Three-digit by One-digit Box Method Divisions With No Remainders ... - Free Printable
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Step-by-step solution for: Three-digit by One-digit Box Method Divisions With No Remainders ...
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Show Answer Key & Explanations
Step-by-step solution for: Three-digit by One-digit Box Method Divisions With No Remainders ...
Let’s solve each division problem using the Box Method (also called Area Model). This method breaks the big number into smaller, easier parts that are divisible by the one-digit number. Since there are no remainders, every part will divide evenly.
We’ll go step by step for each problem.
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Break 932 into parts that are easy to divide by 4:
- 800 ÷ 4 = 200
- 120 ÷ 4 = 30
- 12 ÷ 4 = 3
Add them: 200 + 30 + 3 = 233
✔ Check: 4 × 233 = 932 → Correct!
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Break 768:
- 720 ÷ 8 = 90
- 48 ÷ 8 = 6
Add: 90 + 6 = 96
✔ Check: 8 × 96 = 768 → Correct!
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Break 782:
- 700 ÷ 2 = 350
- 80 ÷ 2 = 40
- 2 ÷ 2 = 1
Add: 350 + 40 + 1 = 391
✔ Check: 2 × 391 = 782 → Correct!
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9 × 29 = 261 → remainder 2 → But the worksheet says “With No Remainders” — so maybe it’s a typo? Let’s double-check the image.
Looking back at the right sheet: Problem 4 is written as “9 | 263” — but 263 ÷ 9 does NOT divide evenly. However, looking closely at the original image, it might be 261 instead of 263? Because 261 ÷ 9 = 29 exactly.
Wait — let me re-examine the user’s image description. The user wrote:
> 4. 9 | 263
> 5. 9 | 990
> 6. 7 | 616
But 263 ÷ 9 leaves remainder 2. That contradicts “With No Remainders”.
However, in many worksheets, sometimes numbers are misread. Let’s assume it’s 261 (which is divisible by 9) because otherwise it breaks the rule.
Alternatively, perhaps it’s 270 - 9 = 261? Or maybe it’s a mistake.
Wait — let’s calculate 9 × 29 = 261, 9 × 30 = 270 → 263 is not divisible.
But looking again at the left sheet, problem 10 is 120 ÷ ? — wait no, left sheet has 10 problems too.
Actually, let’s look at the right sheet again — problem 4 is labeled “4. 9 | 263” — but perhaps it’s 261? Or maybe I should proceed with what’s written and see.
Wait — another thought: Maybe it’s 263 and we’re supposed to do box method even if remainder? But title says “With No Remainders”.
This is confusing. Let me check other problems first.
Problem 5: 990 ÷ 9 = 110 → easy.
Problem 6: 616 ÷ 7 → 7×88=616 → yes.
Problem 7: 180 ÷ 6 = 30
Problem 8: 348 ÷ 6 → 6×58=348 → yes
Problem 9: 105 ÷ 5 = 21
So only problem 4 seems off.
Perhaps it’s a typo and should be 261? Because 2+6+1=9 → divisible by 9.
Or maybe 270? But 270÷9=30.
Given the context, I think it’s likely 261. I’ll proceed with 261 ÷ 9 = 29
If it’s really 263, then it doesn’t fit the worksheet’s promise. So I’ll assume typo and use 261.
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Break 261:
- 180 ÷ 9 = 20
- 81 ÷ 9 = 9
Add: 20 + 9 = 29
✔ Check: 9 × 29 = 261 → Correct!
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Break 990:
- 900 ÷ 9 = 100
- 90 ÷ 9 = 10
Add: 100 + 10 = 110
✔ Check: 9 × 110 = 990 → Correct!
---
Break 616:
- 560 ÷ 7 = 80
- 56 ÷ 7 = 8
Add: 80 + 8 = 88
✔ Check: 7 × 88 = 616 → Correct!
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Break 180:
- 180 ÷ 6 = 30 → or break into 120 + 60 → 120÷6=20, 60÷6=10 → 20+10=30
✔ Answer: 30
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Break 348:
- 300 ÷ 6 = 50
- 48 ÷ 6 = 8
Add: 50 + 8 = 58
✔ Check: 6 × 58 = 348 → Correct!
---
Break 105:
- 100 ÷ 5 = 20
- 5 ÷ 5 = 1
Add: 20 + 1 = 21
✔ Check: 5 × 21 = 105 → Correct!
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Now, let’s also quickly verify the left sheet problems since they were included.
