Column Addition of up to 3 Digits - With Regrouping (B) | Key ... - Free Printable
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Step-by-step solution for: Column Addition of up to 3 Digits - With Regrouping (B) | Key ...
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Show Answer Key & Explanations
Step-by-step solution for: Column Addition of up to 3 Digits - With Regrouping (B) | Key ...
Let's solve this step-by-step, working through each section of the worksheet.
---
We'll perform column addition with regrouping (carrying) where needed.
---
1) 461 + 328
```
4 6 1
+ 3 2 8
-------
```
- Ones column: 1 + 8 = 9 → write 9
- Tens column: 6 + 2 = 8 → write 8
- Hundreds column: 4 + 3 = 7 → write 7
✔ Answer: 789
---
2) 435 + 516
```
4 3 5
+ 5 1 6
-------
```
- Ones: 5 + 6 = 11 → write 1, carry 1
- Tens: 3 + 1 = 4, plus carry 1 = 5 → write 5
- Hundreds: 4 + 5 = 9 → write 9
✔ Answer: 951
---
3) 722 + 45
```
7 2 2
+ 4 5
-------
```
Align right:
```
7 2 2
+ 4 5
-------
```
- Ones: 2 + 5 = 7 → write 7
- Tens: 2 + 4 = 6 → write 6
- Hundreds: 7 → write 7
✔ Answer: 767
---
4) 96 + 547
Align right:
```
9 6
+ 5 4 7
-------
```
```
0 9 6
+ 5 4 7
--------
```
- Ones: 6 + 7 = 13 → write 3, carry 1
- Tens: 9 + 4 = 13, plus carry 1 = 14 → write 4, carry 1
- Hundreds: 0 + 5 = 5, plus carry 1 = 6 → write 6
✔ Answer: 643
---
1) 789
2) 951
3) 767
4) 643
---
We’ll write each sum in column form and add them, showing regrouping if needed.
---
1) 802 + 189
```
8 0 2
+ 1 8 9
-------
```
- Ones: 2 + 9 = 11 → write 1, carry 1
- Tens: 0 + 8 = 8, plus carry 1 = 9 → write 9
- Hundreds: 8 + 1 = 9 → write 9
✔ Answer: 991
---
2) 141 + 86
```
1 4 1
+ 8 6
-------
```
```
1 4 1
+ 8 6
-------
```
- Ones: 1 + 6 = 7 → write 7
- Tens: 4 + 8 = 12 → write 2, carry 1
- Hundreds: 1 + 0 = 1, plus carry 1 = 2 → write 2
✔ Answer: 227
---
3) 227 + 85
```
2 2 7
+ 8 5
-------
```
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 2 + 8 = 10, plus carry 1 = 11 → write 1, carry 1
- Hundreds: 2 + 0 = 2, plus carry 1 = 3 → write 3
✔ Answer: 312
---
4) Three hundred and eighteen plus ninety-six
Convert to numbers:
- 318 + 96
```
3 1 8
+ 9 6
-------
```
- Ones: 8 + 6 = 14 → write 4, carry 1
- Tens: 1 + 9 = 10, plus carry 1 = 11 → write 1, carry 1
- Hundreds: 3 + 0 = 3, plus carry 1 = 4 → write 4
✔ Answer: 414
---
5) 632 + 85 + 245
Add step by step:
First: 632 + 85
```
6 3 2
+ 8 5
-------
7 1 7
```
Now: 717 + 245
```
7 1 7
+ 2 4 5
-------
```
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 1 + 4 = 5, plus carry 1 = 6 → write 6
- Hundreds: 7 + 2 = 9 → write 9
✔ Answer: 962
---
6) 29 + 6 + 195
Add step by step:
First: 29 + 6 = 35
Then: 35 + 195
```
3 5
+ 1 9 5
-------
```
```
0 3 5
+ 1 9 5
-------
```
- Ones: 5 + 5 = 10 → write 0, carry 1
- Tens: 3 + 9 = 12, plus carry 1 = 13 → write 3, carry 1
- Hundreds: 0 + 1 = 1, plus carry 1 = 2 → write 2
✔ Answer: 230
---
7) Five hundred and forty-four add four hundred and seven
Numbers: 544 + 407
```
5 4 4
+ 4 0 7
-------
```
- Ones: 4 + 7 = 11 → write 1, carry 1
- Tens: 4 + 0 = 4, plus carry 1 = 5 → write 5
- Hundreds: 5 + 4 = 9 → write 9
✔ Answer: 951
---
1) 991
2) 227
3) 312
4) 414
5) 962
6) 230
7) 951
---
---
1)
```
657
+ 309
-----
956
```
Let’s check:
- Ones: 7 + 9 = 16 → write 6, carry 1
- Tens: 5 + 0 = 5, plus carry 1 = 6 → write 6
- Hundreds: 6 + 3 = 9 → write 9
So correct answer should be 966, not 956.
