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E.3 Estimate sums and differences: word problems

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What is estimation?

Estimation is finding an answer that is close to the exact answer without doing the exact calculation. We use estimation when we need a quick, reasonable answer or to check if our exact answer makes sense.

Example:
  • If you have 487 stickers and your friend has 312 stickers, you can estimate about how many stickers you have together instead of adding exactly.
Note

Estimation gives you a "ballpark" number, not the exact answer. It helps you understand if your final answer is reasonable.

Rounding to the nearest ten

To round to the nearest ten, look at the ones digit. If it is greater than 5, round up. If it is 4 or less, round down.

Examples:
  • 47 → The ones digit is 7 (5 or greater), so 47 rounds up to 50
  • 132 → The ones digit is 2 (4 or less), so 132 rounds down to 130
  • 385 → The ones digit is 5 (5 or greater), so 385 rounds up to 390
Note

When rounding to the nearest ten, the number will always end with a zero.

Rounding to the nearest hundred

To round to the nearest hundred, look at the tens digit. If it is greater than 5, round up. If it is 4 or less, round down.

Examples:
  • 347 → The tens digit is 4 (4 or less), so 347 rounds down to 300
  • 562 → The tens digit is 6 (5 or greater), so 562 rounds up to 600
  • 850 → The tens digit is 5 (5 or greater), so 850 rounds up to 900
Note

When rounding to the nearest hundred, the number will always end with two zeros.

Estimating sums

To estimate a sum, first round each number, then add the rounded numbers together.

Example:
  • Estimate 238 + 485
  • Round to the nearest hundred: 238 → 200, 485 → 500
  • Add: 200 + 500 = 700
  • The estimated sum is about 700
Note

When estimating sums, always round first, then add. Never add first, then round.

Estimating differences

To estimate a difference, first round each number, then subtract the rounded numbers.

Example:
  • Estimate 724 - 389
  • Round to the nearest ten: 724 → 720, 389 → 390
  • Subtract: 720 - 390 = 330
  • The estimated difference is about 330
Note

When estimating differences, always round first, then subtract. Never subtract first, then round.

Choosing when to round

Sometimes you need to decide whether to round to the nearest ten or hundred. Think about the numbers and what would make the estimation easiest.

Examples:
  • For 47 + 32: Round to tens (50 + 30 = 80)
  • For 287 + 514: Round to hundreds (300 + 500 = 800)
  • For 695 - 238: Round to tens (700 - 240 = 460) or hundreds (700 - 200 = 500)
Note

Generally, round to the nearest hundred when numbers are in the hundreds, and to the nearest ten when numbers are smaller.

Solving word problems with estimation

When solving word problems, first identify what you need to find (sum or difference), then round the numbers appropriately before calculating.

Example:
  • Problem: The school library has 387 fiction books and 452 nonfiction books. About how many books are in the library?
  • Think: I need to find the total, so I'll estimate the sum.
  • Round: 387 → 400, 452 → 500
  • Calculate: 400 + 500 = 900
  • Answer: There are about 900 books in the library.
Note

Always read the word problem carefully to understand whether you need to estimate a sum or a difference.