Lesson 13: Lots of Milk

Property

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.

Examples

Property

To find different reasonable estimates for the same division problem, you can round the divisor to different nearby multiples of 10.
Each rounded divisor will lead to a different choice of compatible number for the dividend, resulting in multiple valid estimates.

Examples

Property

To estimate the result of a real-world division problem, replace the dividend, the divisor, or both with compatible numbers.
Compatible numbers are close to the original numbers and are easy to compute with mentally.

Examples

• A cafeteria has a 1,850 fluid ounce dispenser of milk. If each glass holds 8 fluid ounces, about how many glasses can be filled?

To estimate, find a compatible number for 1,850 that is easy to divide by 8. $1,600$ is a multiple of 8.

About 200 glasses can be filled.

• A dairy farm produces 465 gallons of milk per day. If the milk is stored in 4-gallon containers, about how many containers will be needed?

To estimate, you can use compatible numbers. $400$ is a multiple of 4.

For a closer estimate, you could use $480 \div 4 = 120$. About 100 to 120 containers will be needed.

Explanation

Many real-world problems require you to find how many equal-sized groups can be made from a total amount. Instead of finding an exact answer, you can often use estimation to get a quick and useful approximation. To do this, change the numbers in the problem to "compatible numbers" that are easy to work with, like multiples of 10 or basic multiplication facts. This strategy helps you quickly understand the scale of the answer before performing a more detailed calculation.