Lesson 11
Using an Algorithm to Divide Fractions
Lesson Narrative
In the previous lesson, students began to develop a general algorithm for dividing a fraction by a fraction. They complete that process in this lesson. Students calculate quotients using the steps they observed previously (i.e., to divide by \(\frac ab\), we can multiply by \(b\) and divide by \(a\)), and compare them to quotients found by reasoning with a tape diagram. Through repeated reasoning, they notice that the two methods produce the same quotient and that the steps can be summed up as an algorithm: to divide by \(\frac ab\), we multiply by \(\frac ba\) (MP8). As students use the algorithm to divide different numbers (whole numbers and fractions), they begin to see its flexibility and efficiency.
Learning Goals
Teacher Facing
 Coordinate (orally) different strategies for dividing by a fraction.
 Find the quotient of two fractions, and explain (orally, in writing, and using other representations) the solution method.
 Generalize a process for dividing a number by a fraction, and justify (orally) why this can be abstracted as $n \boldcdot \frac{b}{a}$.
Student Facing
Let’s divide fractions using the rule we learned.
Learning Targets
Student Facing
 I can describe and apply a rule to divide numbers by any fraction.
Glossary Entries

reciprocal
Dividing 1 by a number gives the reciprocal of that number. For example, the reciprocal of 12 is \(\frac{1}{12}\), and the reciprocal of \(\frac25\) is \(\frac52\).