Estimating Quotients worksheet with examples and exercises for students to check and correct estimates.

Let’s go through each problem one by one. We’ll check if the estimate is correct. If it’s not, we’ll fix it.

Remember: Estimating quotients means rounding the numbers to make them easier to divide — usually to the nearest ten or hundred — then dividing those rounded numbers.

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Problem 1: 585 ÷ 29

Given estimate:
- 510 ÷ 30 = 17 → then says 600 ÷ 30 = 20

Wait — they changed the estimate mid-way? Let’s see what makes sense.

Original: 585 ÷ 29
Round 585 → 600 (nearest hundred)
Round 29 → 30 (nearest ten)
So estimated quotient: 600 ÷ 30 = 20

But they wrote “= 17” first — that was from 510 ÷ 30, which is NOT a good round of 585. So their first step is wrong.

✔ Correct estimation: 600 ÷ 30 = 20 → so final answer should be yes, because 20 is correct.

BUT — they wrote two steps and ended with 20. Since the final estimate is correct, we can say yes.

Actually, let’s read the instruction again:
“Check if the given estimates are correct. If it is correct write yes. If not, then write the correct estimation for each.”

They showed:
585 ÷ 29
= 510 ÷ 30 ← this is bad rounding (585 should round to 600, not 510)
= 17 ← wrong
Then they corrected themselves:
= 600 ÷ 30
= 20 ← correct

So overall, they arrived at the right estimate. But the first step was misleading. However, since the final result is correct, we’ll mark it as yes.

Wait — maybe the worksheet expects us to judge the entire process? Let’s look at others.

Actually, looking at the layout, each box has three lines:

Line 1: original problem
Line 2: their estimated division
Line 3: their estimated quotient

In Problem 1, they have:

585 ÷ 29
= 510 ÷ 30
= 17

THEN below that, they have another set:

= 600 ÷ 30
= 20

That seems like they’re showing two different attempts? Or maybe it’s a typo in the worksheet?

Looking at other problems, most have only 3 lines per box. For example:

Problem 2:
143 ÷ 53
= 100 ÷ 50
= 2 ← that’s all

Problem 3:
492 ÷ 41
= 400 ÷ 50
= 8 ← wait, 41 rounds to 40, not 50! That might be wrong.

Ah — I think the worksheet has some errors already built in, and we need to check each one.

Let me re-read the instructions carefully:

> Check if the given estimates are correct. If it is correct write yes. If not, then write the correct estimation for each.

So for each box, we look at what they did and decide if it’s correct.

Let’s go box by box.

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Box 1: 585 ÷ 29

They wrote:
= 510 ÷ 30 = 17 → then also wrote = 600 ÷ 30 = 20

This is confusing. Maybe it’s a formatting error? Perhaps the second part is meant to be the correction? But the instruction says “if not correct, write the correct estimation”.

Since they ended up with 20, which is correct, and 600÷30=20 is valid, I think we can accept it as correct. But strictly speaking, 510 is not a good round of 585. 585 is closer to 600 than 510.

Best approach: The correct estimate is 600 ÷ 30 = 20. They did show that, even if they showed a wrong one first. So perhaps the worksheet intends for us to evaluate the final answer they give.

To avoid confusion, let’s assume that for each box, the last line is their final estimated quotient, and we check if that’s reasonable based on proper rounding.

So for Box 1: Final estimate is 20 → which comes from 600÷30 → correct rounding → so yes

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Box 2: 143 ÷ 53

They wrote:
= 100 ÷ 50 = 2

Is this correct?

143 rounds to 100? Well, 143 is closer to 100 than 200? No — 143 is between 100 and 200, but typically we round to nearest hundred: 143 → 100 (since <150). Actually, standard rounding: 143 to nearest hundred is 100? Wait no — 143 is closer to 100 than 200? Distance to 100 is 43, to 200 is 57 — so yes, 100.

53 to nearest ten is 50.

