Partial Product Multiplication worksheet with nine problems for practicing multiplication using the partial products method.

Let's solve each of these partial product multiplication problems step by step. The method involves breaking down one or both numbers into their place values (hundreds, tens, ones), multiplying each part separately, and then adding the partial products.

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1) 617 × 5

Break 617 into:
- 600 (hundreds)
- 10 (tens)
- 7 (ones)

Now multiply each by 5:

- 600 × 5 = 3,000
- 10 × 5 = 50
- 7 × 5 = 35

Add them:
```
3,000
50
+ 35
-------
3,085
```

✔ Answer: 3,085

---

2) 529 × 8

Break 529 into:
- 500
- 20
- 9

Multiply by 8:

- 500 × 8 = 4,000
- 20 × 8 = 160
- 9 × 8 = 72

Add:
```
4,000
160
+ 72
-------
4,232
```

✔ Answer: 4,232

---

3) 825 × 6

Break 825 into:
- 800
- 20
- 5

Multiply by 6:

- 800 × 6 = 4,800
- 20 × 6 = 120
- 5 × 6 = 30

Add:
```
4,800
120
+ 30
-------
4,950
```

✔ Answer: 4,950

---

4) 137 × 3

Break 137 into:
- 100
- 30
- 7

Multiply by 3:

- 100 × 3 = 300
- 30 × 3 = 90
- 7 × 3 = 21

Add:
```
300
90
+ 21
------
411
```

✔ Answer: 411

---

5) 764 × 4

Break 764 into:
- 700
- 60
- 4

Multiply by 4:

- 700 × 4 = 2,800
- 60 × 4 = 240
- 4 × 4 = 16

Add:
```
2,800
240
+ 16
-------
3,056
```

✔ Answer: 3,056

---

6) 238 × 9

Break 238 into:
- 200
- 30
- 8

Multiply by 9:

- 200 × 9 = 1,800
- 30 × 9 = 270
- 8 × 9 = 72

Add:
```
1,800
270
+ 72
-------
2,142
```

✔ Answer: 2,142

---

7) 231 × 7

Break 231 into:
- 200
- 30
- 1

Multiply by 7:

- 200 × 7 = 1,400
- 30 × 7 = 210
- 1 × 7 = 7

Add:
```
1,400
210
+ 7
-------
1,617
```

✔ Answer: 1,617

---

8) 953 × 8

Break 953 into:
- 900
- 50
- 3

Multiply by 8:

- 900 × 8 = 7,200
- 50 × 8 = 400
- 3 × 8 = 24

Add:
```
7,200
400
+ 24
-------
7,624
```

✔ Answer: 7,624

---

9) 337 × 2

Break 337 into:
- 300
- 30
- 7

Multiply by 2:

- 300 × 2 = 600
- 30 × 2 = 60
- 7 × 2 = 14

Add:
```
600
60
+ 14
------
674
```

✔ Answer: 674

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) 617 × 5 | 3,085 |
| 2) 529 × 8 | 4,232 |
| 3) 825 × 6 | 4,950 |
| 4) 137 × 3 | 411 |
| 5) 764 × 4 | 3,056 |
| 6) 238 × 9 | 2,142 |
| 7) 231 × 7 | 1,617 |
| 8) 953 × 8 | 7,624 |
| 9) 337 × 2 | 674 |

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📝 Explanation Summary:

The partial product method helps students understand multiplication by decomposing numbers into place values (like hundreds, tens, ones), multiplying each part separately, and then summing those products. This builds number sense and reinforces understanding of place value.

For example:
617 × 5 → (600 + 10 + 7) × 5 = (600×5) + (10×5) + (7×5) = 3,000 + 50 + 35 = 3,085

This method is especially helpful in teaching multi-digit multiplication before moving to standard algorithms.

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