5-Digit by 3-Digit Long Division with Remainders and Steps Shown ... - Free Printable

Let’s solve each division problem step by step. We’ll do long division for each one, carefully checking our work.

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Problem 1: 52222 ÷ 323

We want to find how many times 323 fits into 52222.

Step 1: Look at first few digits of 52222 — start with 522 (since 323 is 3-digit).

323 × 1 = 323 → too small
323 × 2 = 646 → too big (bigger than 522)
So, use 1. Write 1 above the third digit (hundreds place).

Subtract: 522 - 323 = 199

Bring down next digit: 2 → now we have 1992

Step 2: How many times does 323 go into 1992?

Try 323 × 6 = 1938
323 × 7 = 2261 → too big

So, 6. Write 6 above the tens place.

Subtract: 1992 - 1938 = 54

Bring down last digit: 2 → now we have 542

Step 3: How many times does 323 go into 542?

323 × 1 = 323
323 × 2 = 646 → too big

So, 1. Write 1 above the ones place.

Subtract: 542 - 323 = 219

No more digits to bring down. So remainder is 219.

But wait — let’s check if we did this right. Maybe we made a mistake in placement.

Actually, let’s try multiplying 323 × 161:

323 × 100 = 32300
323 × 60 = 19380 → total so far: 32300 + 19380 = 51680
323 × 1 = 323 → total: 51680 + 323 = 52003

But 52222 - 52003 = 219 → same as before.

Wait — that means quotient is 161 with remainder 219? But let’s double-check with calculator-style thinking.

Actually, maybe I miscounted positions. Let me redo it properly.

Better approach: Use estimation.

323 × 160 = 323 × 100 + 323 × 60 = 32300 + 19380 = 51680
52222 - 51680 = 542
Now 323 × 1 = 323 → 542 - 323 = 219 → still remainder 219.

So quotient is 161, remainder 219.

But the problem says “calculate each quotient” — probably expects exact decimal or just integer part? In school math, often they want whole number quotient and remainder, or sometimes decimal.

Looking at other problems — likely they expect full division including decimals? Or maybe just integer?

Wait — let’s look at another problem to see pattern.

Actually, let’s do all using calculator verification since this is for accuracy.

I’ll compute each one precisely.

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Problem 1: 52222 ÷ 323

Calculate: 52222 ÷ 323

Do division:

323 × 161 = 323×160 + 323 = 51680 + 323 = 52003
52222 - 52003 = 219 → so 161 R219

But perhaps they want decimal? Let’s continue dividing.

Add decimal point and zeros: 52222.000...

After 542, we had 219, bring down 0 → 2190

323 × 6 = 1938
2190 - 1938 = 252 → write .6

Bring down 0 → 2520

323 × 7 = 2261
2520 - 2261 = 259 → write 7 → now .67

Bring down 0 → 2590

323 × 8 = 2584
2590 - 2584 = 6 → write 8 → .678

And so on. But maybe for this worksheet, they just want integer quotient? Let’s check other problems.

Actually, looking at the format — it's standard long division setup, and often in such worksheets, they expect the full quotient including decimal if needed, but sometimes only integer.

To be safe, I'll compute exact value.

But let’s move to next problem and see.

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Problem 2: 34204 ÷ 274

Estimate: 274 × 100 = 27400
34204 - 27400 = 6804

274 × 20 = 5480
6804 - 5480 = 1324

274 × 4 = 1096
1324 - 1096 = 228

So total: 100 + 20 + 4 = 124, remainder 228

Check: 274 × 124 = ?

274 × 100 = 27400
274 × 20 = 5480 → total 32880
274 × 4 = 1096 → total 32880 + 1096 = 33976

34204 - 33976 = 228 → correct.

So quotient 124, remainder 228.

Again, not exact.

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This suggests that these divisions may not come out evenly. But let’s check Problem 3.

Problem 3: 61304 ÷ 148

Try 148 × 400 = 59200
61304 - 59200 = 2104

148 × 14 = 2072 (since 148×10=1480, 148×4=592; 1480+592=2072)

2104 - 2072 = 32

So 400 + 14 = 414, remainder 32

Check: 148 × 414 = 148×400 + 148×14 = 59200 + 2072 = 61272
61304 - 61272 = 32 → correct.

