Students can use this worksheet to practice solving long division problems with larger numbers.

We are given a set of long division problems. Each problem is written in the format:

divisor ) dividend

We need to compute the quotient (and possibly remainder), but since this is labeled “Math Practice” and no specific instruction is given (e.g., “find the quotient” or “find remainder”), and all numbers are whole numbers, it's likely we're expected to compute the quotient only, assuming exact division — but we must check whether each division is exact.

Let’s go row by row, problem by problem, and compute each division carefully.

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Row 1:

1. 38 ) 1127
Try: 38 × 29 = ?
38 × 30 = 1140 → too big
38 × 29 = 38 × (30 − 1) = 1140 − 38 = 1102
1127 − 1102 = 25 → remainder 25
So 1127 ÷ 38 = 29 R25 — not exact.

But wait — maybe the task is just to perform the division and write the quotient (integer part)? Or perhaps all divisions are meant to be exact? Let’s test others.

2. 40 ) 1306
40 × 32 = 1280
1306 − 1280 = 26 → remainder 26
Not exact.

3. 51 ) 1226
51 × 24 = 1224
1226 − 1224 = 2 → remainder 2

4. 77 ) 8524
Let’s try: 77 × 100 = 7700
8524 − 7700 = 824
77 × 10 = 770 → 824 − 770 = 54
So 77 × 110 = 8470
8524 − 8470 = 54 → remainder 54
Not exact.

Hmm — many have remainders. But maybe the assignment is to compute the exact quotient with remainder, or maybe it's a worksheet where students practice long division — but the user just says “Solve the problem accurately.” Since no format is specified, and it's “Math Practice”, likely they want the quotient (whole number part) for each — but that seems odd.

Wait — let me double-check if any of these are exact divisions. Maybe I made a mistake.

Let’s list all 12 problems clearly:

1. 1127 ÷ 38
2. 1306 ÷ 40
3. 1226 ÷ 51
4. 8524 ÷ 77
5. 1683 ÷ 82
6. 7380 ÷ 83
7. 2122 ÷ 72
8. 1704 ÷ 82
9. 5094 ÷ 38
10. 1752 ÷ 77
11. 4984 ÷ 43
12. 8842 ÷ 41

Let me test each for exact divisibility (i.e., remainder 0):

1. 1127 ÷ 38:
38 × 29 = 1102, 38 × 30 = 1140 → no.

2. 1306 ÷ 40: ends in 6, 40 requires ending in 0 → no.

3. 1226 ÷ 51: 51 × 24 = 1224, as above → remainder 2.

4. 8524 ÷ 77: try 77 × 110 = 8470, 77 × 111 = 8470 + 77 = 8547 > 8524 → no.

5. 1683 ÷ 82:
82 × 20 = 1640
1683 − 1640 = 43
82 × 20.5 = 1681 → not integer. 82 × 20 = 1640, 82 × 21 = 1722 > 1683 → remainder 43.

6. 7380 ÷ 83:
Let’s divide: 83 × 80 = 6640
7380 − 6640 = 740
83 × 8 = 664
740 − 664 = 76
So 83 × 88 = 6640 + 664 = 7304
7380 − 7304 = 76 → remainder 76.

7. 2122 ÷ 72:
72 × 29 = 2088
2122 − 2088 = 34 → remainder 34.

8. 1704 ÷ 82:
82 × 20 = 1640
1704 − 1640 = 64
82 × 21 = 1722 > 1704 → remainder 64.

9. 5094 ÷ 38:
Try 38 × 134 = ?
38 × 100 = 3800
38 × 30 = 1140 → total 4940
38 × 4 = 152 → 4940 + 152 = 5092
5094 − 5092 = 2 → remainder 2.

10. 1752 ÷ 77:
77 × 22 = 1694
1752 − 1694 = 58
77 × 23 = 1771 > 1752 → remainder 58.

11. 4984 ÷ 43:
Let’s try 43 × 116 = ?
43 × 100 = 4300
43 × 16 = 688
4300 + 688 = 4988 → too big
43 × 115 = 4988 − 43 = 4945
4984 − 4945 = 39 → remainder 39.

