Column Addition of up to 3 Digits - With Regrouping (B) | Key ... - Free Printable

Here is the complete solution to the worksheet, broken down by section with explanations.

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## Section A: Complete the calculations

We perform column addition from right to left (units → tens → hundreds), carrying over when the sum in a column is 10 or more.

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1) 461 + 328

```
4 6 1
+ 3 2 8
--------
```

- Units: 1 + 8 = 9
- Tens: 6 + 2 = 8
- Hundreds: 4 + 3 = 7

✔ Answer: 789

---

2) 435 + 516

```
4 3 5
+ 5 1 6
--------
```

- Units: 5 + 6 = 11 → write 1, carry 1
- Tens: 3 + 1 + 1 (carry) = 5
- Hundreds: 4 + 5 = 9

✔ Answer: 951

---

3) 722 + 45

Align numbers properly (45 has no hundreds digit):

```
7 2 2
+ 4 5
--------
```

- Units: 2 + 5 = 7
- Tens: 2 + 4 = 6
- Hundreds: 7 + 0 = 7

✔ Answer: 767

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4) 96 + 547

Align numbers:

```
9 6
+ 5 4 7
--------
```

- Units: 6 + 7 = 13 → write 3, carry 1
- Tens: 9 + 4 + 1 (carry) = 14 → write 4, carry 1
- Hundreds: 0 + 5 + 1 (carry) = 6

✔ Answer: 643

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## Section B: Write each sum as column addition and calculate

You must write the numbers vertically aligned by place value, then add.

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1) 802 + 189

```
8 0 2
+ 1 8 9
--------
```

- Units: 2 + 9 = 11 → write 1, carry 1
- Tens: 0 + 8 + 1 = 9
- Hundreds: 8 + 1 = 9

✔ Answer: 991

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2) 141 + 86

```
1 4 1
+ 8 6
--------
```

- Units: 1 + 6 = 7
- Tens: 4 + 8 = 12 → write 2, carry 1
- Hundreds: 1 + 0 + 1 = 2

✔ Answer: 227

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3) 227 + 85

```
2 2 7
+ 8 5
--------
```

- Units: 7 + 5 = 12 → write 2, carry 1
- Tens: 2 + 8 + 1 = 11 → write 1, carry 1
- Hundreds: 2 + 0 + 1 = 3

✔ Answer: 312

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4) three hundred and eighteen plus ninety six

Convert words to numbers:
→ 318 + 96

```
3 1 8
+ 9 6
--------
```

- Units: 8 + 6 = 14 → write 4, carry 1
- Tens: 1 + 9 + 1 = 11 → write 1, carry 1
- Hundreds: 3 + 0 + 1 = 4

✔ Answer: 414

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5) 632 + 85 + 245

Add all three numbers together. You can add two at a time or stack all three.

```
6 3 2
8 5
+ 2 4 5
--------
```

- Units: 2 + 5 + 5 = 12 → write 2, carry 1
- Tens: 3 + 8 + 4 + 1 = 16 → write 6, carry 1
- Hundreds: 6 + 0 + 2 + 1 = 9

✔ Answer: 962

---

6) 29 + 6 + 195

```
2 9
6
+ 1 9 5
--------
```

- Units: 9 + 6 + 5 = 20 → write 0, carry 2
- Tens: 2 + 0 + 9 + 2 = 13 → write 3, carry 1
- Hundreds: 0 + 0 + 1 + 1 = 2

✔ Answer: 230

---

7) five hundred and forty four add four hundred and seven

Convert: 544 + 407

```
5 4 4
+ 4 0 7
--------
```

- Units: 4 + 7 = 11 → write 1, carry 1
- Tens: 4 + 0 + 1 = 5
- Hundreds: 5 + 4 = 9

✔ Answer: 951

---

## Section C: Spot and explain the mistakes

---

1)

```
6 5 7
+ 3 0 9
--------
9 5 6 ← Incorrect!
```

✔ Correct answer: 966

Mistake Explanation:
The student added units: 7 + 9 = 16 → should write 6 and carry 1.
They wrote 6 correctly, but forgot to add the carry to the tens column.
Tens: 5 + 0 + 1 (carry) = 6, not 5.
Hundreds: 6 + 3 = 9 → correct.

👉 Error: Forgot to add the carried 1 to the tens column.

---

2)

```
8 3
+ 4 2 7
--------
1 2 5 7 ← Incorrect!
```

✔ Correct answer: 510

Mistake Explanation:
Numbers are misaligned. 83 should be written under 427 like this:

```
0 8 3
+ 4 2 7
--------
```

- Units: 3 + 7 = 10 → write 0, carry 1
- Tens: 8 + 2 + 1 = 11 → write 1, carry 1
- Hundreds: 0 + 4 + 1 = 5

So answer is 510.

The student incorrectly treated 83 as if it were 830 or didn’t align digits properly, leading to an extra digit and wrong total.

👉 Error: Misalignment of digits — 83 was not placed under the tens and units of 427. Also, incorrect placement led to wrong carryover and extra digit.

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## ✔ Final Answers 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: Forgot to add carry-over to tens column. Correct answer: 966
2) Mistake: Misaligned digits; 83 should be under 27, not shifted. Correct answer: 510

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