Still remainder.

Perhaps all have remainders? But let’s check one that might divide evenly.

Look at Problem 4: 75574 ÷ 586

Try 586 × 129 = ?

First, 586 × 100 = 58600
586 × 20 = 11720 → total 70320
586 × 9 = 5274 → total 70320 + 5274 = 75594 → too big (75594 > 75574)

Try 586 × 128 = 586×100 + 586×28

586×20=11720, 586×8=4688 → 11720+4688=16408

Total: 58600 + 16408 = 75008

75574 - 75008 = 566

Now 586 × 0.966... but again, not integer.

This is taking too long. Perhaps I should just calculate each one accurately using division algorithm or accept that they may have remainders.

But let’s think differently — maybe the worksheet expects the quotient as a whole number with remainder, or perhaps decimal rounded? But the instruction says "calculate each quotient" — in math, quotient can include decimal.

However, in elementary school context, often they stop at integer quotient and remainder.

But to be precise, I'll compute the exact decimal for each, but that might be messy.

Alternatively, let's use a different strategy: since this is for a student, and the problems are designed to be solvable, perhaps some divide evenly.

Let me try Problem 5: 26846 ÷ 144

144 × 186 = ?

144 × 180 = 25920
144 × 6 = 864
Total 25920 + 864 = 26784

26846 - 26784 = 62 → not even.

Problem 6: 63885 ÷ 851

851 × 75 = 851×70 + 851×5 = 59570 + 4255 = 63825

63885 - 63825 = 60 → not even.

Problem 7: 80658 ÷ 886

886 × 91 = 886×90 + 886×1 = 79740 + 886 = 80626

80658 - 80626 = 32 → not even.

Problem 8: 57062 ÷ 351

351 × 162 = 351×160 + 351×2 = 56160 + 702 = 56862

57062 - 56862 = 200 → not even.

Problem 9: 77127 ÷ 567

567 × 136 = 567×100=56700, 567×36= let's compute 567×30=17010, 567×6=3402, total 17010+3402=20412, so 56700+20412=77112

77127 - 77112 = 15 → not even.

So none of them divide evenly? That seems odd for a worksheet. Perhaps I made a mistake.

Let me double-check Problem 1: 52222 ÷ 323

Let me do proper long division.

_______
323 ) 52222

323 goes into 522 once (323*1=323), subtract from 522: 522-323=199

Bring down 2 -> 1992

323 goes into 1992 six times (323*6=1938), subtract: 1992-1938=54

Bring down 2 -> 542

323 goes into 542 once (323*1=323), subtract: 542-323=219

So quotient is 161, remainder 219.

Similarly for others.

Perhaps the worksheet allows remainders, or wants the answer as mixed number, but typically in such formats, they might expect the quotient as integer and remainder, or perhaps decimal.

But the instruction says "calculate each quotient", and in mathematics, quotient can be the result of division, which may be decimal.

For example, 52222 ÷ 323 = 161.678... etc.

But for a student, it might be better to provide the integer quotient and remainder.

However, looking at the source "Math-Drills.com", these worksheets usually expect the full division with decimal or just the integer part.

Upon second thought, in many such worksheets, they design problems that divide evenly. Did I miscalculate?

Let me try Problem 3 again: 61304 ÷ 148

148 * 414 = as before 61272, difference 32.

But 148 * 414.216... not nice.

Another idea: perhaps I should calculate each one and round to nearest whole number, but that doesn't make sense.

Let's list all and compute accurately.

I recall that in some cases, the divisor and dividend are chosen so that it divides evenly. Let me verify with actual calculation.

Use calculator simulation:

1. 52222 ÷ 323 = 161.6780185758514 → approximately 161.68, but not integer.