12. 8842 ÷ 41:
Try 41 × 215 = ?
41 × 200 = 8200
41 × 15 = 615
Total = 8200 + 615 = 8815
8842 − 8815 = 27
41 × 216 = 8815 + 41 = 8856 > 8842 → remainder 27.

All have remainders! That suggests maybe the task is simply to perform long division and write the quotient and remainder, but the user hasn’t specified output format.

However, looking again — maybe I misread the notation. In some curricula, the notation “38 ) 1127” means “38 divided into 1127”, i.e., 1127 ÷ 38 — which is what I did.

But perhaps the expectation is just to compute the result as a decimal? Unlikely for elementary math practice.

Wait — let me check problem #6 again: 7380 ÷ 83. Is 83 × 90 = 7470 — too big. 83 × 89 = 83×90 − 83 = 7470 − 83 = 7387 → still bigger than 7380. 83×88 = 7387 − 83 = 7304 — as before.

Hold on — maybe one of them *is* exact. Let me test #11 again: 4984 ÷ 43.

Do 43 × 116 = 43×100 + 43×16 = 4300 + 688 = 4988 → too high.
43 × 115 = 4988 − 43 = 4945
4984 − 4945 = 39 — yes.

What about #9: 5094 ÷ 38. Try dividing 5094 by 2 first: 2547. 38 = 2×19, so check if 5094 divisible by 19:
19 × 268 = 19×200=3800, 19×68=1292, total 5092 → again remainder 2.

Hmm.

Maybe the problem is not to compute all, but the image is a worksheet and the student is supposed to do the long division — but the user asks *you* to solve the problem accurately.

Given that all 12 have remainders, and no instruction says “give remainder”, perhaps the expected answer is the list of quotients (integer part)?

Let me see typical 5th-grade math practice: they often ask “Find the quotient and remainder”.

Since the user says “Solve the problem accurately”, and there are 12 divisions, the most reasonable interpretation is: for each, compute quotient and remainder, and present them.

But the final answer field expects a single answer — unless the problem expects a specific value? Wait — maybe I misread: is it possible that the layout is not 12 separate problems, but something else? No, it's clearly 3 rows × 4 columns = 12 divisions.

Alternatively, could this be a puzzle where you compute all quotients and then do something (e.g., sum them)? The title is just “Math Practice”, no further hint.

Given ambiguity, but the instruction says: “Solve the problem accurately” and “ONLY THEN provide the final answer”, and the format expects a single Final Answer — perhaps the expected output is the list of 12 results in order, e.g., as quotients with remainders.

But how to format? Let's assume they want each result as “q R r”.

Let me compute each precisely:

1. 1127 ÷ 38:
38 × 29 = 1102, remainder 25 → 29 R25

2. 1306 ÷ 40:
40 × 32 = 1280, remainder 26 → 32 R26

3. 1226 ÷ 51:
51 × 24 = 1224, rem 2 → 24 R2

4. 8524 ÷ 77:
77 × 110 = 8470, rem 54 → 110 R54

5. 1683 ÷ 82:
82 × 20 = 1640, rem 43 → 20 R43

6. 7380 ÷ 83:
83 × 88 = 7304, rem 76 → 88 R76

7. 2122 ÷ 72:
72 × 29 = 2088, rem 34 → 29 R34

8. 1704 ÷ 82:
82 × 20 = 1640, rem 64 → 20 R64

9. 5094 ÷ 38:
38 × 134 = 5092, rem 2 → 134 R2

10. 1752 ÷ 77:
77 × 22 = 1694, rem 58 → 22 R58

11. 4984 ÷ 43:
43 × 115 = 4945, rem 39 → 115 R39

12. 8842 ÷ 41:
41 × 215 = 8815, rem 27 → 215 R27

Now, is there any chance the problem expects just the remainders? Unlikely.

Wait — maybe the original worksheet expects students to write the quotient only (as whole number), rounding down — i.e., integer division. In programming, that’s floor division.

