Using Compatible Numbers to Estimate Quotients
To estimate a whole number quotient, round the divisor to the nearest ten, then find a compatible dividend close to the original that can be easily divided by the rounded divisor using basic facts. This Grade 5 math skill from Eureka Math Chapter 12 covers partial quotients and multi-digit whole number division estimation strategies.
Key Concepts
To estimate a quotient, first round the divisor to the nearest ten. Then, find a compatible number for the dividend that is close to the original dividend and can be easily divided by the rounded divisor. This estimation can be represented as $a \div b \approx a' \div b'$, where $b'$ is the rounded divisor and $a'$ is the compatible dividend.
Common Questions
How do you use compatible numbers to estimate a quotient?
Round the divisor to the nearest ten, then choose a dividend close to the original that you can easily divide by the rounded divisor using a basic fact. For example, for 84 divided by 21, use 80 divided by 20 equals 4.
What are compatible numbers in division?
Compatible numbers are a rounded divisor and an adjusted dividend that work well together using basic multiplication facts, making the division easy to perform mentally.
Why should you round the divisor before finding a compatible dividend?
Rounding the divisor first simplifies the problem by creating an easy base-ten number to divide by, then you adjust the dividend to a nearby number that divides cleanly by that rounded divisor.
What is an example of estimating 475 divided by 58?
Round 58 to 60, then find a compatible dividend near 475 that divides evenly by 60: 480 divided by 60 equals 8, so 475 divided by 58 is approximately 8.