Left Sheet:
1. 912 ÷ 4 → 900÷4=225, 12÷4=3 → 228? Wait, better: 800÷4=200, 112÷4=28 → 200+28=228 → 4×228=912 ✔
2. 1161 ÷ 3 → 900÷3=300, 261÷3=87 → 300+87=387 → 3×387=1161 ✔
3. 782 ÷ 2 → same as right sheet #3 → 391 ✔
4. 765 ÷ 5 → 750÷5=150, 15÷5=3 → 153 → 5×153=765 ✔
5. 848 ÷ 8 → 800÷8=100, 48÷8=6 → 106 → 8×106=848 ✔
6. 816 ÷ 6 → 600÷6=100, 216÷6=36 → 136 → 6×136=816 ✔
7. 318 ÷ 3 → 300÷3=100, 18÷3=6 → 106 → 3×106=318 ✔
8. 514 ÷ 2 → 500÷2=250, 14÷2=7 → 257 → 2×257=514 ✔
9. 328 ÷ 4 → 320÷4=80, 8÷4=2 → 82 → 4×82=328 ✔
10. 120 ÷ ? — wait, it says “10. 120” — probably 120 ÷ something? Looking at format, likely 120 ÷ 6 or similar? But not specified. In the image, it might be 120 ÷ 6? But let’s skip since not clear.
Actually, in the left sheet, problem 10 is just “10. 120” with three boxes — probably meant to be divided by a single digit. Common would be 120 ÷ 6 = 20, or 120 ÷ 5 = 24, etc. But since not specified, and right sheet is main focus, I’ll stick to right sheet.
---
Final Answers for Right Sheet (as per standard interpretation):
1. 932 ÷ 4 = 233
2. 768 ÷ 8 = 96
3. 782 ÷ 2 = 391
4. 261 ÷ 9 = 29 *(assuming typo from 263)*
5. 990 ÷ 9 = 110
6. 616 ÷ 7 = 88
7. 180 ÷ 6 = 30
8. 348 ÷ 6 = 58
9. 105 ÷ 5 = 21
---
Final Answer:
1. 233
2. 96
3. 391
4. 29
5. 110
6. 88
7. 30
8. 58
9. 21
We’ll go step by step for each problem.
---
Problem 1: 932 ÷ 4
Break 932 into parts that are easy to divide by 4:
- 800 ÷ 4 = 200
- 120 ÷ 4 = 30
- 12 ÷ 4 = 3
Add them: 200 + 30 + 3 = 233
✔ Check: 4 × 233 = 932 → Correct!
---
Problem 2: 768 ÷ 8
Break 768:
- 720 ÷ 8 = 90
- 48 ÷ 8 = 6
Add: 90 + 6 = 96
✔ Check: 8 × 96 = 768 → Correct!
---
Problem 3: 782 ÷ 2
Break 782:
- 700 ÷ 2 = 350
- 80 ÷ 2 = 40
- 2 ÷ 2 = 1
Add: 350 + 40 + 1 = 391
✔ Check: 2 × 391 = 782 → Correct!
---
Problem 4: 263 ÷ 9 → Wait! Let’s check if this divides evenly.
9 × 29 = 261 → remainder 2 → But the worksheet says “With No Remainders” — so maybe it’s a typo? Let’s double-check the image.
Looking back at the right sheet: Problem 4 is written as “9 | 263” — but 263 ÷ 9 does NOT divide evenly. However, looking closely at the original image, it might be 261 instead of 263? Because 261 ÷ 9 = 29 exactly.
Wait — let me re-examine the user’s image description. The user wrote:
> 4. 9 | 263
> 5. 9 | 990
> 6. 7 | 616
But 263 ÷ 9 leaves remainder 2. That contradicts “With No Remainders”.
However, in many worksheets, sometimes numbers are misread. Let’s assume it’s 261 (which is divisible by 9) because otherwise it breaks the rule.
Alternatively, perhaps it’s 270 - 9 = 261? Or maybe it’s a mistake.
Wait — let’s calculate 9 × 29 = 261, 9 × 30 = 270 → 263 is not divisible.
But looking again at the left sheet, problem 10 is 120 ÷ ? — wait no, left sheet has 10 problems too.
Actually, let’s look at the right sheet again — problem 4 is labeled “4. 9 | 263” — but perhaps it’s 261? Or maybe I should proceed with what’s written and see.
Wait — another thought: Maybe it’s 263 and we’re supposed to do box method even if remainder? But title says “With No Remainders”.
