In this lesson, students learn to find the quotient of two decimals. This work requires students to integrate their understanding of place value, division strategies, and the relationship between multiplication and division.

Students begin by observing that the value of a quotient does not change when both the divisor and the dividend are multiplied by the same multiple of 10. For example, and both have a value of 8. Then, they write division expressions that have the same value as a given expression.

Next, students apply this insight to divide a number by a decimal divisor. They see that they can multiply the divisor by a power of 10 to make it a whole number, which makes it easier to divide, but to maintain the original quotient, the dividend needs to be multiplied by the same power of 10.

An optional activity is included to allow students to take a closer look: to compare the calculations for two equivalent division expressions ( and ) and to practice explaining why such expressions produce the same quotient.

In the last activity, students apply their understanding about equivalent expressions to divide a decimal by another decimal.