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B.1 Estimate sums and differences of whole numbers

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What does it mean to estimate sums and differences?

Estimation means finding a number that is close to the exact answer. It helps you check your work and make quick calculations in real-life situations.

Example:
  • Exact problem: 47,892 + 22,105
  • Estimate: 47,900 + 22,100 ≈ 70,000
Note

Estimates do not have to be exact. They should be reasonable and make sense for the problem you are solving.

How to estimate sums and differences

To estimate, first round each number to the same place value (such as the nearest ten, hundred, or thousand), then add or subtract the rounded numbers.

Example:
  • Problem: 385,672 − 129,418
  • Round each number to the nearest thousand: 386,000 − 129,000
  • Estimate: 257,000
Note

Always round both numbers to the same place value before adding or subtracting. This keeps your estimate balanced and accurate.

Rounding numbers before estimating

Rounding means changing a number to the nearest ten, hundred, or thousand to make it easier to work with while keeping its value close to the original.

Examples:
  • Round 84,762 to the nearest thousand → 85,000
  • Round 236,549 to the nearest hundred → 236,500
  • Round 57,928 to the nearest ten → 57,930
Note

When rounding, look at the digit to the right of your rounding place. If it is 5 or more, round up. If it is 4 or less, round down.

When and why to estimate

Estimation helps you decide if an answer makes sense, plan budgets, or solve problems quickly without needing an exact total.

Example:
  • You are shopping and see items that cost $248 and $356. Rounding both to the nearest hundred gives $200 + $400 = $600.
  • Your estimate tells you the total cost is about $600 before tax.
Note

Use estimation whenever you need a quick, reasonable answer and exact calculation is not necessary.

Checking the reasonableness of your estimate

After you find an estimate, compare it to the exact answer to see if it makes sense. This helps you develop good number sense and accuracy.

Example:
  • Exact sum: 425,730 + 173,290 = 599,020
  • Estimate using nearest thousand: 426,000 + 173,000 = 599,000
  • The estimate (599,000) is very close to the exact answer (599,020), so it is reasonable.
Note

If your estimate is far from the exact answer, check your rounding and place value steps again.