Estimating Quotients Worksheets - 15 Worksheets Library - Free Printable

Let's solve the "Estimating Quotients" worksheet step by step.

We are asked to:
- Check if the given estimates are correct.
- If correct, write "yes".
- If not, write the correct estimation.

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Understanding Estimation of Quotients

To estimate quotients, we round the dividend and divisor to compatible numbers (usually multiples of 10 or 100) that are easy to divide.

We then perform the division with the rounded numbers to get an estimated quotient.

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Now let’s go through each problem:

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1. 585 ÷ 29

- Given:
- Rounded: 510 ÷ 30 = 17
- But they wrote: 600 ÷ 30 = 20

Wait — actually, the problem says:
> 585 ÷ 29
> ≈ 510 ÷ 30
> = 17
> Then they write: = 600 ÷ 30 = 20

But wait — this seems inconsistent. Let's clarify:

The student is supposed to check whether the estimate shown is correct.

So here, the given estimate is:
585 ÷ 29 ≈ 510 ÷ 30 = 17

But then someone wrote 600 ÷ 30 = 20 as a correction?

Actually, looking at the layout:

It appears that the first line is the actual problem:
585 ÷ 29

Then the next line shows the estimate used:
≈ 510 ÷ 30 = 17

And then below it, in blue, someone wrote:
= 600 ÷ 30 = 20

But that’s likely not part of the original problem — probably a student’s attempt.

But since the instruction is to check if the given estimate is correct, we should evaluate:

> Is 585 ÷ 29 ≈ 510 ÷ 30 = 17 a good estimate?

Let’s analyze:

- 585 ÷ 29 → Let's estimate.
- Round 585 to 600, 29 to 30 → 600 ÷ 30 = 20
- But they used 510 ÷ 30 = 17 → That’s too low because 510 is less than 585.
- So 510 ÷ 30 = 17 is not a good estimate.

Better estimate:
585 ≈ 600, 29 ≈ 30 → 600 ÷ 30 = 20

✔ So the given estimate (17) is incorrect.

👉 Correct estimation: 600 ÷ 30 = 20

Answer: ✘ No, correct estimation: 20

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2. 143 ÷ 53

- Given: ≈ 100 ÷ 50 = 2
- Actual: 143 ≈ 150, 53 ≈ 50 → 150 ÷ 50 = 3
- But they used 100 ÷ 50 = 2 → too low

Check:
100 ÷ 50 = 2, but 143 is closer to 150 than 100.

So 100 ÷ 50 = 2 is not accurate.

Better: 150 ÷ 50 = 3

So estimate should be around 3

👉 Incorrect estimate.

Answer: ✘ No, correct estimation: 150 ÷ 50 = 3

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3. 492 ÷ 41

- Given: ≈ 400 ÷ 50 = 8
- But 41 is close to 40, not 50!
- So rounding 41 to 50 is bad.

Better: 492 ≈ 500, 41 ≈ 40 → 500 ÷ 40 = 12.5 → about 12 or 13

But they used 400 ÷ 50 = 8 → that’s way off.

Also, 400 ÷ 50 = 8 → but 492 is much larger than 400.

So this estimate is wrong.

Better: 492 ≈ 500, 41 ≈ 40 → 500 ÷ 40 = 12.5 → estimate 12 or 13

Alternatively: 492 ÷ 41 → think: 41 × 12 = 492 → exact!

So actual answer is 12

So estimate should be around 12

They said 8 → incorrect.

Answer: ✘ No, correct estimation: 500 ÷ 40 = 12.5 → ~12

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4. 346 ÷ 123

- Given: ≈ 400 ÷ 100 = 4
- 346 is closer to 300 or 350; 123 is close to 100 or 120
- 400 ÷ 100 = 4 → but 346 < 400, so quotient should be less than 4
- Try: 300 ÷ 100 = 3 → better
- Or 350 ÷ 120 ≈ 2.9 → about 3

So 400 ÷ 100 = 4 is slightly high, but maybe acceptable?

But 346 ÷ 123 ≈ ?

123 × 2 = 246
123 × 3 = 369 → too big
So 346 is between 2× and 3× → closer to 3?
369 - 346 = 23 → so only 23 less than 369 → so about 2.8

So estimate should be around 3

But they used 400 ÷ 100 = 4 → which is higher than actual.

Is it acceptable? Maybe borderline, but not very accurate.

