Estimating Product worksheet for practicing multiplication estimation and exact calculation.

Let’s work through each problem step by step.

We are told to:
1. Estimate the product by rounding both numbers to the nearest hundred.
2. Calculate the exact product.
3. Compare them (though we don’t need to write the comparison — just fill in the blanks).

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Problem 1 is already done as an example:
- 323 × 458 → round to 300 × 500 = 150,000
- Exact: 323 × 458 = let’s verify:
323 × 400 = 129,200
323 × 50 = 16,150
323 × 8 = 2,584
Total: 129,200 + 16,150 = 145,350 + 2,584 = 147,934 ✔

Now let’s do the rest.

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Problem 2: 121 × 145

Round to nearest hundred:
- 121 → 100
- 145 → 100 (since 145 is less than 150, it rounds down)
→ Estimated: 100 × 100 = 10,000

Exact: 121 × 145
Break it down:
121 × 100 = 12,100
121 × 40 = 4,840
121 × 5 = 605
Add: 12,100 + 4,840 = 16,940 + 605 = 17,545

✔ So:
Estimated: 100 × 100 = 10,000
Exact: 17,545

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Problem 3: 432 × 451

Round:
- 432 → 400
- 451 → 500 (since 451 ≥ 450, rounds up)
→ Estimated: 400 × 500 = 200,000

Exact: 432 × 451
Use distributive property or standard multiplication:

432 × 400 = 172,800
432 × 50 = 21,600
432 × 1 = 432
Total: 172,800 + 21,600 = 194,400 + 432 = 194,832

✔ So:
Estimated: 400 × 500 = 200,000
Exact: 194,832

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Problem 4: 671 × 132

Round:
- 671 → 700
- 132 → 100
→ Estimated: 700 × 100 = 70,000

Exact: 671 × 132
Break it:
671 × 100 = 67,100
671 × 30 = 20,130
671 × 2 = 1,342
Add: 67,100 + 20,130 = 87,230 + 1,342 = 88,572

✔ So:
Estimated: 700 × 100 = 70,000
Exact: 88,572

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Problem 5: 231 × 412

Round:
- 231 → 200
- 412 → 400
→ Estimated: 200 × 400 = 80,000

Exact: 231 × 412
231 × 400 = 92,400
231 × 12 = ?
231 × 10 = 2,310
231 × 2 = 462 → total 2,310 + 462 = 2,772
So total: 92,400 + 2,772 = 95,172

✔ So:
Estimated: 200 × 400 = 80,000
Exact: 95,172

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Problem 6: 523 × 363

Round:
- 523 → 500
- 363 → 400 (since 363 ≥ 350)
→ Estimated: 500 × 400 = 200,000

Exact: 523 × 363
Break it:
523 × 300 = 156,900
523 × 60 = 31,380
523 × 3 = 1,569
Add: 156,900 + 31,380 = 188,280 + 1,569 = 189,849

✔ So:
Estimated: 500 × 400 = 200,000
Exact: 189,849

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Problem 7: 713 × 512

Round:
- 713 → 700
- 512 → 500
→ Estimated: 700 × 500 = 350,000

Exact: 713 × 512
713 × 500 = 356,500
713 × 12 = ?
713 × 10 = 7,130
713 × 2 = 1,426 → total 8,556
Total: 356,500 + 8,556 = 365,056

✔ So:
Estimated: 700 × 500 = 350,000
Exact: 365,056

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Problem 8: 512 × 621

Round:
- 512 → 500
- 621 → 600
→ Estimated: 500 × 600 = 300,000

Exact: 512 × 621
512 × 600 = 307,200
512 × 21 = ?
512 × 20 = 10,240
512 × 1 = 512 → total 10,752
Total: 307,200 + 10,752 = 317,952

✔ So:
Estimated: 500 × 600 = 300,000
Exact: 317,952

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Problem 9: 523 × 323

Round:
- 523 → 500
- 323 → 300
→ Estimated: 500 × 300 = 150,000

Exact: 523 × 323
523 × 300 = 156,900
523 × 20 = 10,460
523 × 3 = 1,569
Add: 156,900 + 10,460 = 167,360 + 1,569 = 168,929

✔ So:
Estimated: 500 × 300 = 150,000
Exact: 168,929

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Problem 10: 768 × 123

Round:
- 768 → 800
- 123 → 100
→ Estimated: 800 × 100 = 80,000

Exact: 768 × 123
768 × 100 = 76,800
768 × 20 = 15,360
768 × 3 = 2,304
Add: 76,800 + 15,360 = 92,160 + 2,304 = 94,464

✔ So:
Estimated: 800 × 100 = 80,000
Exact: 94,464

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Final Answer:

2. Estimated: 100 × 100 = 10000; Exact answer: 17545
3. Estimated: 400 × 500 = 200000; Exact answer: 194832
4. Estimated: 700 × 100 = 70000; Exact answer: 88572
5. Estimated: 200 × 400 = 80000; Exact answer: 95172
6. Estimated: 500 × 400 = 200000; Exact answer: 189849
7. Estimated: 700 × 500 = 350000; Exact answer: 365056
8. Estimated: 500 × 600 = 300000; Exact answer: 317952
9. Estimated: 500 × 300 = 150000; Exact answer: 168929
10. Estimated: 800 × 100 = 80000; Exact answer: 94464