So 100 ÷ 50 = 2 → correct.

Actual quotient: 143 ÷ 53 ≈ 2.698 → so estimate of 2 is reasonable.

✔ yes

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Box 3: 492 ÷ 41

They wrote:
= 400 ÷ 50 = 8

Check rounding:

492 → nearest hundred: 500 (since 492 ≥ 450)

41 → nearest ten: 40

So better estimate: 500 ÷ 40 = 12.5 → about 12 or 13

But they used 400 ÷ 50 = 8

400 is too low for 492 (should be 500), and 50 is too high for 41 (should be 40).

So their estimate is not accurate.

Correct estimation: 500 ÷ 40 = 12.5 → we can say 12 or 13, but since it's estimation, often we keep it as whole number.

500 ÷ 40 = 12.5 → round to 13? Or leave as 12.5? In elementary math, they might expect 12 or 13.

But let’s calculate: 500 ÷ 40 = 50 ÷ 4 = 12.5

We can write 12.5 or approximately 13.

But perhaps simplify: 500 ÷ 40 = 50 ÷ 4 = 12.5

For estimation purposes, sometimes they want integer.

Note: 492 ÷ 41 actual value: 492 ÷ 41 = 12 exactly? 41*12=492 → oh! Exactly 12.

Wow — so actual quotient is 12.

Their estimate gave 8, which is way off.

Correct estimation should be: 500 ÷ 40 = 12.5 → close to 12.

Or since 492 is very close to 500, and 41 close to 40, 500÷40=12.5≈12 or 13.

But since actual is 12, best estimate is 12.

How to get 12? 480 ÷ 40 = 12, but 480 is not round of 492.

Standard way: round dividend and divisor to compatible numbers.

492 → 500, 41 → 40 → 500÷40=12.5→ say 12 or 13.

But in many curricula, they accept 12.5 or round to nearest whole.

However, looking at other problems, they use whole numbers.

Perhaps: 492 ÷ 41 ≈ 500 ÷ 40 = 12.5 → but since quotient should be integer, maybe 12.

But let's see what the worksheet expects.

They have =8, which is wrong.

Correct estimation: 500 ÷ 40 = 12.5, but perhaps write 12 or 13.

I think for consistency, since others are integers, and 12.5 is fine, but let's check the answer.

Actual is 12, so estimate of 12 is perfect.

How to get 12? Round 492 to 480? But 480 is not standard rounding.

Better: 492 is almost 500, 41 is almost 40, 500/40=12.5≈13? But 13*40=520, too big.

12*40=480, which is close to 492.

So perhaps 480 ÷ 40 = 12 is a good estimate, but 480 is not the rounded version of 492; 492 rounds to 500.

This is tricky.

In many textbooks, for 492÷41, they would round 492 to 500, 41 to 40, and say 500÷40=12.5, and since it's estimation, 12 or 13 is acceptable, but often they might write 12.

But in this case, since actual is 12, and 500÷40=12.5, it's close.

Their estimate was 400÷50=8, which is incorrect.

So we need to provide correct estimation.

Let me calculate: 492 ÷ 41.

As said, 41*12=492, so exact.

For estimation, rounding 492 to 500, 41 to 40, 500÷40=12.5.

We can write 12.5 or approximately 13, but to match the format, perhaps 12 or 13.

Looking at other answers, they have integers.

In Box 1, they have 20, Box 2 has 2, etc.

So probably expect integer.

500÷40=12.5, so round to 13? But 13*40=520 > 492, while 12*40=480 < 492, difference 12 vs 28, so 12 is closer.

492 - 480 = 12, 520 - 492 = 28, so 12 is better.

So estimate 12.

How to justify? Perhaps round 492 to 480? But 480 is not standard.

Another way: 492 ÷ 41 ≈ 500 ÷ 40 = 12.5, and since 0.5, round to even or something, but I think for this level, they might accept 12 or 13.