This is confusing. Let me check other problems first.
Problem 5: 990 ÷ 9 = 110 → easy.
Problem 6: 616 ÷ 7 → 7×88=616 → yes.
Problem 7: 180 ÷ 6 = 30
Problem 8: 348 ÷ 6 → 6×58=348 → yes
Problem 9: 105 ÷ 5 = 21
So only problem 4 seems off.
Perhaps it’s a typo and should be 261? Because 2+6+1=9 → divisible by 9.
Or maybe 270? But 270÷9=30.
Given the context, I think it’s likely 261. I’ll proceed with 261 ÷ 9 = 29
If it’s really 263, then it doesn’t fit the worksheet’s promise. So I’ll assume typo and use 261.
---
Problem 4 (assumed): 261 ÷ 9
Break 261:
- 180 ÷ 9 = 20
- 81 ÷ 9 = 9
Add: 20 + 9 = 29
✔ Check: 9 × 29 = 261 → Correct!
---
Problem 5: 990 ÷ 9
Break 990:
- 900 ÷ 9 = 100
- 90 ÷ 9 = 10
Add: 100 + 10 = 110
✔ Check: 9 × 110 = 990 → Correct!
---
Problem 6: 616 ÷ 7
Break 616:
- 560 ÷ 7 = 80
- 56 ÷ 7 = 8
Add: 80 + 8 = 88
✔ Check: 7 × 88 = 616 → Correct!
---
Problem 7: 180 ÷ 6
Break 180:
- 180 ÷ 6 = 30 → or break into 120 + 60 → 120÷6=20, 60÷6=10 → 20+10=30
✔ Answer: 30
---
Problem 8: 348 ÷ 6
Break 348:
- 300 ÷ 6 = 50
- 48 ÷ 6 = 8
Add: 50 + 8 = 58
✔ Check: 6 × 58 = 348 → Correct!
---
Problem 9: 105 ÷ 5
Break 105:
- 100 ÷ 5 = 20
- 5 ÷ 5 = 1
Add: 20 + 1 = 21
✔ Check: 5 × 21 = 105 → Correct!
---
Now, let’s also quickly verify the left sheet problems since they were included.
Left Sheet:
1. 912 ÷ 4 → 900÷4=225, 12÷4=3 → 228? Wait, better: 800÷4=200, 112÷4=28 → 200+28=228 → 4×228=912 ✔
2. 1161 ÷ 3 → 900÷3=300, 261÷3=87 → 300+87=387 → 3×387=1161 ✔
3. 782 ÷ 2 → same as right sheet #3 → 391 ✔
4. 765 ÷ 5 → 750÷5=150, 15÷5=3 → 153 → 5×153=765 ✔
5. 848 ÷ 8 → 800÷8=100, 48÷8=6 → 106 → 8×106=848 ✔
6. 816 ÷ 6 → 600÷6=100, 216÷6=36 → 136 → 6×136=816 ✔
7. 318 ÷ 3 → 300÷3=100, 18÷3=6 → 106 → 3×106=318 ✔
8. 514 ÷ 2 → 500÷2=250, 14÷2=7 → 257 → 2×257=514 ✔
9. 328 ÷ 4 → 320÷4=80, 8÷4=2 → 82 → 4×82=328 ✔
10. 120 ÷ ? — wait, it says “10. 120” — probably 120 ÷ something? Looking at format, likely 120 ÷ 6 or similar? But not specified. In the image, it might be 120 ÷ 6? But let’s skip since not clear.
Actually, in the left sheet, problem 10 is just “10. 120” with three boxes — probably meant to be divided by a single digit. Common would be 120 ÷ 6 = 20, or 120 ÷ 5 = 24, etc. But since not specified, and right sheet is main focus, I’ll stick to right sheet.
---
Final Answers for Right Sheet (as per standard interpretation):
1. 932 ÷ 4 = 233
2. 768 ÷ 8 = 96
3. 782 ÷ 2 = 391
4. 261 ÷ 9 = 29 *(assuming typo from 263)*
5. 990 ÷ 9 = 110
6. 616 ÷ 7 = 88
7. 180 ÷ 6 = 30
8. 348 ÷ 6 = 58
9. 105 ÷ 5 = 21
---
Final Answer:
1. 233
2. 96
3. 391
4. 29
5. 110
6. 88
7. 30
8. 58
9. 21
Parent Tip: Review the logic above to help your child master the concept of division worksheet with boxes.
