Estimating Quotients worksheet with examples and space to write correct answers.

We are given several division problems with estimated quotients. For each, we need to check whether the estimate is correct. If it’s not correct, we must write the correct estimation.

The method used in the examples is rounding both the dividend and divisor to friendly numbers (usually to the nearest 10 or 100) and then dividing.

Let’s go one by one.

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1. 585 ÷ 29

Given estimate:
510 ÷ 30 = 17
Then they also show: 600 ÷ 30 = 20
They marked the second one (20) as correct — but wait, the instruction says: *Check if the given estimates are correct.* So we need to see which estimate they’re claiming is correct.

Looking at the layout:
First line: 585 ÷ 29
= 510 ÷ 30 = 17
Then below that (in blue): = 600 ÷ 30 = 20

It seems they tried two estimates, and the blue one (20) is what they think is correct — but we must verify.

Actual value: 585 ÷ 29 ≈ 20.17 → so 20 is a good estimate.

Rounding:
585 → 600 (nearest 100)
29 → 30 (nearest 10)
600 ÷ 30 = 20 ✔ Correct estimate.

So the correct estimate is 20. The first estimate (510 ÷ 30 = 17) is less accurate (510 is too low for 585), so it's not the best estimate.

But per instructions: *If it is correct write yes. If not, then write the correct estimation.*

Since the sheet shows “= 600 ÷ 30 = 20” in blue, likely they want us to confirm that 20 is correct — and it is.

So for this one: ✔ Correct — answer is 20.

But wait — the problem says: “Check if the given estimates are correct.” Each box has some work shown. We need to judge whether the final number shown is correct.

Let’s list all 9 problems with their given estimates:

1. 585 ÷ 29
Given steps:
= 510 ÷ 30 = 17
= 600 ÷ 30 = 20
→ They likely intend 20 as the answer. Since 585÷29≈20.17, 20 is good. So correct.

2. 143 ÷ 53
Given: = 100 ÷ 50 = 2
Check: 143 → 100? That’s rounding down too much. Better: 143 ≈ 150, 53 ≈ 50 → 150 ÷ 50 = 3
Actual: 143 ÷ 53 ≈ 2.698 → closer to 3 than 2.
So estimate of 2 is not correct. Correct estimate: 3

3. 492 ÷ 41
Given: = 400 ÷ 50 = 8
But 492 ≈ 500, 41 ≈ 40 → 500 ÷ 40 = 12.5 → ~13
Or 492 ÷ 41 ≈ 12.0
Let’s compute: 41 × 12 = 492 exactly! So exact quotient is 12.
Their estimate: 400 ÷ 50 = 8 → too low.
So incorrect; correct estimate: 12

4. 346 ÷ 123
Given: = 400 ÷ 100 = 4
Round: 346 ≈ 300 or 350? 123 ≈ 120 or 100?
Better: 346 ≈ 350, 123 ≈ 120 → 350 ÷ 120 ≈ 2.92 → ~3
Actual: 346 ÷ 123 ≈ 2.81
So estimate of 4 is too high.
Their estimate = 4 → incorrect
Correct estimate: 3

5. 259 ÷ 127
Given: = 240 ÷ 120 = 2
Round: 259 ≈ 260, 127 ≈ 130 → 260 ÷ 130 = 2
Actual: 259 ÷ 127 ≈ 2.04 → very close to 2
So estimate 2 is correct

6. 567 ÷ 33
Given: = 600 ÷ 30 = 20
Round: 567 ≈ 600, 33 ≈ 30 → 600 ÷ 30 = 20
Actual: 567 ÷ 33 = 17.18… (since 33×17 = 561, 33×18 = 594)
So 17.18 → closer to 17
Estimate 20 is a bit high.
Better rounding: 567 ≈ 570, 33 ≈ 30 → 570 ÷ 30 = 19
Or 567 ÷ 33 ≈ 17.2 → best estimate is 17
So given estimate 20 is incorrect; correct: 17

7. 482 ÷ 74
Given: = 500 ÷ 100 = 5
Round: 482 ≈ 500, 74 ≈ 70 or 75?
500 ÷ 70 ≈ 7.14
Actual: 482 ÷ 74 = ? 74×6 = 444, 74×7 = 518 → so between 6 and 7 → ≈6.5
So estimate 5 is too low.
Better: 480 ÷ 80 = 6
So correct estimate: 6

8. 345 ÷ 178
Given: = 400 ÷ 200 = 2
Round: 345 ≈ 350, 178 ≈ 180 → 350 ÷ 180 ≈ 1.94 → ~2
Actual: 345 ÷ 178 ≈ 1.94 → yes, 2 is fine.
So estimate is correct