But let's see the next boxes.

Perhaps the worksheet has a mistake, but we have to correct it.

I think the intended correct estimation is 500 ÷ 40 = 12.5, but since the quotient is written as integer in others, perhaps 12.

Notice that in Box 6: 567÷33, they have 600÷30=20, and 567÷33=17.18, so 20 is estimate.

Similarly here.

For 492÷41, 500÷40=12.5, so perhaps write 12 or 13.

But to be precise, let's calculate what is commonly done.

I recall that in some systems, they round to the nearest ten for both.

492 to nearest ten is 490, 41 to nearest ten is 40, so 490÷40=12.25≈12.

Yes! That's better.

492 rounded to nearest ten is 490 (since 2<5, so down? 492, units digit 2<5, so round down to 490.

41 to nearest ten is 40.

490 ÷ 40 = 49 ÷ 4 = 12.25 → approximately 12.

And actual is 12, so perfect.

So correct estimation: 490 ÷ 40 = 12.25, but they might write 12.

In the worksheet, they have =8, which is wrong.

So for this box, we need to write the correct estimation.

The format is: in the empty space, write the correct one.

Looking at the image description, each box has three lines, and for some, there is an empty line below.

In Box 3, they have:

492 ÷ 41
= 400 ÷ 50
= 8

And then presumably an empty line for correction.

Similarly for others.

So for Box 3, since 8 is wrong, we write the correct estimation.

Correct: round 492 to 490, 41 to 40, so 490 ÷ 40 = 12.25, but since quotients are integers in examples, perhaps 12.

490 ÷ 40 = 49/4 = 12.25, so estimate 12.

Some might say 500÷40=12.5≈13, but 12 is closer to actual.

Actual is 12, so 12 is best.

So we'll put 490 ÷ 40 = 12

But 490 is not always used; sometimes they round to hundreds.

492 to nearest hundred is 500, as I said.

But 500÷40=12.5, which is fine.

To match the format, let's see what other boxes do.

In Box 1, they used 600 and 30, which are hundreds and tens.

In Box 2, 100 and 50.

In Box 4: 346÷123, they have 400÷100=4

346 to nearest hundred is 300? 346 is closer to 300 than 400? Distance to 300 is 46, to 400 is 54, so 300.

But they used 400, which is not accurate.

346 ÷ 123.

123 to nearest hundred is 100.

346 to nearest hundred: 300 or 400? 346 - 300 = 46, 400 - 346 = 54, so closer to 300.

But they used 400÷100=4.

Actual quotient: 346÷123≈2.81, so estimate of 4 is a bit high.

Better estimate: 300÷100=3, or 350÷125=2.8, but 125 is not round of 123.

123 to nearest ten is 120, 346 to nearest ten is 350, so 350÷120≈2.916, say 3.

Or 300÷100=3.

So their estimate of 4 is not great, but perhaps acceptable? 4 is farther from 2.81 than 3 is.

3 is better.

But they have =4, and we need to check if correct.

Instruction: "check if the given estimates are correct"

What does "correct" mean? Reasonable estimate, or exact match to actual? Probably reasonable.

In Box 2, 143÷53≈2.7, they estimated 2, which is close.

Here, 346÷123≈2.81, they estimated 4, which is not very close; 3 would be better.

So perhaps not correct.

This is getting complicated.

Perhaps "correct" means that the rounding is appropriate and the division is done correctly with the rounded numbers.

For example, in Box 3, they rounded 492 to 400 (which is not correct; should be 500), and 41 to 50 (should be 40), so the rounding is wrong, and thus the estimate is invalid.

Similarly, in Box 4, 346 to 400 is not accurate rounding (should be 300 or 350), 123 to 100 is ok, but 400÷100=4, while actual is 2.81, so poor estimate.

But let's systematize.

Let me define: for each, round the dividend and divisor to the nearest ten or hundred as appropriate, then divide, and see if their estimate matches that.

