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Estimate the answers to the following subtractions by rounding to the nearest 1000, then calculate the exact answer and the difference: a) 3857 - 2436 b) 7576 - 5125 c) 5387 - 4263

Mathematics

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Answers

3 parts
a
1421
b
2451
c
1124

Step-by-step solution

12 steps

Here are the solutions for each part:

Part a· 4 steps

3857−24363857 - 2436

  1. Round off to the nearest 1000.

    3857≈40003857 \approx 4000 2436≈20002436 \approx 2000

  2. Subtract the rounded numbers.

    4000−2000=20004000 - 2000 = 2000

  3. Subtract the original numbers.

    3857−2436=14213857 - 2436 = 1421

  4. Compare the answers.

    The rounded answer (2000) is an overestimation compared to the exact answer (1421).
    Difference: 2000−1421=5792000 - 1421 = 579.
    The final answer for a) is 1421\boxed{1421}.

Part b2451

7576−51257576 - 5125

  1. Round off to the nearest 1000.

    7576≈80007576 \approx 8000 5125≈50005125 \approx 5000

  2. Subtract the rounded numbers.

    8000−5000=30008000 - 5000 = 3000

  3. Subtract the original numbers.

    7576−5125=24517576 - 5125 = 2451

  4. Compare the answers.

    The rounded answer (3000) is an overestimation compared to the exact answer (2451).
    Difference: 3000−2451=5493000 - 2451 = 549.
    The final answer for b) is 2451\boxed{2451}.

Part c1124

5387−42635387 - 4263

  1. Round off to the nearest 1000.

    5387≈50005387 \approx 5000 4263≈40004263 \approx 4000

  2. Subtract the rounded numbers.

    5000−4000=10005000 - 4000 = 1000

  3. Subtract the original numbers.

    5387−4263=11245387 - 4263 = 1124

  4. Compare the answers.

    The rounded answer (1000) is an underestimation compared to the exact answer (1124).
    Difference: 1124−1000=1241124 - 1000 = 124.
    The final answer for c) is 1124\boxed{1124}.

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