3 Digit by 2 Digit Box Method Division Worksheets: 5th Grade Division With and Without Remainders - Free Printable

Let’s solve each division problem using the box method (also called partial quotients). We’ll break down how many times the divisor fits into parts of the dividend, subtract, and keep going until we can’t divide anymore. The leftover is the remainder.

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Problem 1: 210 ÷ 12

We ask: How many times does 12 go into 210?

- 12 × 0 = 0 → subtract from 210? Not helpful yet.
- Try 12 × 10 = 120 → too small? Let’s try bigger.
Actually, let’s follow the box steps shown:

Step-by-step as in the answer key:

First box:
12 goes into 21 once? Wait — actually, they started with 0? That seems odd. Let me recalculate properly.

Wait — looking at the provided answer key, it shows:

For 210 ÷ 12:

They did:
- First: 12 × 0 = 0 → 210 - 0 = 210? No, that doesn’t make sense.

Actually, looking again — the boxes show:

Box 1: 12 into 21 → 1 time? But they wrote 0? Hmm.

Wait — perhaps they’re breaking 210 into chunks.

Let me do it correctly:

We want to divide 210 by 12.

How many times does 12 go into 210?

Try 12 × 10 = 120 → 210 - 120 = 90
Then 12 × 7 = 84 → 90 - 84 = 6
Total quotient = 10 + 7 = 17, remainder 6 → ✔ matches answer key: 17 R6

But in their box method, they showed:

Top row: 0, 1, 7 → maybe representing place values?

Actually, looking at the grid:

It says:

```
0 1 7
12 | 2 21 90
-0 -12 -84
2 9 6
```

This seems like they are doing digit-by-digit or chunking differently.

Actually, this might be a misalignment. Let me reinterpret.

Perhaps they mean:

Start with 210.

Divide 210 by 12.

They took 12 × 10 = 120? But they wrote 0 first? Maybe it's a typo or different approach.

Alternatively, maybe they broke 210 as 200 + 10? Not matching.

Wait — look at the subtraction:

First column: 2 - 0 = 2 → then next step 21 - 12 = 9 → then 90 - 84 = 6.

Ah! I think they are treating it as:

Break 210 into hundreds, tens, units? But 210 is 2 hundreds, 1 ten, 0 units? Doesn't fit.

Another idea: Maybe they are doing long division style but in boxes.

Let me just trust the answer key since it’s given, and verify the math.

210 ÷ 12:

12 × 17 = 204 → 210 - 204 = 6 → so 17 R6 → correct.

Similarly for others.

Since the user wants us to solve accurately, and the image contains answer keys, I will verify each one manually.

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Problem 1: 210 ÷ 12

12 × 17 = 204
210 - 204 = 6 → 17 R6 ✔

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Problem 2: 823 ÷ 23

23 × 35 = ?

23 × 30 = 690
23 × 5 = 115
690 + 115 = 805
823 - 805 = 18 → 35 R18 ✔

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Problem 3: 670 ÷ 30

30 × 22 = 660
670 - 660 = 10 → 22 R10 ✔

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Problem 4: 541 ÷ 41

41 × 13 = 533
541 - 533 = 8 → 13 R8 ✔

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Problem 5: 880 ÷ 27

27 × 32 = ?

27 × 30 = 810
27 × 2 = 54
810 + 54 = 864
880 - 864 = 16 → 32 R16 ✔

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Problem 6: 464 ÷ 36

36 × 12 = 432
464 - 432 = 32 → 12 R32 ✔

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Problem 7: 934 ÷ 46

46 × 20 = 920
934 - 920 = 14 → 20 R14 ✔

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Problem 8: 685 ÷ 15

15 × 45 = 675
685 - 675 = 10 → 45 R10 ✔

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All answers match the provided answer key. Since the task was to solve the problems accurately, and we’ve verified each one, here are the final answers.

Final Answer:
1. 17 R6
2. 35 R18
3. 22 R10
4. 13 R8
5. 32 R16
6. 12 R32
7. 20 R14
8. 45 R10