Multiply in columns: 3 by 3-digit numbers | Worsheets library - Free Printable

Let's solve each of the multiplication problems in the worksheet step by step. These are 3-digit by 3-digit multiplications, and we'll use the column method (also known as long multiplication).

---

1. 299 × 362

We break down 362 into 300 + 60 + 2:

```
299
×362
-----
598 ← 299 × 2
1794 ← 299 × 60 = 299 × 6 × 10 = 1794 → shift one place left
897 ← 299 × 300 = 299 × 3 × 100 = 897 → shift two places left
------
108,238
```

Now add:
- 598
- 17940
- 89700

Add:
598 + 17940 = 18,538
18,538 + 89,700 = 108,238

✔ Answer: 108,238

---

2. 188 × 740

Note: 740 = 700 + 40 + 0 → so we can simplify.

But let’s do it properly:

```
188
×740
-----
0 ← 188 × 0
752 ← 188 × 40 = 188 × 4 × 10 = 752 → shift one left
1316 ← 188 × 700 = 188 × 7 × 100 = 1316 → shift two left
-------
139,280
```

Wait — actually, better to write:

```
188
×740
-----
0 ← 188 × 0
7520 ← 188 × 40 = 7520
131600 ← 188 × 700 = 131,600
-------
139,120
```

Wait! Let's compute correctly:

188 × 740 = 188 × (700 + 40) = 188×700 + 188×40

- 188 × 700 = 188 × 7 × 100 = (1316) × 100 = 131,600
- 188 × 40 = 188 × 4 × 10 = 752 × 10 = 7,520

Now add:
131,600 + 7,520 = 139,120

✔ Answer: 139,120

---

3. 191 × 129

Break 129 = 100 + 20 + 9

```
191
×129
-----
1719 ← 191 × 9
382 ← 191 × 20 = 3820 → shift left
191 ← 191 × 100 = 19100 → shift two left
-------
24,639
```

Now compute:

- 191 × 9 = 1,719
- 191 × 20 = 3,820
- 191 × 100 = 19,100

Add them:

1,719 + 3,820 = 5,539
5,539 + 19,100 = 24,639

✔ Answer: 24,639

---

4. 340 × 962

Note: 340 ends with zero → easier.

340 = 34 × 10 → so multiply 34 × 962, then ×10

First: 34 × 962

```
962
× 34
-----
3848 ← 962 × 4
2886 ← 962 × 30 = 28,860 → shift left
------
32,708
```

Now ×10 → 327,080

✔ Answer: 327,080

---

5. 529 × 132

Break 132 = 100 + 30 + 2

```
529
×132
-----
1058 ← 529 × 2
1587 ← 529 × 30 = 15,870 → shift left
529 ← 529 × 100 = 52,900 → shift two left
-------
69,928
```

Now compute:

- 529 × 2 = 1,058
- 529 × 30 = 15,870
- 529 × 100 = 52,900

Add:

1,058 + 15,870 = 16,928
16,928 + 52,900 = 69,828

Wait — double-check:

529 × 132

Do it directly:

```
529
×132
-----
1058 ← 529 × 2
1587 ← 529 × 3 → but shifted → 15,870
529 ← 529 × 1 → shifted → 52,900
-------
69,828
```

Yes:
1,058 + 15,870 = 16,928
16,928 + 52,900 = 69,828

✔ Answer: 69,828

---

6. 290 × 426

290 = 29 × 10 → so 29 × 426 × 10

First: 29 × 426

```
426
× 29
-----
3834 ← 426 × 9
852 ← 426 × 20 = 8,520 → shift left
------
12,354
```

Then ×10 → 123,540

✔ Answer: 123,540

---

7. 850 × 707

850 = 85 × 10 → so compute 85 × 707, then ×10

First: 85 × 707

Break 707 = 700 + 7

- 85 × 700 = 85 × 7 × 100 = 595 × 100 = 59,500
- 85 × 7 = 595

Add: 59,500 + 595 = 60,095

Now ×10 → 600,950

✔ Answer: 600,950

---

8. 468 × 162

Break 162 = 100 + 60 + 2

```
468
×162
-----
936 ← 468 × 2
2808 ← 468 × 60 = 28,080 → shift left
468 ← 468 × 100 = 46,800 → shift two left
-------
75,516
```

Now add:

- 936
- 28,080
- 46,800

936 + 28,080 = 29,016
29,016 + 46,800 = 75,816

Wait — let's recalculate:

468 × 162

Step-by-step:

- 468 × 2 = 936
- 468 × 60 = 468 × 6 × 10 = 2,808 × 10 = 28,080
- 468 × 100 = 46,800

Now sum:

936 + 28,080 = 29,016
29,016 + 46,800 = 75,816

✔ Answer: 75,816

---

9. 513 × 653

Break 653 = 600 + 50 + 3

```
513
×653
-----
1539 ← 513 × 3
2565 ← 513 × 50 = 25,650 → shift left
3078 ← 513 × 600 = 307,800 → shift two left
-------
335,489
```

Compute:

- 513 × 3 = 1,539
- 513 × 50 = 25,650
- 513 × 600 = 307,800

Now add:

1,539 + 25,650 = 27,189
27,189 + 307,800 = 334,989

Wait — check:

513 × 653

Let me verify with another method or re-add:

Actually, let's do it carefully:

```
513
×653
-----
1539 ← 513 × 3
2565 ← 513 × 50 → 25,650 → written as 2565 with one shift
3078 ← 513 × 600 → 307,800 → written as 3078 with two shifts
-------
334,989
```

Now adding:

1,539
+25,650 = 27,189
+307,800 = 334,989

✔ Answer: 334,989

---

✔ Final Answers:

1. 108,238
2. 139,120
3. 24,639
4. 327,080
5. 69,828
6. 123,540
7. 600,950
8. 75,816
9. 334,989

---

✔ Summary Table:

| Problem | Answer |
|--------|--------------|
| 1 | 108,238 |
| 2 | 139,120 |
| 3 | 24,639 |
| 4 | 327,080 |
| 5 | 69,828 |
| 6 | 123,540 |
| 7 | 600,950 |
| 8 | 75,816 |
| 9 | 334,989 |

Let me know if you'd like a visual explanation for any of them!