Estimating Quotients Worksheets - 15 Worksheets Library - Free Printable

You're working on “Estimating Quotients” by using compatible numbers.

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## ✔ What are Compatible Numbers?

Compatible numbers are numbers that are easy to compute mentally, often because they divide evenly or are close to round numbers (like multiples of 10, 5, or 100). When estimating quotients (division), we round the dividend and/or divisor to nearby compatible numbers so the division is simple to do in your head.

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## 🧠 Strategy:

For each problem:
1. Look at the dividend (the big number) and divisor (the small number).
2. Round them to numbers that are easy to divide — usually to the nearest ten or hundred, but make sure they “go together” nicely.
3. Do the mental division.
4. Write the estimated quotient.

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Let’s solve all 30 problems with explanations:

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🔢 Column 1

1. 324 ÷ 5
→ 324 ≈ 325 (because 325 ÷ 5 = 65)
✔ Estimate: 65

2. 567 ÷ 15
→ 567 ≈ 570, 15 stays → 570 ÷ 15 = 38
✔ Estimate: 38

3. 268 ÷ 20
→ 268 ≈ 270 → 270 ÷ 20 = 13.5 → round to 14 or keep as 13.5? Since it's estimation, 14 is fine.
✔ Estimate: 14 (or 13.5)

4. 345 ÷ 50
→ 345 ≈ 350 → 350 ÷ 50 = 7
✔ Estimate: 7

5. 326 ÷ 24
→ 326 ≈ 324 (which is 24×13.5), or 320 ÷ 20 = 16 → better: 324 ÷ 24 = 13.5 → use 13 or 14
✔ Estimate: 13 or 14

*Better: 326 ≈ 300, 24 ≈ 25 → 300 ÷ 25 = 12*
✔ Better estimate: 12

6. 523 ÷ 3
→ 523 ≈ 522 (divisible by 3: 5+2+2=9 → divisible) → 522 ÷ 3 = 174
✔ Estimate: 174

7. 251 ÷ 20
→ 251 ≈ 250 → 250 ÷ 20 = 12.5 → round to 13
✔ Estimate: 13

8. 123 ÷ 15
→ 123 ≈ 120 → 120 ÷ 15 = 8
✔ Estimate: 8

9. 321 ÷ 12
→ 321 ≈ 324 → 324 ÷ 12 = 27
✔ Estimate: 27

10. 562 ÷ 22
→ 562 ≈ 550, 22 ≈ 22 → 550 ÷ 22 = 25
✔ Estimate: 25

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🔢 Column 2

11. 675 ÷ 7
→ 675 ≈ 672 (since 7×96=672) → 672 ÷ 7 = 96
✔ Estimate: 96

12. 321 ÷ 9
→ 321 ≈ 315 (9×35) or 324 (9×36) → 324 ÷ 9 = 36
✔ Estimate: 36

13. 765 ÷ 17
→ 765 ≈ 765 (exact: 17×45=765!) → 765 ÷ 17 = 45
✔ Estimate: 45

14. 862 ÷ 19
→ 862 ≈ 855 (19×45=855) → 855 ÷ 19 = 45
✔ Estimate: 45

15. 543 ÷ 5
→ 543 ≈ 545 → 545 ÷ 5 = 109
✔ Estimate: 109

16. 652 ÷ 12
→ 652 ≈ 660 → 660 ÷ 12 = 55
✔ Estimate: 55

17. 761 ÷ 11
→ 761 ≈ 770 → 770 ÷ 11 = 70
✔ Estimate: 70

18. 453 ÷ 12
→ 453 ≈ 456 → 456 ÷ 12 = 38
✔ Estimate: 38

19. 321 ÷ 8
→ 321 ≈ 320 → 320 ÷ 8 = 40
✔ Estimate: 40

20. 672 ÷ 11
→ 672 ≈ 660 → 660 ÷ 11 = 60
✔ Estimate: 60

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🔢 Column 3

21. 321 ÷ 19
→ 321 ≈ 323 (19×17=323) → 323 ÷ 19 = 17
✔ Estimate: 17

22. 524 ÷ 12
→ 524 ≈ 528 → 528 ÷ 12 = 44
✔ Estimate: 44

23. 756 ÷ 23
→ 756 ≈ 759 (23×33=759) → 759 ÷ 23 = 33
✔ Estimate: 33

24. 782 ÷ 8
→ 782 ≈ 784 → 784 ÷ 8 = 98
✔ Estimate: 98

25. 541 ÷ 11
→ 541 ≈ 550 → 550 ÷ 11 = 50
✔ Estimate: 50

26. 512 ÷ 7
→ 512 ≈ 511 (7×73=511) → 511 ÷ 7 = 73
✔ Estimate: 73

27. 876 ÷ 9
→ 876 ≈ 873 (9×97=873) → 873 ÷ 9 = 97
✔ Estimate: 97

28. 519 ÷ 40
→ 519 ≈ 520 → 520 ÷ 40 = 13
✔ Estimate: 13

29. 987 ÷ 33
→ 987 ≈ 990 → 990 ÷ 33 = 30
✔ Estimate: 30

30. 298 ÷ 12
→ 298 ≈ 300 → 300 ÷ 12 = 25
✔ Estimate: 25

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## 📋 Final Answer Key (Estimated Quotients):

| Problem | Estimate |
|---------|----------|
| 1 | 65 |
| 2 | 38 |
| 3 | 14 |
| 4 | 7 |
| 5 | 12 |
| 6 | 174 |
| 7 | 13 |
| 8 | 8 |
| 9 | 27 |
| 10 | 25 |
| 11 | 96 |
| 12 | 36 |
| 13 | 45 |
| 14 | 45 |
| 15 | 109 |
| 16 | 55 |
| 17 | 70 |
| 18 | 38 |
| 19 | 40 |
| 20 | 60 |
| 21 | 17 |
| 22 | 44 |
| 23 | 33 |
| 24 | 98 |
| 25 | 50 |
| 26 | 73 |
| 27 | 97 |
| 28 | 13 |
| 29 | 30 |
| 30 | 25 |

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## 💡 Tip for Students:

Always ask yourself:
> “What number close to this is easy to divide by the divisor?”

You’re not looking for exact answers — you’re learning to think flexibly and estimate quickly using friendly numbers!

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✔ You can now fill in your worksheet with these estimates! Let me know if you want a printable version or practice quiz.