2. 34204 ÷ 274 = 124.83211678832117 → 124.83

3. 61304 ÷ 148 = 414.2162162162162 → 414.22

4. 75574 ÷ 586 = 128.96587030716724 → 128.97

5. 26846 ÷ 144 = 186.43055555555554 → 186.43

6. 63885 ÷ 851 = 75.0705052878966 → 75.07

7. 80658 ÷ 886 = 91.03611738149097 → 91.04

8. 57062 ÷ 351 = 162.56980056980057 → 162.57

9. 77127 ÷ 567 = 136.02645502645503 → 136.03

None are integers. This is strange for a drill sheet.

Perhaps the worksheet is for practicing long division with remainders, and they want the quotient as integer and remainder.

In that case, for each, we can give quotient and remainder.

Or perhaps "quotient" here means the integer part.

Given that, and to match typical school expectations, I'll provide the integer quotient and remainder for each.

Let's do that systematically.

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Final Calculations with Remainder:

1. 52222 ÷ 323
Quotient: 161, Remainder: 219
Because 323 × 161 = 52003, 52222 - 52003 = 219

2. 34204 ÷ 274
Quotient: 124, Remainder: 228
274 × 124 = 33976, 34204 - 33976 = 228

3. 61304 ÷ 148
Quotient: 414, Remainder: 32
148 × 414 = 61272, 61304 - 61272 = 32

4. 75574 ÷ 586
Quotient: 128, Remainder: 566
586 × 128 = 75008, 75574 - 75008 = 566

5. 26846 ÷ 144
Quotient: 186, Remainder: 62
144 × 186 = 26784, 26846 - 26784 = 62

6. 63885 ÷ 851
Quotient: 75, Remainder: 60
851 × 75 = 63825, 63885 - 63825 = 60

7. 80658 ÷ 886
Quotient: 91, Remainder: 32
886 × 91 = 80626, 80658 - 80626 = 32

8. 57062 ÷ 351
Quotient: 162, Remainder: 200
351 × 162 = 56862, 57062 - 56862 = 200

9. 77127 ÷ 567
Quotient: 136, Remainder: 15
567 × 136 = 77112, 77127 - 77112 = 15

All verified.

Since the problem says "calculate each quotient", and in many contexts, especially with long division setup, they might expect the full answer including remainder, or perhaps just the quotient number.

But to be safe, and since the user didn't specify, I'll provide the integer quotient for each, as that is commonly what is asked in such drills when remainders are present.

However, upon checking online or standard practice, for "5-digit by 3-digit division", they often include the remainder or expect the decimal.

But given the format, and to keep it simple for a student, I'll box the integer quotient for each.

Alternatively, perhaps the worksheet has a typo, but I think for this purpose, providing the quotient as integer is fine.

Let's see the title: "5-Digit by 3-Digit Division (A)" — likely from Math-Drills, and their worksheets usually have answers with remainders or decimals.

But since the user said "solve the problem accurately", and to avoid confusion, I'll provide the exact quotient as a decimal rounded to two places, but that might not be accurate.

Another idea: perhaps "quotient" here means the result of the division, so I should give the full decimal.

But for a student, it might be overwhelming.

I recall that in some systems, they write the quotient as a mixed number, but that's rare.

Perhaps for this response, since it's for homework help, I'll provide the integer quotient and mention the remainder, but the final answer should be concise.

Looking back at the user's request: "Solve the problem accurately." and "provide only the final correct answer" after reasoning.

Also, the options are false, so no explanation needed in output, but I need to reason first.

In the final answer, I should list the quotients.

Perhaps the expected answer is the integer part of the quotient for each.

I think that's standard.

So I'll go with that.

Final Answer for each:

1. 161
2. 124
3. 414
4. 128
5. 186
6. 75
7. 91
8. 162
9. 136

But to be thorough, let's confirm one more time with a reliable method.

For example, Problem 9: 77127 ÷ 567

567 * 136 = let's calculate: 500*136=68000, 67*136.

67*100=6700, 67*36=2412, so 6700+2412=9112, total 68000+9112=77112, yes, 77127-77112=15, so quotient 136.

Similarly, all are correct.

So for the final answer, I'll list the integer quotients.

If the worksheet expects something else, but based on common practice, this should be fine.

Perhaps they want the full division result, but I think for now, this is acceptable.

So Final Answer will be the list of quotients.

To present it clearly.