Division worksheet using the area model to find quotients.

You're working on a division worksheet that asks you to use the area model (also called the “box method” or “partial quotients”) to find the quotient and remainder for each problem.

The area model breaks the dividend into parts (hundreds, tens, ones), divides each part by the divisor, and adds up the partial quotients to get the total quotient. Any leftover amount is the remainder.

Let’s solve each problem step-by-step using the area model.

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Problem 1: 868 ÷ 4

Break 868 into: 800 + 60 + 8

- 800 ÷ 4 = 200
- 60 ÷ 4 = 15
- 8 ÷ 4 = 2

Add partial quotients: 200 + 15 + 2 = 217

✔ Answer: 217 R 0

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Problem 2: 365 ÷ 5

Break 365 into: 300 + 60 + 5

- 300 ÷ 5 = 60
- 60 ÷ 5 = 12
- 5 ÷ 5 = 1

Add: 60 + 12 + 1 = 73

✔ Answer: 73 R 0

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Problem 3: 567 ÷ 2

Break 567 into: 500 + 60 + 7

- 500 ÷ 2 = 250
- 60 ÷ 2 = 30
- 7 ÷ 2 = 3 with remainder 1 → So we write 3, and carry the 1 as remainder

Total quotient: 250 + 30 + 3 = 283, remainder 1

✔ Answer: 283 R 1

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Problem 4: 449 ÷ 9

Break 449 into: 400 + 40 + 9

- 400 ÷ 9 → 9 × 44 = 396 → so 44, remainder 4 → but let’s break it differently for easier area model:

Better to break as: 360 + 80 + 9? Or stick to place value:

Actually, standard area model uses hundreds, tens, ones.

So:

- 400 ÷ 9 → 9 × 44 = 396 → too messy. Let's do:

Use place value:

- 400 ÷ 9 = 44 with remainder 4 → but we want to keep it simple.

Alternative approach (common in area model):

Divide 400 → 9 × 40 = 360 → subtract → remainder 40 → bring down next digit? Wait — this is area model, not long division.

In area model, we can choose convenient chunks.

Let’s do:

- 449 = 450 - 1 → but that’s not helpful.

Try:

- 9 × 40 = 360 → 449 - 360 = 89
- 9 × 9 = 81 → 89 - 81 = 8
- So total quotient = 40 + 9 = 49, remainder 8

But using strict place value:

Break 449 as 400 + 40 + 9

- 400 ÷ 9 → 44 (since 9×44=396), remainder 4 → then add 40 → 44 → 44 ÷ 9 = 4, remainder 8 → then add 9 → 17 → 17 ÷ 9 = 1, remainder 8 → messy.

Easier way: Use the largest easy multiples.

In area model, you can pick any chunks — but since the worksheet has boxes labeled “00”, “0”, “+”, it implies breaking into hundreds, tens, ones.

So:

- Hundreds: 400 ÷ 9 → 9 × 40 = 360 → write 40, remainder 40 → now combine with tens: 40 + 40 = 80
- Tens: 80 ÷ 9 → 9 × 8 = 72 → write 8, remainder 8 → now combine with ones: 8 + 9 = 17
- Ones: 17 ÷ 9 → 9 × 1 = 9 → write 1, remainder 8

Total quotient: 40 + 8 + 1 = 49, remainder 8

✔ Answer: 49 R 8

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Problem 5: 785 ÷ 7

Break 785 into: 700 + 80 + 5

- 700 ÷ 7 = 100
- 80 ÷ 7 = 11 (since 7×11=77), remainder 3 → then add 5 → 8
- 8 ÷ 7 = 1, remainder 1

Total quotient: 100 + 11 + 1 = 112, remainder 1

✔ Answer: 112 R 1

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Problem 6: 878 ÷ 2

Break 878 into: 800 + 70 + 8

- 800 ÷ 2 = 400
- 70 ÷ 2 = 35
- 8 ÷ 2 = 4

Add: 400 + 35 + 4 = 439

✔ Answer: 439 R 0

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Problem 7: 403 ÷ 3

Break 403 into: 400 + 0 + 3 → or better: 300 + 100 + 3

- 300 ÷ 3 = 100
- 100 ÷ 3 = 33 (since 3×33=99), remainder 1 → then add 3 → 4
- 4 ÷ 3 = 1, remainder 1

Total quotient: 100 + 33 + 1 = 134, remainder 1

✔ Answer: 134 R 1

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Problem 8: 765 ÷ 6

Break 765 into: 700 + 60 + 5

- 700 ÷ 6 → 6 × 116 = 696 → too big. Better:

Use:

- 600 ÷ 6 = 100
- 165 left → 165 = 120 + 45 → 120 ÷ 6 = 20, 45 ÷ 6 = 7 R 3 → total 100+20+7=127 R 3

Or via place value:

- 700 ÷ 6 = 116 R 4 → then 4 + 60 = 64 → 64 ÷ 6 = 10 R 4 → then 4 + 5 = 9 → 9 ÷ 6 = 1 R 3 → total quotient 116+10+1=127 R 3

✔ Answer: 127 R 3

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## ✔ Final Answers:

| Problem | Quotient | Remainder |
|---------|----------|---------|
| 1 | 217 | 0 |
| 2 | 73 | 0 |
| 3 | 283 | 1 |
| 4 | 49 | 8 |
| 5 | 112 | 1 |
| 6 | 439 | 0 |
| 7 | 134 | 1 |
| 8 | 127 | 3 |

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## 💡 How to Fill the Area Model Boxes:

For each problem, the box is divided into 3 sections for hundreds, tens, and ones.

Example for #1: 868 ÷ 4

Top row: 800 + 60 + 8
Bottom row:
- Under 800 → write 200 (because 800 ÷ 4 = 200)
- Under 60 → write 15 (because 60 ÷ 4 = 15)
- Under 8 → write 2 (because 8 ÷ 4 = 2)

Then sum: 200 + 15 + 2 = 217 → no remainder.

Similarly for others.

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Let me know if you’d like to see the filled-in boxes visually!