Estimating sums and differences worksheet with rounding exercises and math problems.

Let's solve the problem step by step based on the worksheet titled "Estimating sums and differences".

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Part 1: Round the numbers to the leading digit. Estimate the sum or difference.

We are to round each number to its leading digit, then estimate the sum or difference.

#### Example:
- 3,526 + 4,020 →
- 3,526 → round to nearest thousand: 4,000 (leading digit is 3, but we round up because 526 ≥ 500)
- 4,020 → already close to 4,000
- Estimate: 4,000 + 4,000 = 8,000

But wait — the worksheet says "Round to the leading digit", which means:
- The leading digit is the first non-zero digit.
- Then we round to that place value.

So:
- 3,526: leading digit is 3 in the thousands place → round to nearest thousand: 4,000 (since 526 ≥ 500)
- 4,020: leading digit is 4 in thousands → round to 4,000

So:
3,526 + 4,020 ≈ 4,000 + 4,000 = 8,000

Let’s go through all of them:

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Section 1: Round to leading digit, estimate sum/difference

| Problem | Rounded Numbers | Estimate |
|--------|------------------|---------|
| 3,526 + 4,020 | 4,000 + 4,000 | 8,000 |
| 198,248 – 200,000 | 200,000 – 200,000 | 0 |
| 1,146 + 7,000 | 1,000 + 7,000 | 8,000 |
| 41,000 + 17,000 | 40,000 + 20,000 | 60,000 |

> Note: For 41,000 → leading digit is 4 (ten-thousands), so round to 40,000; 17,000 → leading digit is 1 (ten-thousands), so round to 20,000? Wait — let’s be careful.

Actually, "leading digit" means the first digit, and we round to the place value of that digit.

- 41,000: leading digit is 4 in the ten-thousands place → round to nearest ten-thousand → 40,000
- 17,000: leading digit is 1 in the ten-thousands place → round to nearest ten-thousand → 20,000 (since 7,000 ≥ 5,000)

So: 40,000 + 20,000 = 60,000 ✔

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Now let’s do the next section.

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Section 2: Round to nearest hundred, estimate sum/difference

We now round to the nearest hundred, not just the leading digit.

Let’s go one by one:

#### 1. 485 + 21,455
- 485 → nearest hundred: 500
- 21,455 → nearest hundred: 21,500
- Sum: 500 + 21,500 = 22,000

#### 2. 2,520 – 1,680
- 2,520 → 2,500
- 1,680 → 1,700
- Difference: 2,500 – 1,700 = 800

#### 3. 2,434 + 3,192
- 2,434 → 2,400
- 3,192 → 3,200
- Sum: 2,400 + 3,200 = 5,600

#### 4. 682,726 + 1,520,150
- 682,726 → 682,700 (nearest hundred)
- 1,520,150 → 1,520,200
- Sum: 682,700 + 1,520,200 = 2,202,900

Wait — let's check rounding:
- 682,726 → hundreds: look at tens digit: 2 < 5 → 682,700
- 1,520,150 → tens digit is 5 → round up → 1,520,200
- Total: 682,700 + 1,520,200 = 2,202,900

#### 5. 56,499 + 22,114
- 56,499 → 56,500
- 22,114 → 22,100
- Sum: 56,500 + 22,100 = 78,600

#### 6. 962,276 + 4,880
- 962,276 → 962,300
- 4,880 → 4,900
- Sum: 962,300 + 4,900 = 967,200

#### 7. 80,925 + 3,125,000
- 80,925 → 80,900
- 3,125,000 → already at hundred place → 3,125,000
- Sum: 80,900 + 3,125,000 = 3,205,900

#### 8. 9,234 + 5,734
- 9,234 → 9,200
- 5,734 → 5,700
- Sum: 9,200 + 5,700 = 14,900

#### 9. 4,505 + 4,185
- 4,505 → 4,500
- 4,185 → 4,200
- Sum: 4,500 + 4,200 = 8,700

#### 10. 45,000 – 21,480
- 45,000 → already rounded
- 21,480 → 21,500
- Difference: 45,000 – 21,500 = 23,500

#### 11. 3,212 + 1,422
- 3,212 → 3,200
- 1,422 → 1,400
- Sum: 3,200 + 1,400 = 4,600

#### 12. 172,397 – 182,911
- 172,397 → 172,400
- 182,911 → 182,900
- Difference: 172,400 – 182,900 = –10,500

Note: This is negative, but estimation is fine.

