Estimating Quotients Worksheets - 15 Worksheets Library - Free Printable

Let’s solve each problem by estimating the quotient using compatible numbers — that means we’ll round the divisor and dividend to numbers that are easier to divide mentally, like multiples of 10 or numbers you know from multiplication tables.

We’ll go one by one:

---

1. 64 ) 525

Round 64 → 60
Round 525 → 540 (because 540 ÷ 60 is easy)
540 ÷ 60 = 9 ✔ (already given as example)

---

2. 52 ) 320

Round 52 → 50
320 stays close to 300 or 350? Let’s try 300 ÷ 50 = 6
But 50 × 6 = 300 → too low
Try 350 ÷ 50 = 7 → 50 × 7 = 350 → a bit high
Actual: 52 × 6 = 312 → very close to 320
So estimate: 6

Compatible: 320 ÷ 50 ≈ 6.4 → round to 6

---

3. 22 ) 467

Round 22 → 20
Round 467 → 460 or 480?
460 ÷ 20 = 23
480 ÷ 20 = 24
Check: 22 × 21 = 462 → very close to 467
So estimate: 21

Compatible: 460 ÷ 20 = 23 → but actual is closer to 21
Better: Use 440 ÷ 22 = 20 → 467 - 440 = 27 → so about 21
Estimate: 21

---

4. 19 ) 225

Round 19 → 20
Round 225 → 220 or 240?
220 ÷ 20 = 11
240 ÷ 20 = 12
Check: 19 × 11 = 209
19 × 12 = 228 → very close to 225
So estimate: 12

Compatible: 225 ÷ 20 ≈ 11.25 → round to 11 or 12? Since 228 is closer than 209, pick 12

---

5. 41 ) 765

Round 41 → 40
Round 765 → 760 or 800?
760 ÷ 40 = 19
800 ÷ 40 = 20
Check: 41 × 18 = 738
41 × 19 = 779 → too high
765 - 738 = 27 → so about 18.6 → estimate 19? Wait, 779 is over 765 → better to say 18

Wait: 40 × 19 = 760 → super close to 765
So even though 41×19=779, for estimation with compatible numbers, we use 760÷40=19
Estimate: 19

---

6. 57 ) 678

Round 57 → 60
Round 678 → 660 or 720?
660 ÷ 60 = 11
720 ÷ 60 = 12
Check: 57 × 11 = 627
57 × 12 = 684 → very close to 678
684 - 678 = 6 → so almost 12
Estimate: 12

Compatible: 660 ÷ 60 = 11 → but 684 is closer → use 12

---

7. 83 ) 654

Round 83 → 80
Round 654 → 640 or 720?
640 ÷ 80 = 8
720 ÷ 80 = 9
Check: 83 × 7 = 581
83 × 8 = 664 → very close to 654
664 - 654 = 10 → so about 7.9 → estimate 8

Compatible: 640 ÷ 80 = 8 → perfect
Estimate: 8

---

8. 37 ) 810

Round 37 → 40
Round 810 → 800
800 ÷ 40 = 20
Check: 37 × 20 = 740
37 × 22 = 814 → very close to 810
So estimate: 22

Compatible: 800 ÷ 40 = 20 → but actual is higher → adjust to 22

Alternatively: 37 ≈ 40, 810 ≈ 800 → 20, but since 37 < 40, actual quotient will be higher → so 22 makes sense.

---

9. 12 ) 218

Round 12 → 10 or keep 12? Better to use 12 since it's small.
Round 218 → 216 (because 12 × 18 = 216)
216 ÷ 12 = 18
218 - 216 = 2 → so about 18.16 → estimate 18

Compatible: 216 ÷ 12 = 18 → perfect
Estimate: 18

---

10. 49 ) 712

Round 49 → 50
Round 712 → 700
700 ÷ 50 = 14
Check: 49 × 14 = 686
49 × 15 = 735 → too high
712 - 686 = 26 → so about 14.5 → estimate 14

Compatible: 700 ÷ 50 = 14 → good
Estimate: 14

---

11. 21 ) 451

Round 21 → 20
Round 451 → 440 or 460?
440 ÷ 20 = 22
460 ÷ 20 = 23
Check: 21 × 21 = 441
21 × 22 = 462 → too high
451 - 441 = 10 → so about 21.5 → estimate 21

Compatible: 440 ÷ 20 = 22 → but actual is closer to 21 → use 21

---

12. 33 ) 671

Round 33 → 30
Round 671 → 660 or 690?
660 ÷ 30 = 22
690 ÷ 30 = 23
Check: 33 × 20 = 660
33 × 21 = 693 → too high
671 - 660 = 11 → so about 20.3 → estimate 20

Compatible: 660 ÷ 30 = 22 → wait, that’s not matching
Wait: 33 × 20 = 660 → yes! So 660 ÷ 33 = 20
So if we use 660 ÷ 33 = 20 → that’s exact for compatible numbers
Estimate: 20

---

Now let’s list all answers clearly:

Final Answer:
1. 9
2. 6
3. 21
4. 12
5. 19
6. 12
7. 8
8. 22
9. 18
10. 14
11. 21
12. 20