These worksheets help students master 2-digit by 2-digit multiplication using both area models and the partial products method.
Two 4th grade math worksheets covering 2-digit by 2-digit multiplication using area model and partial products methods.
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Show Answer Key & Explanations
Step-by-step solution for: Area Model, Partial Products, & Long Multiplication Worksheets ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Area Model, Partial Products, & Long Multiplication Worksheets ...
Let’s solve each problem step by step. We’ll do the area model problems first (Set A1), then the partial products problems (Set B2).
---
Set A1: Area Model Multiplication
---
Problem 1: 43 × 32
Break 43 into 40 + 3
Break 32 into 30 + 2
Area model grid:
- Top row: 40 and 3
- Left column: 30 and 2
Fill in the boxes:
- 30 × 40 = 1,200
- 30 × 3 = 90
- 2 × 40 = 80
- 2 × 3 = 6 ← *This box is missing in the image! But we need it.*
Wait — looking at the given grid in Problem 1:
It shows:
```
40 + 3
30 |1200 | 90
+ |-----|----
2 | 80 | ??
```
The bottom-right box (2 × 3) is blank. That should be 6.
Now add all four parts:
1,200 + 90 = 1,290
80 + 6 = 86
Total: 1,290 + 86 = 1,376
Check answer choices:
A. 1,276
B. 1,376 ← ✔
C. 1,266
D. 1,373
→ Answer for #1: B
---
Problem 2: 14 × 45
Break 14 → 10 + 4
Break 45 → 40 + 5
Grid:
```
10 + 4
40 |400 | ???
+ |-----|----
5 |??? | ???
```
We are told top-left is 400 → that’s 40 × 10 ✔️
Now fill rest:
- 40 × 4 = 160
- 5 × 10 = 50
- 5 × 4 = 20
Add them:
400 + 160 = 560
50 + 20 = 70
Total: 560 + 70 = 630
Answer choices:
A. 430
B. 530
C. 630 ← ✔
D. 730
→ Answer for #2: C
---
Problem 3: 25 × 24
Break 25 → 20 + 5
Break 24 → 20 + 4
Grid:
```
20 + 5
20 |??? | ???
+ |-----|----
4 |??? | ???
```
Calculate each part:
- 20 × 20 = 400
- 20 × 5 = 100
- 4 × 20 = 80
- 4 × 5 = 20
Add:
400 + 100 = 500
80 + 20 = 100
Total: 500 + 100 = 600
Answer choices:
A. 580
B. 500
C. 680
D. 600 ← ✔
→ Answer for #3: D
---
Problem 4: 52 × 53
Break 52 → 50 + 2
Break 53 → 50 + 3
Grid:
```
50 + 2
50 |??? | ???
+ |-----|----
3 |??? | ???
```
Parts:
- 50 × 50 = 2,500
- 50 × 2 = 100
- 3 × 50 = 150
- 3 × 2 = 6
Add:
2,500 + 100 = 2,600
150 + 6 = 156
Total: 2,600 + 156 = 2,756
Answer choices:
A. 2,556
B. 2,656
C. 2,756 ← ✔
D. 2,856
→ Answer for #4: C
---
✔ Set A1 Answers:
1. B
2. C
3. D
4. C
---
Set B2: Partial Products Method
We’ll solve each one by breaking down the multiplication using place value.
---
Problem 1: 35 × 76
Already partially filled:
They show:
- 6 × 5 = 30
- 6 × 30 = 180
- 70 × 5 = 350
- 70 × 30 = 2,100
Add them:
30 + 180 = 210
350 + 2,100 = 2,450
Total: 210 + 2,450 = 2,660
But wait — let me double-check:
Actually, 35 × 76:
Standard way:
35 × 70 = 2,450
35 × 6 = 210
Total: 2,450 + 210 = 2,660
✔️ Correct.
But since this is just an example (already solved), we move to unsolved ones.