Better estimate: 350 ÷ 120 ≈ 2.9 → so 3

So 4 is too high

Answer: ✘ No, correct estimation: 350 ÷ 120 = ~3

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5. 259 ÷ 127

- Given: ≈ 240 ÷ 120 = 2
- 259 ≈ 240? Not really — 259 is closer to 260
- 127 ≈ 120 → okay
- 240 ÷ 120 = 2 → but 259 > 240, so actual quotient > 2

Try: 260 ÷ 130 = 2 → same

But 259 ÷ 127 → 127 × 2 = 254 → 259 - 254 = 5 → so 2 + 5/127 → about 2.04

So actual is about 2.04

So estimate of 2 is very close — acceptable

But they used 240 ÷ 120 = 2 → but 240 is less than 259 → so underestimates numerator

Still, 240 ÷ 120 = 2 is close enough for estimation

So is it correct?

Yes — it's a reasonable estimate.

Answer: ✔ Yes

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6. 567 ÷ 33

- Given: ≈ 600 ÷ 30 = 20
- 567 ≈ 600 → yes
- 33 ≈ 30 → yes
- 600 ÷ 30 = 20 → good

Actual: 33 × 17 = 561 → 567 - 561 = 6 → so about 17.18

Wait! 600 ÷ 30 = 20 → but actual is 17.18, so 20 is too high

Why? Because 567 is less than 600, and 33 is greater than 30, so quotient should be less than 20

Better estimate: 570 ÷ 30 = 19 → still high

Or 567 ≈ 570, 33 ≈ 30 → 570 ÷ 30 = 19 → still over

Better: 567 ÷ 33 → 33 × 17 = 561 → so about 17

So better estimate: 570 ÷ 30 = 19 → too high

Or 540 ÷ 30 = 18 → closer

Or 510 ÷ 30 = 17 → good

So use: 510 ÷ 30 = 17

But they used 600 ÷ 30 = 20 → which is too high

So incorrect

Answer: ✘ No, correct estimation: 510 ÷ 30 = 17 or 570 ÷ 30 = 19, but best: 540 ÷ 30 = 18

But since 33 is close to 30, and 567 is close to 570, 570 ÷ 30 = 19 is better than 20

But 567 ÷ 33 ≈ 17.18 → so 17 is best

So better to use: 570 ÷ 30 = 19 or 510 ÷ 30 = 17

But 510 is too low.

Best: 570 ÷ 30 = 19

Wait — 570 ÷ 30 = 19, but 567 is less → so 19 is still high

So perhaps: 540 ÷ 30 = 18

But simplest: 570 ÷ 30 = 19 is acceptable, but 17 is better.

But they used 600 ÷ 30 = 20 → which is way off

So no.

Answer: ✘ No, correct estimation: 570 ÷ 30 = 19 or 540 ÷ 30 = 18

But since actual is ~17.18, 510 ÷ 30 = 17 is best.

So: 510 ÷ 30 = 17

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7. 482 ÷ 74

- Given: ≈ 500 ÷ 70 = 5
- 482 ≈ 500 → okay
- 74 ≈ 70 → okay
- 500 ÷ 70 ≈ 7.14 → but they say = 5? Wait!

Wait — 500 ÷ 70 = 7.14, but they wrote = 5 → that’s wrong!

Wait — the sheet says:

> 482 ÷ 74
> = 500 ÷ 70
> = 5

But 500 ÷ 70 is not 5 — it’s about 7.14

So the estimate is wrong — they claimed 500 ÷ 70 = 5, but it's not.

Even if we accept the rounding, the result is wrong.

So the entire estimate is invalid

Correct: 500 ÷ 70 ≈ 7.14 → so estimate 7

Or 490 ÷ 70 = 7 → perfect

So correct estimation: 490 ÷ 70 = 7

Answer: ✘ No, correct estimation: 490 ÷ 70 = 7

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8. 345 ÷ 178

- Given: ≈ 400 ÷ 200 = 2
- 345 ≈ 400 → a bit high
- 178 ≈ 200 → okay
- 400 ÷ 200 = 2 → but actual: 345 ÷ 178 ≈ ?

178 × 1 = 178
178 × 2 = 356 → 356 > 345 → so less than 2

345 - 178 = 167 → so about 1.94 → so about 2

So estimate of 2 is acceptable

Even though 400 is a little high, 200 is a little high, but ratio is similar.

So yes, it's a reasonable estimate.

