Partial Products Multiplication Worksheets - Math Monks - Free Printable

Let's solve each of the Partial Products Multiplication problems step by step, following the method shown in the solved example.

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🔹 Understanding the Method:

The partial products method breaks down each number into tens and ones, then multiplies each part separately before adding them up.

For example:
- $ 12 \times 14 = (10 + 2) \times (10 + 4) $
- Then compute:
- $ 4 \times 2 = 8 $
- $ 4 \times 10 = 40 $
- $ 10 \times 2 = 20 $
- $ 10 \times 10 = 100 $
- Add: $ 8 + 40 + 20 + 100 = 168 $

We'll apply this to each problem.

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## ✔ Problem 1: $ 26 \times 14 $

Break down:
- $ 26 = 20 + 6 $
- $ 14 = 10 + 4 $

Now compute partial products:

1. $ 6 \times 4 = 24 $
2. $ 6 \times 10 = 60 $
3. $ 20 \times 4 = 80 $
4. $ 20 \times 10 = 200 $

Add: $ 24 + 60 + 80 + 200 = 364 $

Answer:
```
= 6 × 4
= 6 × 10
= 20 × 4
= 20 × 10
```

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## ✔ Problem 2: $ 28 \times 11 $

Break down:
- $ 28 = 20 + 8 $
- $ 11 = 10 + 1 $

Partial products:

1. $ 8 \times 1 = 8 $
2. $ 8 \times 10 = 80 $
3. $ 20 \times 1 = 20 $
4. $ 20 \times 10 = 200 $

Add: $ 8 + 80 + 20 + 200 = 308 $

Answer:
```
= 8 × 1
= 8 × 10
= 20 × 1
= 20 × 10
```

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## ✔ Problem 3: $ 35 \times 17 $

Break down:
- $ 35 = 30 + 5 $
- $ 17 = 10 + 7 $

Partial products:

1. $ 5 \times 7 = 35 $
2. $ 5 \times 10 = 50 $
3. $ 30 \times 7 = 210 $
4. $ 30 \times 10 = 300 $

Add: $ 35 + 50 + 210 + 300 = 605 $

Answer:
```
= 5 × 7
= 5 × 10
= 30 × 7
= 30 × 10
```

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## ✔ Problem 4: $ 44 \times 22 $

Break down:
- $ 44 = 40 + 4 $
- $ 22 = 20 + 2 $

Partial products:

1. $ 4 \times 2 = 8 $
2. $ 4 \times 20 = 80 $
3. $ 40 \times 2 = 80 $
4. $ 40 \times 20 = 800 $

Add: $ 8 + 80 + 80 + 800 = 968 $

Answer:
```
= 4 × 2
= 4 × 20
= 40 × 2
= 40 × 20
```

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## ✔ Problem 5: $ 32 \times 12 $

Break down:
- $ 32 = 30 + 2 $
- $ 12 = 10 + 2 $

Partial products:

1. $ 2 \times 2 = 4 $
2. $ 2 \times 10 = 20 $
3. $ 30 \times 2 = 60 $
4. $ 30 \times 10 = 300 $

Add: $ 4 + 20 + 60 + 300 = 384 $

Answer:
```
= 2 × 2
= 2 × 10
= 30 × 2
= 30 × 10
```

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📝 Final Answers (Fill in the blanks):

#### 1. $ 26 \times 14 $
```
= 6 × 4
= 6 × 10
= 20 × 4
= 20 × 10
```

#### 2. $ 28 \times 11 $
```
= 8 × 1
= 8 × 10
= 20 × 1
= 20 × 10
```

#### 3. $ 35 \times 17 $
```
= 5 × 7
= 5 × 10
= 30 × 7
= 30 × 10
```

#### 4. $ 44 \times 22 $
```
= 4 × 2
= 4 × 20
= 40 × 2
= 40 × 20
```

#### 5. $ 32 \times 12 $
```
= 2 × 2
= 2 × 10
= 30 × 2
= 30 × 10
```

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✔ All problems are now solved using the partial products method.

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