---
Problem 2: 63 × 87
Break 63 → 60 + 3
Break 87 → 80 + 7
Partial products:
- 7 × 3 = 21
- 7 × 60 = 420
- 80 × 3 = 240
- 80 × 60 = 4,800
Add:
21 + 420 = 441
240 + 4,800 = 5,040
Total: 441 + 5,040 = 5,481
Let me verify with standard multiplication:
63 × 87:
63 × 80 = 5,040
63 × 7 = 441
Total: 5,040 + 441 = 5,481 ✔️
→ Answer for #2: 5,481
---
Problem 3: 72 × 67
Break 72 → 70 + 2
Break 67 → 60 + 7
Partial products:
- 7 × 2 = 14
- 7 × 70 = 490
- 60 × 2 = 120
- 60 × 70 = 4,200
Add:
14 + 490 = 504
120 + 4,200 = 4,320
Total: 504 + 4,320 = 4,824
Verify:
72 × 67:
72 × 60 = 4,320
72 × 7 = 504
Total: 4,320 + 504 = 4,824 ✔️
→ Answer for #3: 4,824
---
Problem 4: 54 × 89
Break 54 → 50 + 4
Break 89 → 80 + 9
Partial products:
- 9 × 4 = 36
- 9 × 50 = 450
- 80 × 4 = 320
- 80 × 50 = 4,000
Add:
36 + 450 = 486
320 + 4,000 = 4,320
Total: 486 + 4,320 = 4,806
Verify:
54 × 89:
54 × 80 = 4,320
54 × 9 = 486
Total: 4,320 + 486 = 4,806 ✔️
→ Answer for #4: 4,806
---
Problem 5: 24 × 68
Break 24 → 20 + 4
Break 68 → 60 + 8
Partial products:
- 8 × 4 = 32
- 8 × 20 = 160
- 60 × 4 = 240
- 60 × 20 = 1,200
Add:
32 + 160 = 192
240 + 1,200 = 1,440
Total: 192 + 1,440 = 1,632
Verify:
24 × 68:
24 × 60 = 1,440
24 × 8 = 192
Total: 1,440 + 192 = 1,632 ✔️
→ Answer for #5: 1,632
---
Problem 6: 48 × 96
Break 48 → 40 + 8
Break 96 → 90 + 6
Partial products:
- 6 × 8 = 48
- 6 × 40 = 240
- 90 × 8 = 720
- 90 × 40 = 3,600
Add:
48 + 240 = 288
720 + 3,600 = 4,320
Total: 288 + 4,320 = 4,608
Verify:
48 × 96:
48 × 90 = 4,320
48 × 6 = 288
Total: 4,320 + 288 = 4,608 ✔️
→ Answer for #6: 4,608
---
✔ Set B2 Answers:
1. (Already done: 2,660)
2. 5,481
3. 4,824
4. 4,806
5. 1,632
6. 4,608
---
Final Answer:
Set A1:
1. B
2. C
3. D
4. C
Set B2:
1. 2,660
2. 5,481
3. 4,824
4. 4,806
5. 1,632
6. 4,608
---
Set A1: Area Model Multiplication
---
Problem 1: 43 × 32
Break 43 into 40 + 3
Break 32 into 30 + 2
Area model grid:
- Top row: 40 and 3
- Left column: 30 and 2
Fill in the boxes:
- 30 × 40 = 1,200
- 30 × 3 = 90
- 2 × 40 = 80
- 2 × 3 = 6 ← *This box is missing in the image! But we need it.*
Wait — looking at the given grid in Problem 1:
It shows:
```
40 + 3
30 |1200 | 90
+ |-----|----
2 | 80 | ??
```
The bottom-right box (2 × 3) is blank. That should be 6.
Now add all four parts:
1,200 + 90 = 1,290
80 + 6 = 86
Total: 1,290 + 86 = 1,376
Check answer choices:
A. 1,276
B. 1,376 ← ✔
C. 1,266
D. 1,373
→ Answer for #1: B
---
Problem 2: 14 × 45
Break 14 → 10 + 4
Break 45 → 40 + 5
Grid:
```
10 + 4
40 |400 | ???
+ |-----|----
5 |??? | ???
```
We are told top-left is 400 → that’s 40 × 10 ✔️
Now fill rest:
- 40 × 4 = 160
- 5 × 10 = 50
- 5 × 4 = 20
Add them:
400 + 160 = 560
50 + 20 = 70
Total: 560 + 70 = 630
Answer choices:
A. 430
B. 530
C. 630 ← ✔
D. 730
→ Answer for #2: C
---
Problem 3: 25 × 24
Break 25 → 20 + 5
Break 24 → 20 + 4
Grid:
```
20 + 5
20 |??? | ???
+ |-----|----
4 |??? | ???
```
Calculate each part:
- 20 × 20 = 400
- 20 × 5 = 100
- 4 × 20 = 80
- 4 × 5 = 20
Add:
400 + 100 = 500
80 + 20 = 100
Total: 500 + 100 = 600
Answer choices:
A. 580
B. 500
C. 680
D. 600 ← ✔
→ Answer for #3: D
---
Problem 4: 52 × 53
Break 52 → 50 + 2
Break 53 → 50 + 3
Grid:
```
50 + 2
50 |??? | ???