✘ Mistake: The tens column was added incorrectly. They wrote 5 instead of 6.
✔ Explanation: When adding 7 + 9 = 16, they carried 1 to the tens place. Then 5 + 0 + 1 = 6, but they wrote 5 instead of 6. So the answer is wrong.
---
2)
```
83
+ 427
-----
1257
```
This is clearly wrong because:
- 83 + 427 should be around 500, not 1257.
Let’s do it properly:
```
83
+ 427
-----
```
Align:
```
0 8 3
+ 4 2 7
-------
```
- Ones: 3 + 7 = 10 → write 0, carry 1
- Tens: 8 + 2 = 10, plus carry 1 = 11 → write 1, carry 1
- Hundreds: 0 + 4 = 4, plus carry 1 = 5 → write 5
✔ Correct answer: 510
✘ Mistake: Numbers were misaligned or added incorrectly. Likely they added 83 + 427 as if it were 83 + 4270 or made a mistake in alignment.
✔ Explanation: The hundreds digit was incorrectly calculated. The sum of 83 + 427 is only 510, not 1257. This error may have come from adding digits in the wrong columns or misreading the problem.
---
1)
- Mistake: Incorrect tens digit.
- Correct calculation: 657 + 309 = 966
- Error: Failed to add the carried 1 to the tens column.
2)
- Mistake: Wrong total — 1257 is way too large.
- Correct calculation: 83 + 427 = 510
- Error: Misalignment or incorrect carrying. Possibly added 83 + 427 as if both were 3-digit numbers without proper alignment.
---
#### Section A
1. 789
2. 951
3. 767
4. 643
#### Section B
1. 991
2. 227
3. 312
4. 414
5. 962
6. 230
7. 951
#### Section C
1. Mistake: Tens digit is wrong (should be 6, not 5). Correct answer: 966
2. Mistake: Total is far too high. Correct answer: 510
Let me know if you'd like a printable version or visual layout!
---
Section A: Complete the calculations
We'll perform column addition with regrouping (carrying) where needed.
---
1) 461 + 328
```
4 6 1
+ 3 2 8
-------
```
- Ones column: 1 + 8 = 9 → write 9
- Tens column: 6 + 2 = 8 → write 8
- Hundreds column: 4 + 3 = 7 → write 7
✔ Answer: 789
---
2) 435 + 516
```
4 3 5
+ 5 1 6
-------
```
- Ones: 5 + 6 = 11 → write 1, carry 1
- Tens: 3 + 1 = 4, plus carry 1 = 5 → write 5
- Hundreds: 4 + 5 = 9 → write 9
✔ Answer: 951
---
3) 722 + 45
```
7 2 2
+ 4 5
-------
```
Align right:
```
7 2 2
+ 4 5
-------
```
- Ones: 2 + 5 = 7 → write 7
- Tens: 2 + 4 = 6 → write 6
- Hundreds: 7 → write 7
✔ Answer: 767
---
4) 96 + 547
Align right:
```
9 6
+ 5 4 7
-------
```
```
0 9 6
+ 5 4 7
--------
```
- Ones: 6 + 7 = 13 → write 3, carry 1
- Tens: 9 + 4 = 13, plus carry 1 = 14 → write 4, carry 1
- Hundreds: 0 + 5 = 5, plus carry 1 = 6 → write 6
✔ Answer: 643
---
✔ Section A Answers:
1) 789
2) 951
3) 767
4) 643
---
Section B: Write as column addition and calculate
We’ll write each sum in column form and add them, showing regrouping if needed.