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Section 3: Write < or > in each problem

We need to compare the actual sum/difference with the estimated value.

Let’s go one by one.

#### 1. 329 + 495 = 825
Actual sum: 329 + 495 = 824
Compare: 824 vs 825 → 824 < 825 → So: <

#### 2. 11,540 – 6,130 = 6,420
Actual: 11,540 – 6,130 = 5,410
Compare: 5,410 vs 6,420 → 5,410 < 6,420 → <

#### 3. 863 + 311 = 835
Actual: 863 + 311 = 1,174
Compare: 1,174 vs 835 → 1,174 > 835 → >

#### 4. 8,193 – 6,448 = 1,600
Actual: 8,193 – 6,448 = 1,745
Compare: 1,745 vs 1,600 → 1,745 > 1,600 → >

#### 5. 41,924 – 12,445 = 52,000
Actual: 41,924 – 12,445 = 29,479
Compare: 29,479 vs 52,000 → 29,479 < 52,000 → <

#### 6. 634,572 + 197,530 = 652,000
Actual: 634,572 + 197,530 = 832,102
Compare: 832,102 vs 652,000 → 832,102 > 652,000 → >

#### 7. 15,883 + 12,694 = 30,000
Actual: 15,883 + 12,694 = 28,577
Compare: 28,577 vs 30,000 → 28,577 < 30,000 → <

#### 8. 733,096 – 351,645 = 453,000
Actual: 733,096 – 351,645 = 381,451
Compare: 381,451 vs 453,000 → 381,451 < 453,000 → <

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✔ Final Answers:

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#### Part 1: Estimate using leading digit

| Problem | Estimate |
|--------|---------|
| 3,526 + 4,020 | 8,000 |
| 198,248 – 200,000 | 0 |
| 1,146 + 7,000 | 8,000 |
| 41,000 + 17,000 | 60,000 |

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#### Part 2: Round to nearest hundred, estimate

| Problem | Estimate |
|--------|---------|
| 485 + 21,455 | 22,000 |
| 2,520 – 1,680 | 800 |
| 2,434 + 3,192 | 5,600 |
| 682,726 + 1,520,150 | 2,202,900 |
| 56,499 + 22,114 | 78,600 |
| 962,276 + 4,880 | 967,200 |
| 80,925 + 3,125,000 | 3,205,900 |
| 9,234 + 5,734 | 14,900 |
| 4,505 + 4,185 | 8,700 |
| 45,000 – 21,480 | 23,500 |
| 3,212 + 1,422 | 4,600 |
| 172,397 – 182,911 | –10,500 |

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#### Part 3: Compare actual vs estimate

| Problem | Symbol |
|--------|--------|
| 329 + 495 = 825 | < |
| 11,540 – 6,130 = 6,420 | < |
| 863 + 311 = 835 | > |
| 8,193 – 6,448 = 1,600 | > |
| 41,924 – 12,445 = 52,000 | < |
| 634,572 + 197,530 = 652,000 | > |
| 15,883 + 12,694 = 30,000 | < |
| 733,096 – 351,645 = 453,000 | < |

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✔ Summary of Key Concepts:

- Leading digit rounding: Round to the place value of the first digit (e.g., 3,526 → 4,000).
- Nearest hundred: Look at the tens digit; if ≥ 5, round up.
- Estimation: Helps quickly approximate results.
- Comparison: Actual vs estimate shows whether estimate is high or low.

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