Skill: Estimate quotients with compatible numbers

Explanation and Free Practice Resources

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÷7≈280÷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.

Learn by doing: Estimate quotients with compatible numbers

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Division - Estimate Quotient - 3 by 1 digit


    ?

    Download/Modify Free Grade 3 'Estimate quotients with compatible numbers' Worksheet

    Print this free 'Estimate quotients with compatible numbers' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

    Units Teaching This Skill

    These adaptive units introduce, teach, or reinforce this skill (Estimate quotients with compatible numbers) through scaffolded problems that grow in difficulty as concepts are understood.

    Explore More Grade 3 Math