Estimating Sum and Difference worksheet with exercises for rounding and calculating approximate sums and differences.

Let's solve the problem step by step. The task is to estimate the sum or difference by rounding off the numbers to the nearest hundred (or thousand, depending on the size of the numbers), then performing the operation.

We'll go through each one carefully.

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🔹 Estimate the Sum

We round each number to the nearest hundred unless it's large enough that rounding to the nearest thousand makes more sense. We'll use nearest hundred for most cases, but adjust if needed.

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1. 3,854 + 6,028

- Round 3,854 → 3,900 (nearest hundred)
- Round 6,028 → 6,000 (nearest hundred)
- Estimated sum:
$ 3,900 + 6,000 = 9,900 $

✔ Answer: $ 3,900 + 6,000 = 9,900 $

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2. 8,322 + 1,103

- 8,322 → 8,300
- 1,103 → 1,100
- $ 8,300 + 1,100 = 9,400 $

✔ Answer: $ 8,300 + 1,100 = 9,400 $

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3. 67,551 + 85,302

These are larger numbers — better to round to the nearest thousand.

- 67,551 → 68,000 (since 551 ≥ 500)
- 85,302 → 85,000 (since 302 < 500)
- $ 68,000 + 85,000 = 153,000 $

✔ Answer: $ 68,000 + 85,000 = 153,000 $

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4. 10,364 + 59,493

Again, round to nearest thousand:

- 10,364 → 10,000 (364 < 500)
- 59,493 → 59,000 (493 < 500)
- $ 10,000 + 59,000 = 69,000 $

✔ Answer: $ 10,000 + 59,000 = 69,000 $

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5. 94,650 + 2,113

Round to nearest hundred or thousand?

- 94,650 → 94,700 (nearest hundred)
- 2,113 → 2,100 (nearest hundred)
- $ 94,700 + 2,100 = 96,800 $

Alternatively, if we round to thousands:
- 94,650 → 95,000
- 2,113 → 2,000
- $ 95,000 + 2,000 = 97,000 $

But since both numbers are close to hundreds, let’s stick with nearest hundred for consistency.

✔ Answer: $ 94,700 + 2,100 = 96,800 $

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🔹 Estimate the Difference

Now subtract after rounding.

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6. 9,493 – 2,324

Round to nearest hundred:

- 9,493 → 9,500
- 2,324 → 2,300
- $ 9,500 - 2,300 = 7,200 $

✔ Answer: $ 9,500 - 2,300 = 7,200 $

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7. 5,036 – 1,945

- 5,036 → 5,000
- 1,945 → 1,900
- $ 5,000 - 1,900 = 3,100 $

✔ Answer: $ 5,000 - 1,900 = 3,100 $

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8. 68,931 – 11,585

Round to nearest thousand:

- 68,931 → 69,000
- 11,585 → 12,000 (since 585 ≥ 500)
- $ 69,000 - 12,000 = 57,000 $

✔ Answer: $ 69,000 - 12,000 = 57,000 $

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9. 74,832 – 15,002

- 74,832 → 75,000 (832 ≥ 500)
- 15,002 → 15,000
- $ 75,000 - 15,000 = 60,000 $

✔ Answer: $ 75,000 - 15,000 = 60,000 $

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10. 35,846 – 5,394

Round to nearest hundred:

- 35,846 → 35,800
- 5,394 → 5,400
- $ 35,800 - 5,400 = 30,400 $

✔ Answer: $ 35,800 - 5,400 = 30,400 $

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✔ Final Answers

#### Estimate the sum:
1. $ 3,854 + 6,028 $ → $ \boxed{3,900} + \boxed{6,000} = \boxed{9,900} $
2. $ 8,322 + 1,103 $ → $ \boxed{8,300} + \boxed{1,100} = \boxed{9,400} $
3. $ 67,551 + 85,302 $ → $ \boxed{68,000} + \boxed{85,000} = \boxed{153,000} $
4. $ 10,364 + 59,493 $ → $ \boxed{10,000} + \boxed{59,000} = \boxed{69,000} $
5. $ 94,650 + 2,113 $ → $ \boxed{94,700} + \boxed{2,100} = \boxed{96,800} $

#### Estimate the difference:
6. $ 9,493 - 2,324 $ → $ \boxed{9,500} - \boxed{2,300} = \boxed{7,200} $
7. $ 5,036 - 1,945 $ → $ \boxed{5,000} - \boxed{1,900} = \boxed{3,100} $
8. $ 68,931 - 11,585 $ → $ \boxed{69,000} - \boxed{12,000} = \boxed{57,000} $
9. $ 74,832 - 15,002 $ → $ \boxed{75,000} - \boxed{15,000} = \boxed{60,000} $
10. $ 35,846 - 5,394 $ → $ \boxed{35,800} - \boxed{5,400} = \boxed{30,400} $

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📌 Summary of Rounding Rules Used:

- For numbers in the thousands, we rounded to the nearest hundred or thousand, depending on magnitude.
- We used nearest hundred for smaller numbers (< 10,000) and nearest thousand for larger ones (> 10,000).
- When rounding: look at the tens digit — if ≥ 50, round up; otherwise, down.

This method gives a quick and reasonable estimate for sums and differences.