9. 512 ÷ 27
Given: = 510 ÷ 30 = 17
Round: 512 ≈ 510, 27 ≈ 30 → 510 ÷ 30 = 17
Actual: 27 × 18 = 486, 27 × 19 = 513 → so 512 ÷ 27 ≈ 18.96 → almost 19
So 17 is too low.
Better estimate: 510 ÷ 27 ≈ 18.9 → round to 19
Or round 512→500, 27→25 → 500÷25=20 — also okay, but 19 is better.
Since actual ≈18.96, best whole-number estimate is 19
So given estimate 17 is incorrect; correct: 19

Now let’s compile all answers clearly:

1. 585 ÷ 29 → estimate 20 → ✔ correct
2. 143 ÷ 53 → estimate 2 → ✘ correct estimate: 3
3. 492 ÷ 41 → estimate 8 → ✘ correct estimate: 12
4. 346 ÷ 123 → estimate 4 → ✘ correct estimate: 3
5. 259 ÷ 127 → estimate 2 → ✔ correct
6. 567 ÷ 33 → estimate 20 → ✘ correct estimate: 17
7. 482 ÷ 74 → estimate 5 → ✘ correct estimate: 6
8. 345 ÷ 178 → estimate 2 → ✔ correct
9. 512 ÷ 27 → estimate 17 → ✘ correct estimate: 19

But the worksheet format shows blank boxes where we need to fill in either “yes” (if correct) or the correct estimate.

Assuming the student is to fill the blank boxes under each problem:

- For problems where the given final estimate is correct: write “yes”
- Else: write the correct estimate (a whole number)

Let’s double-check each with more precision:

1. 585 ÷ 29 = 20.172… → estimate 20 → acceptable → yes
2. 143 ÷ 53 = 2.698 → nearest whole = 3 → estimate was 2 → 3
3. 492 ÷ 41 = 12 exactly → estimate was 8 → 12
4. 346 ÷ 123 = 2.813 → nearest = 3 → estimate was 4 → 3
5. 259 ÷ 127 = 2.039 → nearest = 2 → estimate was 2 → yes
6. 567 ÷ 33 = 17.181… → nearest = 17 → estimate was 20 → 17
7. 482 ÷ 74 = 6.513… → nearest = 7? Wait — 6.5 rounds to 7, but estimation often uses compatible numbers, and 500÷100=5 is poor. Let's reconsider:

482 ÷ 74:
Compatible rounding: 74 ≈ 75, 482 ≈ 450? 450 ÷ 75 = 6
Or 480 ÷ 80 = 6
Actual 6.51 → many would estimate 6 or 7. In elementary estimation, they usually round to get a clean division, and 6 is common. Since 6.5 is halfway, but the problem used 500÷100=5, which is worse. The best simple estimate is 6 or 7?

Let’s see what typical curriculum does: For 482 ÷ 74, round 482 → 480, 74 → 70 → 480 ÷ 70 ≈ 6.86 → 7
Or 74 → 75, 482 → 450 → 6
But 74 × 6 = 444, 74 × 7 = 518 → 482 is closer to 518?
Difference: 482−444 = 38, 518−482 = 36 → actually closer to 7.
So 6.51 is closer to 7 than 6. So 7 may be better.

However, in the worksheet, they used 500 ÷ 100 = 5, which is far off. The expected answer likely is 6 or 7. Let's compute error:
- Estimate 5 → error = |6.51−5| = 1.51
- Estimate 6 → error = 0.51
- Estimate 7 → error = 0.49
So 7 is slightly better.

But many textbooks teach rounding divisor to nearest 10 and dividend to nearest 100 or compatible:
74 → 70, 482 → 490 → 490 ÷ 70 = 7
Yes! 490 ÷ 70 = 7. That’s clean.

So correct estimate should be 7, not 5.

I’ll update: #7 → 7

8. 345 ÷ 178 = 1.94 → rounds to 2 → ✔ yes
9. 512 ÷ 27 = 18.96 → rounds to 19 → estimate was 17 → 19

Now final list:

1. yes
2. 3
3. 12
4. 3
5. yes
6. 17
7. 7
8. yes
9. 19

But the worksheet shows three columns of three rows — 9 boxes. In each box, there is some work and a final number. The blank is below that — we fill either “yes” or the correct estimate.

So the answers to write in the blanks are:

Box 1: yes
Box 2: 3
Box 3: 12
Box 4: 3
Box 5: yes
Box 6: 17
Box 7: 7
Box 8: yes
Box 9: 19

Let me verify #6 again: 567 ÷ 33
33 × 17 = 561
33 × 18 = 594
567 − 561 = 6, so 17 + 6/33 = 17.18 → yes, 17 is best whole estimate.

#4: 346 ÷ 123
123 × 2 = 246
123 × 3 = 369
346 − 246 = 100, 369 − 346 = 23 → closer to 3 → yes, 3.

All good.

Final Answer:
yes, 3, 12, 3, yes, 17, 7, yes, 19