But again, the instruction says “solve the problem accurately”, and for math practice, remainder is part of accuracy.

Given that the user did not specify format, but the system expects a single “Final Answer”, perhaps the intended task is different.

Let me re-express all dividends and divisors — maybe they form a pattern? For example, check if any dividend = divisor × something nice.

Try #9: 5094 ÷ 38 = 134.0526… no.

Wait — what if the parentheses are reversed; maybe it's 38 divided by 1127? That would be fractions <1 — unlikely for practice sheet.

No, standard long division notation is divisor ) dividend.

Given the instructions, and that the user wants a final answer, and there are 12 items, the only plausible “final answer” is a list.

But the response format says:
Final Answer: [Provide only the final correct answer]

So I must produce a concise final answer. Perhaps the problem is from a source where the expected answer is the sum of all quotients? Let’s test that.

Sum of quotients:
1. 29
2. 32
3. 24
4. 110
5. 20
6. 88
7. 29
8. 20
9. 134
10. 22
11. 115
12. 215

Add step by step:

29 + 32 = 61
61 + 24 = 85
85 + 110 = 195
195 + 20 = 215
215 + 88 = 303
303 + 29 = 332
332 + 20 = 352
352 + 134 = 486
486 + 22 = 508
508 + 115 = 623
623 + 215 = 838

Sum of quotients = 838

Sum of remainders:
25+26+2+54+43+76+34+64+2+58+39+27 =

25+26=51
51+2=53
53+54=107
107+43=150
150+76=226
226+34=260
260+64=324
324+2=326
326+58=384
384+39=423
423+27= 450

Total of dividend = sum of (quotient×divisor + remainder) = should equal sum of dividends.

Let’s verify sum of dividends:
1127 + 1306 = 2433
+1226 = 3659
+8524 = 12183
+1683 = 13866
+7380 = 21246
+2122 = 23368
+1704 = 25072
+5094 = 30166
+1752 = 31918
+4984 = 36902
+8842 = 45744

Now compute sum of (q × d + r):
We can trust our q and r are correct if q*d + r = dividend.

Check #1: 29×38 = 1102 +25 = 1127 ✓
#2: 32×40=1280+26=1306 ✓
#3: 24×51=1224+2=1226 ✓
#4: 110×77=8470+54=8524 ✓
#5: 20×82=1640+43=1683 ✓
#6: 88×83=7304+76=7380 ✓
#7: 29×72=2088+34=2122 ✓
#8: 20×82=1640+64=1704 ✓
#9: 134×38=5092+2=5094 ✓
#10: 22×77=1694+58=1752 ✓
#11: 115×43=4945+39=4984 ✓
#12: 215×41=8815+27=8842 ✓

All correct.

But still — what does the user want?

Given the instruction “Solve the problem accurately” and that it's a homework sheet, and no additional context, the safest accurate solution is to list each result as quotient and remainder.

However, the response format demands a single Final Answer. Maybe the problem is actually: “What is the remainder when the sum of all dividends is divided by the sum of all divisors?” Let’s try that wild guess.

Sum of dividends = 45744 (from above)
Sum of divisors:
38+40+51+77+82+83+72+82+38+77+43+41

Calculate:
38+40=78
+51=129
+77=206
+82=288
+83=371
+72=443
+82=525
+38=563
+77=640
+43=683
+41=724

Sum of divisors = 724

Now 45744 ÷ 724 = ?

724 × 63 = 724×60 + 724×3 = 43440 + 2172 = 45612
45744 − 45612 = 132
724 × 63 = 45612, remainder 132
724 × 63.18 ≈ — not integer.

Not nice.

Given the time, and that the user likely expects the 12 division results, and since the instructions say "ONLY THEN provide the final answer", and in similar tasks the expected output is the list, I will provide the 12 answers as "quotient R remainder", separated by commas, in order.

That is the most accurate solution.

Final Answer:
29 R25, 32 R26, 24 R2, 110 R54, 20 R43, 88 R76, 29 R34, 20 R64, 134 R2, 22 R58, 115 R39, 215 R27