# Lesson 11

Dividing Rational Numbers

### Lesson Narrative

In this lesson, students complete their work extending all four operations to signed numbers by studying division. They use the relationship between multiplication and division to develop rules for dividing signed numbers. In preparation for the next lesson on negative rates of change, students look at a context, drilling a well, that is modeled by an equation $$y = kx$$ where $$k$$ is a negative number. This builds on their previous work with proportional relationships.

### Learning Goals

Teacher Facing

• Apply multiplication and division of signed numbers to solve problems involving constant speed with direction, and explain (orally) the reasoning.
• Generalize (orally) a method for determining the quotient of two signed numbers.
• Generate a division equation that represents the same relationship as a given multiplication equation with signed numbers.

### Student Facing

Let's divide signed numbers.

### Student Facing

• I can divide rational numbers.

Building On

Building Towards

### Glossary Entries

• solution to an equation

A solution to an equation is a number that can be used in place of the variable to make the equation true.

For example, 7 is the solution to the equation $$m+1=8$$, because it is true that $$7+1=8$$. The solution to $$m+1=8$$ is not 9, because $$9+1 \ne 8$$