Also, in the worksheet, for some, they have only one estimate, for others like Box 1, they have two, but perhaps Box 1 is special.

Let's list all boxes:

Box 1: 585÷29
Their: 510÷30=17, then 600÷30=20
Final: 20
Correct rounding: 585->600, 29->30, 600÷30=20 -> correct, so yes.

Box 2: 143÷53
Their: 100÷50=2
Rounding: 143->100 (nearest hundred), 53->50 (nearest ten), 100÷50=2 -> correct, and actual ~2.7, so reasonable. Yes.

Box 3: 492÷41
Their: 400÷50=8
Rounding: 492 should be 500 (nearest hundred), 41 should be 40 (nearest ten), so 500÷40=12.5, not 8. Also, 400 is not correct round of 492. So incorrect.
Correct estimation: 500÷40=12.5, or as integer 12 or 13. Since actual is 12, and 500÷40=12.5, perhaps write 12.5, but to match format, maybe 12.
In the empty space, we can write: 500 ÷ 40 = 12.5 or 12.
But looking at other answers, they have integers, so perhaps 12.
Note that 490÷40=12.25, same thing.
I think 12 is fine.

Box 4: 346÷123
Their: 400÷100=4
Rounding: 346 to nearest hundred: 300 (since 346<350), 123 to nearest hundred: 100, so 300÷100=3.
Actual ~2.81, so 3 is better than 4.
Their rounding of 346 to 400 is incorrect; should be 300.
So estimate is not correct.
Correct: 300÷100=3

Box 5: 259÷127
Their: 240÷120=2
Rounding: 259 to nearest ten: 260, 127 to nearest ten: 130, so 260÷130=2.
Or to hundred: 300÷100=3, but 260÷130=2 is good.
Actual: 259÷127≈2.039, so 2 is excellent.
Is 240÷120 correct rounding? 259 to 240? 240 is not nearest ten or hundred. Nearest ten is 260, nearest hundred is 300.
240 is 259-19, while 260 is +1, so 260 is better.
But 240÷120=2, and 260÷130=2, same result.
127 to 120? 127-120=7, 130-127=3, so 130 is closer.
But 240÷120=2, and it gives the correct estimate.
Perhaps it's acceptable, as long as the quotient is reasonable.
Since 2 is very close to actual, and 240 and 120 are multiples, it might be intended.
But strictly, rounding should be to nearest, so 260 and 130.
However, 240÷120=2 is correct calculation, and estimate is good.
So perhaps yes.

To be consistent, let's see if the rounding is proper.

In Box 2, they used 100 and 50, which are proper rounds.

Here, 259 to 240 is not proper; should be 260 or 300.

240 is not a standard round.

So probably not correct rounding.

Correct estimation: 260÷130=2 or 300÷100=3.

260÷130=2 is better.

So their estimate is numerically correct, but the rounding is not standard.

The instruction is "check if the given estimates are correct" — probably meaning if the method is correct, i.e., proper rounding.

In that case, for Box 5, rounding 259 to 240 is wrong; should be 260.

So incorrect.

Correct: 260 ÷ 130 = 2

Same quotient, but different numbers.

In the answer, they have =2, which is correct, but the intermediate is wrong.

The worksheet has "= 240 ÷ 120 = 2", so the estimation process is flawed.

So we should mark it as not correct, and provide correct estimation.

But the quotient is the same.

Perhaps for the purpose, since the final estimate is correct, it's ok, but I think the rounding should be accurate.

Let's look at Box 6.

Box 6: 567÷33
Their: 600÷30=20
Rounding: 567 to nearest hundred: 600 (since 567>550), 33 to nearest ten: 30, so 600÷30=20.
Actual: 567÷33=17.1818..., so 20 is a bit high, but reasonable estimate.
Yes.

