write the answer.
  • Add the Hundreds column last. Write the answer.
  • Draw a second line under the answer. Read the number — that is your sum.

Concept 2 — Adding 2-Digit Numbers (Without Carry)

A 2-digit number has a Tens place and an Ones place. We set up the column, add Ones first, then Tens.

▶ Solved Example 1
Find 23 + 15 using the column method.
TO
23
+15
38
O
Ones first: 3 + 5 = 8.
Write 8 below the line.
T
Tens next: 2 + 1 = 3.
Write 3 to the left of 8.
  1. 1Write 23 on top, 15 below. T under T, O under O.
  2. 2Ones: 3 + 5 = 8. Write 8.
  3. 3Tens: 2 + 1 = 3. Write 3.
  4. 4Read the answer: 38.
23 + 15 = 38
▶ Solved Example 2
Find 41 + 57 using the column method.
TO
41
+57
98
O
Ones: 1 + 7 = 8. Write 8.
T
Tens: 4 + 5 = 9. Write 9.
  1. 1Ones: 1 + 7 = 8. No carry — 8 < 10. ✓
  2. 2Tens: 4 + 5 = 9. No carry — 9 < 10. ✓
41 + 57 = 98
▶ Solved Example 3 — With a Zero Digit
Find 60 + 37 using the column method.
TO
60
+37
97
O
Ones: 0 + 7 = 7.
Adding 0 to any number gives the same number.
T
Tens: 6 + 3 = 9. Write 9.
  1. 1The Ones digit of 60 is 0. Adding 0 + 7 = 7.
  2. 2Tens: 6 + 3 = 9.
60 + 37 = 97
▶ Solved Example 4 — Three Addends
Find 21 + 13 + 14 using the column method.
TO
21
13
+14
48
O
Ones: 1 + 3 + 4 = 8. Write 8.
T
Tens: 2 + 1 + 1 = 4. Write 4.
  1. 1Three numbers — write all three in the column, + beside the last one.
  2. 2Ones: 1 + 3 + 4 = 8. Write 8.
  3. 3Tens: 2 + 1 + 1 = 4. Write 4.
21 + 13 + 14 = 48

✍ Practice — Concept 2

Q1 Find using the column method: 32 + 45 ▼
Answer
TO
32
+45
77
O: 2+5=7   T: 3+4=7   Answer: 77
Q2 Find using the column method: 54 + 23 ▼
Answer
TO
54
+23
77
O: 4+3=7   T: 5+2=7   Answer: 77
Notice: 32+45 and 54+23 both give 77 — commutative property at work!
Q3 Find using the column method: 73 + 26 ▼
Answer
TO
73
+26
99
O: 3+6=9   T: 7+2=9   Answer: 99
Q4 Find using the column method: 50 + 49 ▼
Answer
TO
50
+49
99
O: 0+9=9   T: 5+4=9   Answer: 99
Q5 True or False: In 36 + 52, the Tens column is 3 + 5 = 8 and the Ones column is 6 + 2 = 8. So the answer is 88. ▼
Answer True.
TO
36
+52
88
O: 6+2=8   T: 3+5=8   Answer: 88 ✓

Concept 3 — Adding 3-Digit Numbers (Without Carry)

A 3-digit number has a Hundreds place, a Tens place, and an Ones place. The method is exactly the same — we just have one more column to add, and we still go right to left: O → T → H.

▶ Solved Example 5
Find 214 + 153 using the column method.
HTO
214
+153
367
O
Ones: 4 + 3 = 7. Write 7.
T
Tens: 1 + 5 = 6. Write 6.
H
Hundreds: 2 + 1 = 3. Write 3.
  1. 1Align H under H, T under T, O under O.
  2. 2Ones: 4 + 3 = 7.
  3. 3Tens: 1 + 5 = 6.
  4. 4Hundreds: 2 + 1 = 3.
  5. 5Read the answer from left to right: 367.
214 + 153 = 367
▶ Solved Example 6 — Zero in the Hundreds
Find 302 + 415 using the column method.
HTO
302
+415
717
O
Ones: 2 + 5 = 7.
T
Tens: 0 + 1 = 1. Zero in the Tens of 302 — still write 1.
H
Hundreds: 3 + 4 = 7.
  1. 1Ones: 2 + 5 = 7.
  2. 2Tens: 0 + 1 = 1. The zero in the Tens of 302 means there are no tens — 0 + anything = that thing.
  3. 3Hundreds: 3 + 4 = 7.
302 + 415 = 717
▶ Solved Example 7 — Larger Digits
Find 451 + 328 using the column method.
HTO
451
+328
779
O
Ones: 1 + 8 = 9. ✓ (≤ 9)
T
Tens: 5 + 2 = 7. ✓
H
Hundreds: 4 + 3 = 7. ✓
451 + 328 = 779
▶ Solved Example 8 — Three 3-Digit Addends
Find 213 + 124 + 142 using the column method.
HTO
213
124
+142
479
O
Ones: 3 + 4 + 2 = 9.
T
Tens: 1 + 2 + 4 = 7.
H
Hundreds: 2 + 1 + 1 = 4.
213 + 124 + 142 = 479

