# 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.

### Student Facing

• I can describe and apply a rule to divide numbers by any fraction.

Building On