Box 7: 482÷74
Their: 500÷100=5
Rounding: 482 to nearest hundred: 500, 74 to nearest hundred: 100? 74 is closer to 100 than 0? No, 74 to nearest hundred is 100? Distance to 0 is 74, to 100 is 26, so yes, 100.
500÷100=5.
Actual: 482÷74≈6.513, so 5 is a bit low, but perhaps acceptable.
Is there better? 480÷80=6, or 500÷75≈6.67, but 75 not round of 74.
74 to nearest ten is 70, 482 to nearest ten is 480, so 480÷70≈6.857, say 7.
Or 500÷70≈7.14.
So 5 is not very good; 7 would be better.
Their rounding: 482->500 (ok), 74->100 (ok for hundred), but 500÷100=5, while actual is 6.5, so error of 1.5, whereas 480÷70≈6.86, error 0.35, much better.
So probably not correct estimate.
Correct estimation: 480 ÷ 70 = 6.857 ≈ 7 or 480÷70=48/7≈6.86, so 7.
Or 500÷70≈7.14, same.
So should be around 7.

Box 8: 345÷178
Their: 400÷200=2
Rounding: 345 to nearest hundred: 300 or 400? 345-300=45, 400-345=55, so 300.
178 to nearest hundred: 200 (since 178>150).
So 300÷200=1.5, or 1 or 2.
Actual: 345÷178≈1.938, so 2 is good.
Their used 400÷200=2, which is also 2, and 400 is not accurate round of 345 (should be 300), but 400÷200=2 same as 300÷200=1.5≈2? 1.5 is not 2.
300÷200=1.5, which is closer to 2 than to 1, but usually we round 1.5 to 2.
But their estimate is 2, which is correct for the actual, but the rounding of 345 to 400 is not proper; should be 300.
So again, process is flawed.
Correct: 300÷200=1.5, or approximately 2.
Since actual is 1.938, 2 is fine, but with proper rounding, 300÷200=1.5, which we can round to 2.
So perhaps it's acceptable.

This is messy.

Perhaps the worksheet considers the estimate correct if the final quotient is reasonable, regardless of the rounding steps, as long as the division is correct.

In that case, for most, it's ok.

But for Box 3, 8 is not reasonable for 12.

For Box 4, 4 is not great for 2.81.

Let's calculate the actual quotients and see what estimate is expected.

Perhaps "correct" means that the rounded numbers are chosen properly and the division is correct.

Let me try to do it that way.

For each box:

1. 585÷29:
- Rounded: 600÷30=20 (correct rounding)
- They have 510÷30=17 (wrong rounding) and then 600÷30=20 (correct)
- Since they have the correct one, and final is 20, we can say yes.

2. 143÷53:
- 100÷50=2 (143->100, 53->50, both correct rounds, 100÷50=2) -> yes

3. 492÷41:
- They have 400÷50=8
- Correct rounds: 492->500, 41->40, 500÷40=12.5
- 8 is not correct, so no, and correct estimation is 500÷40=12.5 or 12

4. 346÷123:
- They have 400÷100=4
- Correct rounds: 346->300 (nearest hundred), 123->100, 300÷100=3
- 4 is not correct, so no, correct is 300÷100=3

5. 259÷127:
- They have 240÷120=2
- Correct rounds: 259->260 (nearest ten), 127->130 (nearest ten), 260÷130=2
- Or to hundred: 300÷100=3
- 240 is not correct round of 259; should be 260.
- But 240÷120=2, and 260÷130=2, same result.
- Perhaps it's acceptable, but strictly, rounding is wrong.
- To be safe, let's say the estimate is correct because the quotient is accurate, but the rounding is not standard.
- However, in the context, perhaps they allow it.
- Notice that 240 and 120 are both divisible, and give 2, which is correct.
- So maybe yes.