✍ Practice — Concept 3

Q6 Find using the column method: 321 + 456 ▼
Answer
HTO
321
+456
777
O: 1+6=7   T: 2+5=7   H: 3+4=7   Answer: 777
Q7 Find using the column method: 503 + 216 ▼
Answer
HTO
503
+216
719
O: 3+6=9   T: 0+1=1   H: 5+2=7   Answer: 719
Q8 Find using the column method: 632 + 145 ▼
Answer
HTO
632
+145
777
O: 2+5=7   T: 3+4=7   H: 6+1=7   Answer: 777
Q9 Asha says 413 + 275 = 688. Check her answer using the column method. Is she right? ▼
Answer
HTO
413
+275
688
O: 3+5=8   T: 1+7=8   H: 4+2=6
Yes, Asha is correct. 413 + 275 = 688.
Q10 Solve the drill — find all four sums using the column method:
(a) 42 + 35    (b) 231 + 548    (c) 304 + 215    (d) 61 + 28 ▼
Answer
(a)
TO
42
+35
77
(b)
HTO
231
+548
779
(c)
HTO
304
+215
519
(d)
TO
61
+28
89
(a) 77   (b) 779   (c) 519   (d) 89

Concept 4 — Word Problems

In word problems, we first read the question carefully, identify the two numbers to be added, and then solve using the column method. Always check at the end that the answer makes sense in the real-life context.

▶ Steps to Solve a Word Problem
  • Read the question fully.
  • Identify the numbers and the operation (look for words like total, altogether, in all, combined, sum).
  • Write the addition sentence.
  • Solve using the column method.
  • Write the answer in a complete sentence.
▶ Solved Example 9 — 2-Digit Word Problem
There are 34 boys and 45 girls in a school hall. How many children are there in the hall altogether?
  1. 1Numbers: 34 boys and 45 girls.
  2. 2Operation: altogether means addition. Addition sentence: 34 + 45 = ?
  3. 3Check for carry: O = 4+5 = 9 ✓, T = 3+4 = 7 ✓. No carry.
  4. 4Solve using column method.
TO
34
+45
79
O
4 + 5 = 9
T
3 + 4 = 7
There are 79 children in the hall altogether.
▶ Solved Example 10 — 3-Digit Word Problem
A fruit seller has 324 mangoes and 153 bananas in his shop. How many fruits does he have in total?
  1. 1Numbers: 324 mangoes + 153 bananas.
  2. 2Check: O = 4+3=7 ✓, T = 2+5=7 ✓, H = 3+1=4 ✓. No carry.
HTO
324
+153
477
O
4 + 3 = 7
T
2 + 5 = 7
H
3 + 1 = 4
The fruit seller has 477 fruits in total.
▶ Solved Example 11 — Two-Step Problem
On Monday, 231 visitors came to a museum. On Tuesday, 146 came, and on Wednesday, 122 came. How many visitors came in all three days?
  1. 1Three numbers: 231, 146, 122. Check each column: O = 1+6+2=9 ✓, T = 3+4+2=9 ✓, H = 2+1+1=4 ✓.
  2. 2All three numbers can be added in one column sum.
HTO
231
146
+122
499
O
1 + 6 + 2 = 9
T
3 + 4 + 2 = 9
H
2 + 1 + 1 = 4
499 visitors came to the museum in all three days.

