Double-Digit Multiplication Practice with Partial Products

Let's solve each problem step by step using the partial product box method (also known as the area model or expanded form multiplication). This method breaks down each number into tens and ones, multiplies them in parts, and then adds up all the partial products.

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🔷 General Steps:

1. Break apart both numbers into tens and ones.
2. Draw a 2x2 box.
3. Write the expanded first number on top (tens and ones).
4. Write the expanded second number vertically on the left.
5. Multiply each part and fill in the boxes.
6. Add all partial products to get the final answer.

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## ✔ Problem 1: 32 × 21

Break apart:
- 32 = 30 + 2
- 21 = 20 + 1

| | 30 | 2 |
|-------|----|---|
| 20 | 600 | 40 |
| 1 | 30 | 2 |

Now add:
```
600
40
30
+ 2
-----
672
```

✔ Answer: 672

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## ✔ Problem 2: 54 × 26

Break apart:
- 54 = 50 + 4
- 26 = 20 + 6

| | 50 | 4 |
|-------|----|---|
| 20 | 1000 | 80 |
| 6 | 300 | 24 |

Now add:
```
1000
80
300
+ 24
-----
1404
```

✔ Answer: 1404

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## ✔ Problem 3: 64 × 38

Break apart:
- 64 = 60 + 4
- 38 = 30 + 8

| | 60 | 4 |
|-------|----|---|
| 30 | 1800 | 120 |
| 8 | 480 | 32 |

Now add:
```
1800
120
480
+ 32
-----
2432
```

✔ Answer: 2432

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## ✔ Problem 4: 24 × 23

Break apart:
- 24 = 20 + 4
- 23 = 20 + 3

| | 20 | 4 |
|-------|----|---|
| 20 | 400 | 80 |
| 3 | 60 | 12 |

Now add:
```
400
80
60
+12
-----
552
```

✔ Answer: 552

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## ✔ Problem 5: 41 × 26

Break apart:
- 41 = 40 + 1
- 26 = 20 + 6

| | 40 | 1 |
|-------|----|---|
| 20 | 800 | 20 |
| 6 | 240 | 6 |

Now add:
```
800
20
240
+ 6
-----
1066
```

✔ Answer: 1066

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## ✔ Problem 6: 52 × 34

Break apart:
- 52 = 50 + 2
- 34 = 30 + 4

| | 50 | 2 |
|-------|----|---|
| 30 | 1500 | 60 |
| 4 | 200 | 8 |

Now add:
```
1500
60
200
+ 8
-----
1768
```

✔ Answer: 1768

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📌 Final Answers:

1. 32 × 21 = 672
2. 54 × 26 = 1404
3. 64 × 38 = 2432
4. 24 × 23 = 552
5. 41 × 26 = 1066
6. 52 × 34 = 1768

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✔ Completed Box for Each Problem:

#### 1. 32 × 21
```
30 2
20 | 600 | 40 |
1 | 30 | 2 |
```
Sum: 600 + 40 + 30 + 2 = 672

#### 2. 54 × 26
```
50 4
20 |1000 | 80 |
6 | 300 | 24 |
```
Sum: 1000 + 80 + 300 + 24 = 1404

#### 3. 64 × 38
```
60 4
30 |1800 |120 |
8 | 480 | 32 |
```
Sum: 1800 + 120 + 480 + 32 = 2432

#### 4. 24 × 23
```
20 4
20 | 400 | 80 |
3 | 60 | 12 |
```
Sum: 400 + 80 + 60 + 12 = 552

#### 5. 41 × 26
```
40 1
20 | 800 | 20 |
6 | 240 | 6 |
```
Sum: 800 + 20 + 240 + 6 = 1066

#### 6. 52 × 34
```
50 2
30 |1500 | 60 |
4 | 200 | 8 |
```
Sum: 1500 + 60 + 200 + 8 = 1768

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