---
1) 802 + 189
```
8 0 2
+ 1 8 9
-------
```
- Ones: 2 + 9 = 11 → write 1, carry 1
- Tens: 0 + 8 = 8, plus carry 1 = 9 → write 9
- Hundreds: 8 + 1 = 9 → write 9
✔ Answer: 991
---
2) 141 + 86
```
1 4 1
+ 8 6
-------
```
```
1 4 1
+ 8 6
-------
```
- Ones: 1 + 6 = 7 → write 7
- Tens: 4 + 8 = 12 → write 2, carry 1
- Hundreds: 1 + 0 = 1, plus carry 1 = 2 → write 2
✔ Answer: 227
---
3) 227 + 85
```
2 2 7
+ 8 5
-------
```
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 2 + 8 = 10, plus carry 1 = 11 → write 1, carry 1
- Hundreds: 2 + 0 = 2, plus carry 1 = 3 → write 3
✔ Answer: 312
---
4) Three hundred and eighteen plus ninety-six
Convert to numbers:
- 318 + 96
```
3 1 8
+ 9 6
-------
```
- Ones: 8 + 6 = 14 → write 4, carry 1
- Tens: 1 + 9 = 10, plus carry 1 = 11 → write 1, carry 1
- Hundreds: 3 + 0 = 3, plus carry 1 = 4 → write 4
✔ Answer: 414
---
5) 632 + 85 + 245
Add step by step:
First: 632 + 85
```
6 3 2
+ 8 5
-------
7 1 7
```
Now: 717 + 245
```
7 1 7
+ 2 4 5
-------
```
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 1 + 4 = 5, plus carry 1 = 6 → write 6
- Hundreds: 7 + 2 = 9 → write 9
✔ Answer: 962
---
6) 29 + 6 + 195
Add step by step:
First: 29 + 6 = 35
Then: 35 + 195
```
3 5
+ 1 9 5
-------
```
```
0 3 5
+ 1 9 5
-------
```
- Ones: 5 + 5 = 10 → write 0, carry 1
- Tens: 3 + 9 = 12, plus carry 1 = 13 → write 3, carry 1
- Hundreds: 0 + 1 = 1, plus carry 1 = 2 → write 2
✔ Answer: 230
---
7) Five hundred and forty-four add four hundred and seven
Numbers: 544 + 407
```
5 4 4
+ 4 0 7
-------
```
- Ones: 4 + 7 = 11 → write 1, carry 1
- Tens: 4 + 0 = 4, plus carry 1 = 5 → write 5
- Hundreds: 5 + 4 = 9 → write 9
✔ Answer: 951
---
✔ Section B Answers:
1) 991
2) 227
3) 312
4) 414
5) 962
6) 230
7) 951
---
Section C: Spot and explain the mistakes
---
1)
```
657
+ 309
-----
956
```
Let’s check:
- Ones: 7 + 9 = 16 → write 6, carry 1
- Tens: 5 + 0 = 5, plus carry 1 = 6 → write 6
- Hundreds: 6 + 3 = 9 → write 9
So correct answer should be 966, not 956.
✘ Mistake: The tens column was added incorrectly. They wrote 5 instead of 6.
✔ Explanation: When adding 7 + 9 = 16, they carried 1 to the tens place. Then 5 + 0 + 1 = 6, but they wrote 5 instead of 6. So the answer is wrong.
---
2)
```
83
+ 427
-----
1257
```
This is clearly wrong because:
- 83 + 427 should be around 500, not 1257.
Let’s do it properly:
```
83
+ 427
-----
```
Align:
```
0 8 3
+ 4 2 7
-------
```
- Ones: 3 + 7 = 10 → write 0, carry 1
- Tens: 8 + 2 = 10, plus carry 1 = 11 → write 1, carry 1
- Hundreds: 0 + 4 = 4, plus carry 1 = 5 → write 5
✔ Correct answer: 510
✘ Mistake: Numbers were misaligned or added incorrectly. Likely they added 83 + 427 as if it were 83 + 4270 or made a mistake in alignment.
✔ Explanation: The hundreds digit was incorrectly calculated. The sum of 83 + 427 is only 510, not 1257. This error may have come from adding digits in the wrong columns or misreading the problem.
---
✔ Section C Answers:
1)
- Mistake: Incorrect tens digit.
- Correct calculation: 657 + 309 = 966
- Error: Failed to add the carried 1 to the tens column.
2)
- Mistake: Wrong total — 1257 is way too large.
- Correct calculation: 83 + 427 = 510
- Error: Misalignment or incorrect carrying. Possibly added 83 + 427 as if both were 3-digit numbers without proper alignment.
---
✔ Final Summary:
#### Section A
1. 789
2. 951
3. 767
4. 643
#### Section B
1. 991
2. 227
3. 312
4. 414
5. 962
6. 230
7. 951
#### Section C
1. Mistake: Tens digit is wrong (should be 6, not 5). Correct answer: 966
2. Mistake: Total is far too high. Correct answer: 510
Let me know if you'd like a printable version or visual layout!
Parent Tip: Review the logic above to help your child master the concept of column addition worksheet for year.