6. 567÷33:
- 600÷30=20 (567->600, 33->30, correct, 600÷30=20) -> yes

7. 482÷74:
- They have 500÷100=5
- Correct rounds: 482->500, 74->70 (nearest ten) or 100 (nearest hundred)
- If to hundred: 500÷100=5
- Actual 6.51, so 5 is a bit low, but perhaps acceptable.
- Better: 480÷70≈6.86, so 7.
- But if they use hundred, 500÷100=5 is correct for the rounded numbers.
- So perhaps yes, as long as the division is correct with the rounded numbers they chose.
- In this case, they chose 500 and 100, which are valid rounds (482 to 500, 74 to 100), and 500÷100=5, so the estimate is correct for those rounded numbers.
- The question is whether the rounded numbers are appropriate, but the instruction doesn't specify; it just says "given estimates", so perhaps as long as the math is correct with the numbers they used, it's ok, even if the rounding is not optimal.
- In that case, for Box 3, 400÷50=8, and 400 is a round of 492? 492 to 400 is not standard; usually to 500.
- 492 is closer to 500 than to 400, so 400 is not a good round.
- Similarly, 41 to 50 is not good; should be 40.
- So for Box 3, the rounded numbers are not appropriate.
- For Box 7, 74 to 100 is appropriate for nearest hundred, since 74 is closer to 100 than to 0? 74-0=74, 100-74=26, so yes, 100 is correct for nearest hundred.
- 482 to 500 is correct.
- 500÷100=5, so the estimate is correct for the rounded numbers.
- Actual is 6.51, so it's not very accurate, but the estimate is "correct" in the sense that with the rounded numbers, the division is correct.
- The instruction: "check if the given estimates are correct" — probably means if the estimation process is done correctly, i.e., proper rounding and correct division.
- In Box 3, rounding 492 to 400 is incorrect; should be 500.
- In Box 7, rounding 74 to 100 is correct for nearest hundred.
- So for Box 7, it is correct.
- For Box 3, not correct.

Let's apply that.

For each, check if the rounded numbers are the nearest ten or hundred, and if the division is correct.

Box 1:
- They have two: first 510÷30=17 — 585 to 510? 585-510=75, 600-585=15, so 600 is closer, so 510 is not correct round.
- Then 600÷30=20 — 600 is correct round of 585, 30 is correct round of 29, 600÷30=20 correct.
- Since they have the correct one, and it's listed, perhaps yes.

But to simplify, perhaps for each box, we look at the last estimate they give.

In Box 1, last is 20, which is correct.

In Box 2, 2, correct.

Box 3, 8, but with wrong rounding, so not correct.

Box 4, 4, with 400÷100, but 346 should be 300, not 400, so wrong rounding.

Box 5, 2, with 240÷120, 259 to 240 is not correct; should be 260, so wrong.

Box 6, 20, with 600÷30, correct rounding, so yes.

Box 7, 5, with 500÷100, 482 to 500 correct, 74 to 100 correct (nearest hundred), 500÷100=5 correct, so yes.

Box 8, 2, with 400÷200, 345 to 400? 345-300=45, 400-345=55, so 300 is closer, so 400 is not correct round; should be 300.
178 to 200 correct.
300÷200=1.5, not 2.
So their estimate is not correct for proper rounding.

So summary:

Box 1: yes (since final estimate is correct with proper rounding)
Box 2: yes
Box 3: no, correct: 500 ÷ 40 = 12.5 or 12
Box 4: no, correct: 300 ÷ 100 = 3
Box 5: no, correct: 260 ÷ 130 = 2 (same quotient, but different numbers)
Box 6: yes
Box 7: yes
Box 8: no, correct: 300 ÷ 200 = 1.5 or 2 (since 1.5 rounds to 2)

For Box 5, if we use 260÷130=2, same as their 2, so perhaps we can say the estimate is correct, but the rounding is wrong, but the final number is correct.

To resolve, let's look at the actual values and see what is expected.

Perhaps for Box 5, 240 and 120 are used because 259 is close to 240? No, 259-240=19, while 260-259=1, so 260 is better.

But in some contexts, they might use compatible numbers.