+ |-----|----
3 |??? | ???
```
Parts:
- 50 × 50 = 2,500
- 50 × 2 = 100
- 3 × 50 = 150
- 3 × 2 = 6
Add:
2,500 + 100 = 2,600
150 + 6 = 156
Total: 2,600 + 156 = 2,756
Answer choices:
A. 2,556
B. 2,656
C. 2,756 ← ✔
D. 2,856
→ Answer for #4: C
---
✔ Set A1 Answers:
1. B
2. C
3. D
4. C
---
Set B2: Partial Products Method
We’ll solve each one by breaking down the multiplication using place value.
---
Problem 1: 35 × 76
Already partially filled:
They show:
- 6 × 5 = 30
- 6 × 30 = 180
- 70 × 5 = 350
- 70 × 30 = 2,100
Add them:
30 + 180 = 210
350 + 2,100 = 2,450
Total: 210 + 2,450 = 2,660
But wait — let me double-check:
Actually, 35 × 76:
Standard way:
35 × 70 = 2,450
35 × 6 = 210
Total: 2,450 + 210 = 2,660
✔️ Correct.
But since this is just an example (already solved), we move to unsolved ones.
---
Problem 2: 63 × 87
Break 63 → 60 + 3
Break 87 → 80 + 7
Partial products:
- 7 × 3 = 21
- 7 × 60 = 420
- 80 × 3 = 240
- 80 × 60 = 4,800
Add:
21 + 420 = 441
240 + 4,800 = 5,040
Total: 441 + 5,040 = 5,481
Let me verify with standard multiplication:
63 × 87:
63 × 80 = 5,040
63 × 7 = 441
Total: 5,040 + 441 = 5,481 ✔️
→ Answer for #2: 5,481
---
Problem 3: 72 × 67
Break 72 → 70 + 2
Break 67 → 60 + 7
Partial products:
- 7 × 2 = 14
- 7 × 70 = 490
- 60 × 2 = 120
- 60 × 70 = 4,200
Add:
14 + 490 = 504
120 + 4,200 = 4,320
Total: 504 + 4,320 = 4,824
Verify:
72 × 67:
72 × 60 = 4,320
72 × 7 = 504
Total: 4,320 + 504 = 4,824 ✔️
→ Answer for #3: 4,824
---
Problem 4: 54 × 89
Break 54 → 50 + 4
Break 89 → 80 + 9
Partial products:
- 9 × 4 = 36
- 9 × 50 = 450
- 80 × 4 = 320
- 80 × 50 = 4,000
Add:
36 + 450 = 486
320 + 4,000 = 4,320
Total: 486 + 4,320 = 4,806
Verify:
54 × 89:
54 × 80 = 4,320
54 × 9 = 486
Total: 4,320 + 486 = 4,806 ✔️
→ Answer for #4: 4,806
---
Problem 5: 24 × 68
Break 24 → 20 + 4
Break 68 → 60 + 8
Partial products:
- 8 × 4 = 32
- 8 × 20 = 160
- 60 × 4 = 240
- 60 × 20 = 1,200
Add:
32 + 160 = 192
240 + 1,200 = 1,440
Total: 192 + 1,440 = 1,632
Verify:
24 × 68:
24 × 60 = 1,440
24 × 8 = 192
Total: 1,440 + 192 = 1,632 ✔️
→ Answer for #5: 1,632
---
Problem 6: 48 × 96
Break 48 → 40 + 8
Break 96 → 90 + 6
Partial products:
- 6 × 8 = 48
- 6 × 40 = 240
- 90 × 8 = 720
- 90 × 40 = 3,600
Add:
48 + 240 = 288
720 + 3,600 = 4,320
Total: 288 + 4,320 = 4,608
Verify:
48 × 96:
48 × 90 = 4,320
48 × 6 = 288
Total: 4,320 + 288 = 4,608 ✔️
→ Answer for #6: 4,608
---
✔ Set B2 Answers:
1. (Already done: 2,660)
2. 5,481
3. 4,824
4. 4,806
5. 1,632
6. 4,608
---
Final Answer:
Set A1:
1. B
2. C
3. D
4. C
Set B2:
1. 2,660
2. 5,481
3. 4,824
4. 4,806
5. 1,632
6. 4,608
Parent Tip: Review the logic above to help your child master the concept of one digit multiplication area model multiplication worksheet.
