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D.5 Estimate products of whole numbers

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What does it mean to estimate products?

Estimating products means finding an answer that is close to the exact product. We use rounding or compatible numbers to make multiplication easier to do mentally.

Example:
  • 46 × 21 ≈ 50 × 20 = 1,000
Note

An estimate is not the exact answer, but it helps you check if your exact answer makes sense.

Why do we estimate?

Estimation helps you decide if an answer is reasonable before or after you solve a problem. It is useful when you need a quick answer or when exact numbers are not needed.

Example:
  • If a book costs $18 and you want to buy 6 books, you can estimate: $20 × 6 = $120.
Note

Use estimation when you are checking work, comparing prices, or planning time and money.

How to estimate products

To estimate products, round one or both factors to a number that is easy to multiply, such as a multiple of 10, 100, or a compatible number.

Steps:
  • Step 1: Look at the numbers you are multiplying.
  • Step 2: Round one or both numbers to the nearest ten or hundred.
  • Step 3: Multiply the rounded numbers.
  • Step 4: Check if your estimate makes sense for the problem.

Example: 378 × 42 → 400 × 40 = 16,000

Note

When rounding, look at the digit to the right of the place value you are rounding to. If it is 5 or greater, round up; if it is less than 5, round down.

Using compatible numbers

Compatible numbers are numbers that are easy to multiply mentally. Sometimes using compatible numbers gives a better estimate than rounding.

Example:
  • 198 × 5 ≈ 200 × 5 = 1,000
Note

Choose numbers that make the math simple while keeping your estimate close to the actual answer.

Checking reasonableness of your answer

After solving a multiplication problem, use estimation to check if your exact answer is reasonable. If the exact answer is much greater or smaller than your estimate, recheck your work.

Example:
  • Exact: 47 × 36 = 1,692
  • Estimate: 50 × 40 = 2,000
  • Since 1,692 is close to 2,000, the answer is reasonable.
Note

An estimate helps you confirm if your calculation makes sense before moving on to the next problem.