I think for accuracy, we should use proper rounding.

So let's decide:

- Box 1: yes
- Box 2: yes
- Box 3: no, correct estimation: 500 ÷ 40 = 12.5 (or 12)
- Box 4: no, correct: 300 ÷ 100 = 3
- Box 5: no, correct: 260 ÷ 130 = 2
- Box 6: yes
- Box 7: yes
- Box 8: no, correct: 300 ÷ 200 = 1.5 or 2

For the answer, since the worksheet likely expects integer quotients, and for Box 3, 12, etc.

Also, in Box 3, actual is 12, so 12 is good.

For Box 8, actual is 1.938, so 2 is good, and 300÷200=1.5≈2.

So for the "correct estimation", we can write the rounded division and the quotient.

Now for the response, since ExplainAnswer is false, etc., we only need to provide the final answer, which is for each box, either "yes" or the correct estimation.

The final answer should be the completed worksheet or the corrections.

But the user said "solve the problem accurately", and "provide only the final correct answer".

Probably, for each box, state if yes or the correct estimate.

Since it's a worksheet, perhaps list the corrections.

But to match the format, perhaps for each box, output what should be in the empty space or the judgment.

Looking back at the user's request: "Solve the problem accurately." and "Final Answer: [Provide only the final correct answer]"

And the problem is to check each estimate and correct if wrong.

So the final answer should be the corrected version or the judgments.

Perhaps: for each box, if correct, "yes", else the correct estimation.

And since there are 9 boxes, list them.

From above:

Box 1: yes
Box 2: yes
Box 3: 500 ÷ 40 = 12.5 or 12 — let's use 12 for integer
Box 4: 300 ÷ 100 = 3
Box 5: 260 ÷ 130 = 2
Box 6: yes
Box 7: yes
Box 8: 300 ÷ 200 = 1.5 or 2 — use 2
Box 9: 512 ÷ 27
Their: 510 ÷ 30 = 17
Rounding: 512 to nearest ten: 510, 27 to nearest ten: 30, 510÷30=17.
Actual: 512÷27=18.962, so 17 is a bit low, but with rounding, 510÷30=17 is correct for the rounded numbers.
Is 510 correct round of 512? 512-510=2, 520-512=8, so 510 is closer, yes.
27 to 30 is correct.
510÷30=17, correct division.
Actual is 18.96, so estimate 17 is not very accurate, but the process is correct.
So perhaps yes.
Better estimate: 500÷25=20, but 25 not round of 27.
510÷30=17 is fine.
So yes.

So Box 9: yes

Now for Box 3,4,5,8 need correction.

For Box 5, if we say correct estimation is 260÷130=2, same as their 2, so perhaps the estimate is correct, but the numbers are wrong, but the quotient is correct.

To avoid confusion, since the quotient is what matters, and for Box 5, 2 is correct, so yes.

Similarly for Box 8, 2 is correct for actual, so yes.

But for Box 3, 8 is not correct.

Let's calculate the actual quotients:

1. 585÷29 = 20.1724 -> estimate 20 good
2. 143÷53 = 2.698 -> estimate 2 good
3. 492÷41 = 12 -> estimate 8 bad
4. 346÷123 = 2.813 -> estimate 4 bad (3 would be better)
5. 259÷127 = 2.039 -> estimate 2 good
6. 567÷33 = 17.1818 -> estimate 20 a bit high, but ok
7. 482÷74 = 6.5135 -> estimate 5 a bit low, but with their rounding, it's correct for 500÷100
8. 345÷178 = 1.9382 -> estimate 2 good
9. 512÷27 = 18.962 -> estimate 17 a bit low, but with 510÷30=17, it's correct for the rounded numbers.

For Box 3, 8 is not close to 12, so definitely wrong.

For Box 4, 4 is not close to 2.81; 3 is better.

For others, the estimate is reasonable.

So perhaps only Box 3 and Box 4 are incorrect.

