Estimating Quotients worksheet with 12 division problems for elementary students to practice estimating quotients using compatible numbers.

Let's solve this step by step. The task is to estimate each quotient using compatible numbers.

What are compatible numbers?

Compatible numbers are numbers that are close to the original numbers and are easy to divide mentally. They help us estimate quotients quickly.

We'll go through each problem, round the numbers to make them easier to divide, and then estimate the quotient.

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1. $ 5,581 \div 76 $

- Round 5,581 → 5,600 (close and divisible)
- Round 76 → 70 (easier to divide)
- Now: $ 5,600 \div 70 = 80 $
- ✔ Estimate: 80

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2. $ 1,804 \div 18 $

- Round 1,804 → 1,800
- 18 stays as 18 (already nice)
- $ 1,800 \div 18 = 100 $
- ✔ Estimate: 100

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3. $ 1,250 \div 41 $

- Round 1,250 → 1,200 or 1,240? Let's use 1,200 for ease.
- Round 41 → 40
- $ 1,200 \div 40 = 30 $
- ✔ Estimate: 30

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4. $ 2,318 \div 36 $

- Round 2,318 → 2,400 (since 2,400 ÷ 36 is easier)
- Round 36 → 36 (stay same)
- $ 2,400 \div 36 = ? $
- $ 36 \times 60 = 2,160 $
- $ 36 \times 66 = 2,376 $ — too big
- Try $ 36 \times 60 = 2,160 $, $ 36 \times 67 = 2,412 $
- So 2,400 ÷ 36 ≈ 66.7 → round to 67
- But let’s simplify: use 2,400 ÷ 40 = 60, but we used 36.
- Better: Use 2,400 ÷ 36 ≈ 67
- ✔ Estimate: 67

Alternatively, use:
- 2,318 ≈ 2,400
- 36 ≈ 36
- $ 2,400 \div 36 = 66.\overline{6} $ → ≈ 67

✔ Estimate: 67

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5. $ 5,498 \div 94 $

- Round 5,498 → 5,400
- Round 94 → 90
- $ 5,400 \div 90 = 60 $
- ✔ Estimate: 60

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6. $ 1,748 \div 22 $

- Round 1,748 → 1,800
- Round 22 → 20
- $ 1,800 \div 20 = 90 $
- ✔ Estimate: 90

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7. $ 4,311 \div 59 $

- Round 4,311 → 4,200 or 4,500?
- 59 → 60
- Try 4,200 ÷ 60 = 70
- Or 4,500 ÷ 60 = 75
- 4,311 is closer to 4,200? Actually 4,311 ≈ 4,200 or 4,500?

Better: 4,311 → 4,200 (if rounding down), but 4,311 ÷ 60 ≈ ?

Try: $ 4,200 \div 60 = 70 $
But 4,311 is a bit more than 4,200 → maybe 72?

Wait: 60 × 70 = 4,200
60 × 72 = 4,320 → very close!

So $ 4,311 \div 59 $ ≈ $ 4,320 \div 60 = 72 $

Use compatible: 4,320 ÷ 60 = 72

✔ Estimate: 72

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8. $ 4,015 \div 23 $

- Round 4,015 → 4,000
- Round 23 → 20
- $ 4,000 \div 20 = 200 $
- ✔ Estimate: 200

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9. $ 6,210 \div 89 $

- Round 6,210 → 6,300
- Round 89 → 90
- $ 6,300 \div 90 = 70 $
- ✔ Estimate: 70

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10. $ 1,594 \div 22 $

- Round 1,594 → 1,600
- Round 22 → 20
- $ 1,600 \div 20 = 80 $
- ✔ Estimate: 80

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11. $ 2,938 \div 63 $

- Round 2,938 → 2,800 or 3,000?
- 63 → 60
- Try 3,000 ÷ 60 = 50
- But 2,938 is less than 3,000 → try 2,800 ÷ 60 = 46.66 → ~47
- Or better: 2,938 ≈ 2,700? Not good.

Try: 2,938 → 2,700? No.

Better: 2,938 ≈ 2,800? Still not great.

How about: 63 × 45 = 2,835
63 × 46 = 2,898
63 × 47 = 2,961 → too big

So 2,938 ÷ 63 ≈ 46.6 → so estimate around 47

Use compatible: 2,800 ÷ 60 = 46.66 → ~47

Or: 2,940 ÷ 60 = 49 → but 63 is higher.

Best: Round 2,938 → 2,800, 63 → 70? No, that’s worse.

Use: 2,938 → 2,800, 63 → 60 → 2,800 ÷ 60 = 46.66 → ≈ 47

✔ Estimate: 47

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12. $ 3,052 \div 81 $

- Round 3,052 → 3,200 or 3,000?
- 81 → 80
- Try 3,200 ÷ 80 = 40
- But 3,052 is less → try 3,000 ÷ 80 = 37.5 → ~38
- Or 3,052 ≈ 3,200? Too high.

Better: 3,052 → 3,200? No, it’s less.

Try: 3,052 → 3,000, 81 → 80 → $ 3,000 \div 80 = 37.5 $ → ≈ 38

Or: 3,200 ÷ 80 = 40, but that's overestimating.

So best: $ 3,000 \div 80 = 37.5 $ → ≈ 38

✔ Estimate: 38

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Final Answers:

| Problem | Estimate |
|--------|---------|
| 1 | 80 |
| 2 | 100 |
| 3 | 30 |
| 4 | 67 |
| 5 | 60 |
| 6 | 90 |
| 7 | 72 |
| 8 | 200 |
| 9 | 70 |
| 10 | 80 |
| 11 | 47 |
| 12 | 38 |

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Summary of Estimations Using Compatible Numbers:

1. $ 5,581 \div 76 \approx 5,600 \div 70 = 80 $
2. $ 1,804 \div 18 \approx 1,800 \div 18 = 100 $
3. $ 1,250 \div 41 \approx 1,200 \div 40 = 30 $
4. $ 2,318 \div 36 \approx 2,400 \div 36 = 67 $
5. $ 5,498 \div 94 \approx 5,400 \div 90 = 60 $
6. $ 1,748 \div 22 \approx 1,800 \div 20 = 90 $
7. $ 4,311 \div 59 \approx 4,320 \div 60 = 72 $
8. $ 4,015 \div 23 \approx 4,000 \div 20 = 200 $
9. $ 6,210 \div 89 \approx 6,300 \div 90 = 70 $
10. $ 1,594 \div 22 \approx 1,600 \div 20 = 80 $
11. $ 2,938 \div 63 \approx 2,800 \div 60 = 47 $
12. $ 3,052 \div 81 \approx 3,000 \div 80 = 38 $

✔ All estimates are now complete!