Answer: ✔ Yes

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9. 512 ÷ 27

- Given: ≈ 510 ÷ 30 = 17
- 512 ≈ 510 → yes
- 27 ≈ 30 → okay
- 510 ÷ 30 = 17 → correct calculation

Actual: 27 × 17 = 459
27 × 19 = 513 → so 512 ÷ 27 ≈ 18.96 → about 19

So 17 is a bit low

But is it a good estimate?

510 ÷ 30 = 17 → but 27 is less than 30, so quotient should be larger

Because denominator is smaller → quotient is bigger

So 17 is too low

Better: 510 ÷ 30 = 17 → but 27 is 3 less than 30 → so actual quotient should be higher

Try: 510 ÷ 27 ≈ 18.9 → so 19

So better estimate: 510 ÷ 30 = 17 → underestimates

So not correct

Better: 510 ÷ 30 = 17 → but 27 is smaller → so quotient larger

Use: 510 ÷ 27 ≈ 19 → so estimate: 510 ÷ 30 = 17 is not good

Alternative: 500 ÷ 25 = 20 → but not matching

Or 540 ÷ 30 = 18 → better

But best: 510 ÷ 30 = 17 → no

So incorrect

Answer: ✘ No, correct estimation: 510 ÷ 27 ≈ 19, or 540 ÷ 30 = 18

But since we need to round both, better: 510 ÷ 30 = 17 is not good.

Better: 540 ÷ 30 = 18 → but 540 is higher than 512

Or: 510 ÷ 30 = 17 → but we know it's low

So best: 510 ÷ 30 = 17 is not correct

Correct estimation: 540 ÷ 30 = 18 or 510 ÷ 27 ≈ 19

But since we must use compatible numbers, try: 500 ÷ 25 = 20 → too high

Or: 510 ÷ 30 = 17 → still low

So perhaps: 510 ÷ 30 = 17 is not acceptable

Better: 540 ÷ 30 = 18

But 540 > 512 → so maybe 510 ÷ 30 = 17 is closest?

Wait — actual is ~18.96 → so 19

So best estimate: 540 ÷ 30 = 18 or 510 ÷ 27 ≈ 19

But we can’t use 27 — must round.

So round 512 → 510, 27 → 30 → 510 ÷ 30 = 17 → but actual is ~19 → difference of 2 → not great

But maybe acceptable?

Wait — 512 ÷ 27 → 27 × 19 = 513 → so 512 ÷ 27 ≈ 18.96 → so 19

So better to round to 510 ÷ 30 = 17 → too low

Alternatively, round 512 → 500, 27 → 30 → 500 ÷ 30 ≈ 16.7 → worse

Or 512 → 540, 27 → 30 → 540 ÷ 30 = 18 → better

So 540 ÷ 30 = 18 is better than 17

So they used 510 ÷ 30 = 17, which is not correct

Answer: ✘ No, correct estimation: 540 ÷ 30 = 18

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## ✔ Final Answers:

| Problem | Given Estimate | Correct? | Correct Estimation |
|--------|----------------|----------|--------------------|
| 1. 585 ÷ 29 | 510 ÷ 30 = 17 | ✘ No | 600 ÷ 30 = 20 |
| 2. 143 ÷ 53 | 100 ÷ 50 = 2 | ✘ No | 150 ÷ 50 = 3 |
| 3. 492 ÷ 41 | 400 ÷ 50 = 8 | ✘ No | 500 ÷ 40 = 12.5 → ~12 |
| 4. 346 ÷ 123 | 400 ÷ 100 = 4 | ✘ No | 350 ÷ 120 = ~3 |
| 5. 259 ÷ 127 | 240 ÷ 120 = 2 | ✔ Yes | 2 |
| 6. 567 ÷ 33 | 600 ÷ 30 = 20 | ✘ No | 510 ÷ 30 = 17 |
| 7. 482 ÷ 74 | 500 ÷ 70 = 5 | ✘ No | 490 ÷ 70 = 7 |
| 8. 345 ÷ 178 | 400 ÷ 200 = 2 | ✔ Yes | 2 |
| 9. 512 ÷ 27 | 510 ÷ 30 = 17 | ✘ No | 540 ÷ 30 = 18 |

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✔ Summary of Answers to Write in Boxes:

1. No, correct: 600 ÷ 30 = 20
2. No, correct: 150 ÷ 50 = 3
3. No, correct: 500 ÷ 40 = 12 (or ~12)
4. No, correct: 350 ÷ 120 = 3
5. Yes
6. No, correct: 510 ÷ 30 = 17
7. No, correct: 490 ÷ 70 = 7
8. Yes
9. No, correct: 540 ÷ 30 = 18

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