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Estimate quotients with compatible numbers

Estimation of a whole-number quotient involves replacing a dividend, and when useful the divisor, with nearby compatible numbers that are easy to divide mentally while preserving a reasonable quotient size. For example, 283 ÷ 7 can be estimated as 280 ÷ 7 = 40; the estimate is not necessarily exact and should be judged for reasonableness. The scope is one-digit divisors and whole-number dividends within 1,000, not multi-digit divisors, decimals, or fractions.

Detailed Explanation: Estimate quotients with compatible numbers

To estimate a quotient, replace the dividend with a nearby number that is easy to divide by the divisor. This nearby number is called a compatible number.

Example: Estimate 283÷7283 \div 7.

  1. Find a number close to 283283 that is easy to divide by 77.
    280280 is close to 283283, and 280280 is a multiple of 77.

  2. Replace 283283 with 280280:

283÷7280÷7283 \div 7 \approx 280 \div 7
  1. Divide:

280÷7=40280 \div 7 = 40

So, the estimate is:

40\boxed{40}

This is reasonable because 280280 is very close to 283283, so the quotient should be close to 4040.

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Division - Estimate Quotient - 3 by 1 digit


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