For Box 3, correct estimation: 500 ÷ 40 = 12.5, but since others are integer, and actual is 12, use 12.

How to get 12? 480 ÷ 40 = 12, but 480 not round of 492.

500 ÷ 40 = 12.5, so perhaps write 12.5 or 12.

In the worksheet, for Box 1, they have 20, integer, so likely expect integer.

So for Box 3, 500 ÷ 40 = 12.5, but we can write 12 as approximation.

Or 490 ÷ 40 = 12.25 ≈ 12.

I think 12 is fine.

For Box 4, 300 ÷ 100 = 3.

So final decision:

- Box 1: yes
- Box 2: yes
- Box 3: 500 ÷ 40 = 12 (or 12.5, but let's use 12)
- Box 4: 300 ÷ 100 = 3
- Box 5: yes (since 2 is correct)
- Box 6: yes
- Box 7: yes
- Box 8: yes (2 is good)
- Box 9: yes

For Box 5, even though rounding is not standard, the estimate is correct, so yes.

Similarly for others.

So only Box 3 and Box 4 need correction.

For Box 3, correct estimation: 500 ÷ 40 = 12.5, but to match format, perhaps 12.

In the empty space, write "500 ÷ 40 = 12" or "12.5".

But in Box 1, they have 20, integer, so likely 12.

Actual is 12, so 12 is perfect.

How to justify 500÷40=12.5, but we can say approximately 12.

Or use 480÷40=12, but 480 is not round.

I think it's ok to write 500 ÷ 40 = 12.5, but since the worksheet may expect integer, and in the answer, they have integers, perhaps for this, write 12.

Notice that in Box 6, 567÷33=17.18, they have 20, which is integer, so decimals are not used.

So for Box 3, write 500 ÷ 40 = 12 (rounding 12.5 to 12 or 13, but 12 is actual).

So I'll use 12.

Similarly for Box 4, 3.

So for the final answer, for each box, if yes, "yes", else the correct estimation string.

So:

Box 1: yes
Box 2: yes
Box 3: 500 ÷ 40 = 12
Box 4: 300 ÷ 100 = 3
Box 5: yes
Box 6: yes
Box 7: yes
Box 8: yes
Box 9: yes

For Box 3, is 500 ÷ 40 = 12 accurate? 500÷40=12.5, not 12, so perhaps write 12.5, but to be consistent, or write the division as is.

In the worksheet, for Box 1, they have "= 600 ÷ 30 = 20", so they write the division and the result.

So for correction, write "500 ÷ 40 = 12.5" or "500 ÷ 40 = 12" .

Since 12.5 is not integer, and others are, perhaps they expect to round the quotient.

In many cases, they round the quotient to nearest integer.

12.5 rounds to 12 or 13? Usually to even, so 12, or to 13.

But actual is 12, so 12 is good.

So I'll use 12.

Similarly, for Box 4, 3.

So final answer for the worksheet:

For each box, the content for the "correction" or "judgment".

Since the user will fill in, perhaps list what to write in each box's empty space or the yes/no.

But to simplify, the final answer is the list of what to put for each box.

Perhaps:

1. yes
2. yes
3. 500 ÷ 40 = 12
4. 300 ÷ 100 = 3
5. yes
6. yes
7. yes
8. yes
9. yes

For Box 3, to be precise, 500 ÷ 40 = 12.5, but I think for this level, 12 is acceptable.

We can write "500 ÷ 40 = 12.5" but then it's not integer.

Another way: in some systems, they keep it as fraction, but unlikely.

I think 12 is fine.

So I'll go with that.

Final Answer:
For the nine boxes in order:
1. yes
2. yes
3. 500 ÷ 40 = 12
4. 300 ÷ 100 = 3
5. yes
6. yes
7. yes
8. yes
9. yes

For Box 5, although the rounding is not standard, the estimate is correct, so yes.

Similarly for others.

So this should be it.