Estimating Quotients worksheet for elementary students to practice division estimation using compatible numbers.

Let’s solve each problem step by step using compatible numbers — that means we pick numbers close to the original ones that are easier to divide.

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Problem 1: 38 ÷ 5
We already have the example:
38 is close to 40 → 40 ÷ 5 = 8
✔ Estimated quotient: 8

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Problem 2: 112 ÷ 6
What number near 112 is easy to divide by 6?
→ 120 is divisible by 6 (because 6 × 20 = 120)
112 is close to 120 → 120 ÷ 6 = 20
✔ Estimated quotient: 20

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Problem 3: 483 ÷ 4
What number near 483 is easy to divide by 4?
→ 480 is divisible by 4 (because 4 × 120 = 480)
483 is very close to 480 → 480 ÷ 4 = 120
✔ Estimated quotient: 120

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Problem 4: 76 ÷ 7
What number near 76 is easy to divide by 7?
→ 70 is divisible by 7 (7 × 10 = 70)
76 is closer to 70 than to 77? Actually, 77 is also divisible by 7 (7 × 11 = 77), and 76 is only 1 away from 77.
So better to use 77 → 77 ÷ 7 = 11
✔ Estimated quotient: 11

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Problem 5: 214 ÷ 5
What number near 214 is easy to divide by 5?
→ 210 or 215? Both work. Let’s pick 210 (ends in 0).
210 ÷ 5 = 42
(Or 215 ÷ 5 = 43 — but 214 is closer to 215? Actually, 214 - 210 = 4; 215 - 214 = 1 → so 215 is closer!)
Better: 215 ÷ 5 = 43
✔ Estimated quotient: 43

Wait — let me double-check:
214 ÷ 5 → actual answer is 42.8 → so 43 is a good estimate.
Yes, 215 is closer → 43 is fine.

But sometimes teachers prefer rounding to nearest multiple of 5 or 10 for simplicity.
Alternatively, 200 ÷ 5 = 40 — too far.
210 ÷ 5 = 42 — also good.
Since 214 is between 210 and 215, and closer to 215, we’ll go with 43.

Actually, let’s be consistent: use the closest compatible number.

214 → 215 is 1 away → 215 ÷ 5 = 43
✔ Final choice: 43

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Problem 6: 349 ÷ 9
What number near 349 is divisible by 9?
Try 350? Not divisible by 9.
360 is divisible by 9 (9 × 40 = 360)
349 is 11 away from 360, but 342 is 9×38=342 → 349 - 342 = 7 → so 342 is closer?
Wait: 349 - 342 = 7; 360 - 349 = 11 → so 342 is closer.
But 342 might not be “compatible” if student doesn’t know 9×38.
Easier: round to 350? 350 ÷ 9 ≈ ? Not nice.
Best: 360 is standard compatible number for 9.
Even though 342 is closer, 360 is more commonly used as compatible.
Let’s check: 349 ÷ 9 ≈ 38.77 → so 39 would be actual rounded, but estimating with compatible numbers...

Standard approach: use 360 → 360 ÷ 9 = 40
That’s acceptable estimation.

Alternatively, 350 ÷ 7 = 50, but here it’s ÷9.

I think 360 is best → 40

✔ Estimated quotient: 40

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Problem 7: 724 ÷ 8
What number near 724 is divisible by 8?
720 is divisible by 8 (8 × 90 = 720)
724 is only 4 away → perfect!
720 ÷ 8 = 90
✔ Estimated quotient: 90

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Problem 8: 557 ÷ 7
What number near 557 is divisible by 7?
Try 560 → 7 × 80 = 560
557 is 3 away → very close!
560 ÷ 7 = 80
✔ Estimated quotient: 80

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Problem 9: 182 ÷ 3
What number near 182 is divisible by 3?
180 is divisible by 3 (3 × 60 = 180)
182 is 2 away → great!
180 ÷ 3 = 60
✔ Estimated quotient: 60

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Problem 10: 252 ÷ 3
This one is actually exact!
252 ÷ 3 = 84 → but since we’re estimating, we can still say 252 is compatible.
But if we must estimate, maybe round to 250? 250 ÷ 3 ≈ 83.3 → not helpful.
Actually, 252 is already compatible → 252 ÷ 3 = 84
But the instruction says “estimate”, so perhaps they want us to treat it as is?
No — compatible numbers mean we choose nearby easy numbers.
252 is fine → 84
But let’s see: maybe they expect 240 ÷ 3 = 80 or 270 ÷ 3 = 90?
252 is closer to 240? No, 252 - 240 = 12; 270 - 252 = 18 → so 240 is closer? But 252 is exactly divisible.

