Box Method Multiplication Worksheet - Free Printable

The image shows a multiplication problem solved using the partial products method, which breaks down numbers into their place values (tens and ones) to simplify multiplication. Let's go through the solution step by step.

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🔢 Problem:

Multiply:
34 × 46

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🧩 Step 1: Break Down the Numbers

We break both numbers into tens and ones:

- 34 = 30 + 4
- 46 = 40 + 6

Now, we multiply each part of 34 by each part of 46 using a grid (also called the area model).

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📊 Partial Products Grid

| | 30 | 4 |
|-------|--------|-------|
| 40 | 1200 | 160 |
| 6 | 180 | 24 |

Let’s compute each partial product:

1. 40 × 30 = 1200
2. 40 × 4 = 160
3. 6 × 30 = 180
4. 6 × 4 = 24

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➕ Step 2: Add All Partial Products

Now, add all the partial products:

```
1200
+ 160
+ 180
+ 24
------
1564
```

✔ Final Answer: 1564

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✔ Verification (Optional)

Check with standard multiplication:

```
34
× 46
----
204 ← 34 × 6
1360 ← 34 × 40
-----
1564
```

Same result! ✔️

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✔ Conclusion:

Using the partial products method, we broke down the multiplication into smaller, easier steps and added them up:

> 34 × 46 = 1564

This method helps understand how multiplication works based on place value.