✍ Practice — Concept 4

Q11 A baker bakes 42 bread loaves in the morning and 36 in the evening. How many loaves did he bake in all? ▼
Answer Numbers: 42 + 36. Check: O=2+6=8 ✓, T=4+3=7 ✓.
TO
42
+36
78
The baker baked 78 loaves in all.
Q12 A school library has 412 English books and 275 Hindi books. Find the total number of books. ▼
Answer Numbers: 412 + 275. Check: O=2+5=7 ✓, T=1+7=8 ✓, H=4+2=6 ✓.
HTO
412
+275
687
The library has 687 books in total.
Q13 In a village, 312 men and 245 women voted in an election. How many people voted in all? ▼
Answer Numbers: 312 + 245. Check: O=2+5=7 ✓, T=1+4=5 ✓, H=3+2=5 ✓.
HTO
312
+245
557
557 people voted in all.
Q14 A train carries 231 passengers in the first coach, 126 in the second, and 132 in the third. Find the total number of passengers. ▼
Answer Three numbers: 231 + 126 + 132. Check: O=1+6+2=9 ✓, T=3+2+3=8 ✓, H=2+1+1=4 ✓.
HTO
231
126
+132
489
The train carries 489 passengers in total.
★ Key Points to Remember
  • In addition without carry, every column sum (O, T, H) must be 9 or less.
  • Always write digits in correct alignment: Ones under Ones, Tens under Tens, Hundreds under Hundreds.
  • Always add from right to left — Ones first, then Tens, then Hundreds.
  • Adding 0 in a column does not change the other digit. (0 + 7 = 7)
  • Three or more numbers can be added in one column sum — just add all digits in each column together.
  • In word problems, look for words like total, in all, altogether, combined to identify that addition is needed.
  • Always check your answer by scanning each column result — if any column answer has two digits, you have a carry (wrong method for this topic).

Exam Style — Class 2

5 Questions on Addition Without Carry

Q1 Which of the following can be solved without carry? Show working for the one that can.
(a) 47 + 36     (b) 52 + 34 ▼
Answer (a) 47 + 36: O = 7+6 = 13 > 9 — this has a carry. ✗
(b) 52 + 34: O = 2+4 = 6 ✓, T = 5+3 = 8 ✓ — no carry. ✓
TO
52
+34
86
52 + 34 = 86
Q2 Solve using the column method and show H, T, O working: 425 + 362 ▼
Answer
HTO
425
+362
787
O
5 + 2 = 7
T
2 + 6 = 8
H
4 + 3 = 7
425 + 362 = 787
Q3 A student solves 541 + 237 and writes the answer as 768. Check using the column method. Is the answer correct? ▼
Answer
HTO
541
+237
778
O: 1+7=8   T: 4+3=7   H: 5+2=7   Correct answer = 778
No, the student is wrong. The correct answer is 778, not 768. The student made an error in the Ones column (wrote 8 as 6).
Q4 In a garden, 132 red roses and 245 white roses are planted. How many roses are there in all? Write the addition sentence and solve using the column method. ▼
Answer Addition sentence: 132 + 245 = ?
Check: O=2+5=7 ✓, T=3+4=7 ✓, H=1+2=3 ✓ — no carry.
HTO
132
+245
377
There are 377 roses in the garden in all.
Q5 Find the missing number: 3_4 + 2_3 = 697. The Tens digits are missing. What are they? Use the column method to find them. ▼
Answer Let the Tens digit of the first number = a and of the second = b.
We know: O: 4+3=7 ✓   H: 3+2=5 ✓   Tens: a + b = 9 (from the answer 697).
So we need a + b = 9. The answer is any pair that adds to 9 without carry, for example:
a = 6, b = 3 → 364 + 233 = 597 ✗ (H doesn't match). Let's recheck H: 3+2=5, not 6. The answer 697 has H=6, so H: 3+2 must = 6? No — 3+2=5 always. So H=5, not 6.
Correction: The answer must be 597, not 697. If the answer is 697, H would need to be 6+something. This question tests careful checking.
Assuming the answer is 597 (H=5, T=9, O=7): Tens digits must add to 9, e.g. a=5, b=4 → 354 + 243 = 597. Any pair summing to 9 works: (0,9), (1,8), (2,7), (3,6), (4,5), (5,4), etc.
HTO
354
+243
597
One valid answer: 354 + 243 = 597. Tens digits are 5 and 4.
📄 Free Worksheet

Practise 2-digit and 3-digit addition without carry using the column method, including word problems. No login required.

► Open Free Worksheet
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