Actually, since 252 ÷ 3 = 84 exactly, and it’s easy, we can just use it.
But to follow “estimate”, perhaps round to 250? 250 ÷ 3 ≈ 83.3 → not integer.
Better: 240 ÷ 3 = 80 or 270 ÷ 3 = 90 — neither is super close.
Wait — 252 is 250 + 2 → not helpful.

Actually, 252 is compatible because 2+5+2=9 → divisible by 3. So it’s fine to use 252.

But the worksheet says “use compatible numbers to estimate”, implying we change the dividend to something easier.

In this case, 252 is already easy. Maybe leave as 84? But that’s exact.

Looking back at problem 1: they changed 38 to 40 even though 38÷5=7.6, estimated to 8.

Here, 252÷3=84 exactly — so no need to estimate? But the direction says “estimate each quotient”.

Perhaps for consistency, we should still pick a nearby compatible number.

Let’s try 240: 240 ÷ 3 = 80
Or 270: 270 ÷ 3 = 90
252 is closer to 240? 252-240=12; 270-252=18 → so 240 is closer.
But 252 is much closer to 250, but 250 not divisible by 3.

Another idea: 255 ÷ 3 = 85 → 255 is 3 away from 252 → very close!
And 255 is divisible by 3 (2+5+5=12).
So 255 ÷ 3 = 85
That’s better than 80 or 90.

✔ Estimated quotient: 85

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Problem 11: 626 ÷ 9
What number near 626 is divisible by 9?
Try 630 → 9 × 70 = 630
626 is 4 away → very close!
630 ÷ 9 = 70
✔ Estimated quotient: 70

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Problem 12: 249 ÷ 8
What number near 249 is divisible by 8?
240 ÷ 8 = 30
248 ÷ 8 = 31 (since 8×31=248)
249 is 1 away from 248 → perfect!
248 ÷ 8 = 31
✔ Estimated quotient: 31

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Problem 13: 714 ÷ 8
What number near 714 is divisible by 8?
720 ÷ 8 = 90
712 ÷ 8 = 89 (8×89=712)
714 - 712 = 2; 720 - 714 = 6 → so 712 is closer.
712 ÷ 8 = 89
✔ Estimated quotient: 89

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Problem 14: 453 ÷ 9
What number near 453 is divisible by 9?
450 ÷ 9 = 50 (since 9×50=450)
453 is 3 away → very close!
450 ÷ 9 = 50
✔ Estimated quotient: 50

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Problem 15: 544 ÷ 6
What number near 544 is divisible by 6?
540 ÷ 6 = 90 (6×90=540)
544 is 4 away → good!
540 ÷ 6 = 90
✔ Estimated quotient: 90

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Problem 16: 196 ÷ 4
What number near 196 is divisible by 4?
200 ÷ 4 = 50
196 is 4 away → but 196 itself is divisible by 4? 196 ÷ 4 = 49 exactly.
But again, we’re estimating.
If we use 200 → 50
Or 196 → 49
Which is better? Since 196 is exact, but the task says “estimate”, perhaps use 200.

Check: 196 ÷ 4 = 49 → actual
Estimate with 200 → 50 → difference of 1
With 196 → 49 → exact

But compatible numbers usually mean rounding to make division easy. 200 is easier than 196 for some students.

However, 196 is also easy: 200 - 4 = 196 → 200÷4=50, minus 1 → 49.

But for estimation purposes, many would use 200.

Let’s see what’s typical: in problem 1, they used 40 instead of 38.

Similarly, here, 200 is a round number.

So 200 ÷ 4 = 50
✔ Estimated quotient: 50

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Now, compiling all answers:

1. 8
2. 20
3. 120
4. 11
5. 43
6. 40
7. 90
8. 80
9. 60
10. 85
11. 70
12. 31
13. 89
14. 50
15. 90
16. 50

Final Answer:
[8, 20, 120, 11, 43, 40, 90, 80, 60, 85, 70, 31, 89, 50, 90, 50]