Unit 4, Lesson 11
Using an Algorithm to Divide Fractions
Grade 6
Preparation
Lesson Narrative
In this lesson, students complete the process of developing a general algorithm for dividing a fraction by a fraction.
First, students calculate quotients using the steps they observed previously when dividing a number by a fraction—multiply the number by the denominator of the fraction and divide by the numerator. They compare the results to quotients found by reasoning with a tape diagram and verify that the two methods produce the same quotient. They sum up the steps as an algorithm: To divide a number by , we multiply by . Students learn that is the reciprocal of because the two numbers multiply to 1.
With an additional strategy at their disposal, students practice calculating quotients involving a wider variety of numbers (whole numbers and fractions). They begin to see the flexibility and efficiency of the algorithm, especially when it is impractical to reason about the division in terms of equal-size groups, with or without using diagrams.
- 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 $n$ by a fraction $\frac{a}{b}$, and justify (orally) why it can expressed as $n \boldcdot \frac{b}{a}$.
Let’s divide fractions using the rule we learned.
Required Materials
Activity 2
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.