Dividing Rational Numbers

5 min

Narrative

In this Warm-up, students use what they have learned about multiplication and division with rational numbers to answer questions about the solution to an equation. They use the structure of the equation and patterns they have noticed with the signs of products and quotients of positive and negative numbers to determine the sign of the solution.

Launch

Arrange students in groups of 2.

Remind students that the solution to an equation is a value that makes the equation true.

Give students 1 minute of quiet think time, and ask them to discuss their reasoning with a partner. Follow with a whole-class discussion.

Student Task

Consider the equation:   -27x=-35\text- 27x = \text- 35

Without computing:

  1. Is the solution to this equation positive or negative?

  2. Are either of these two numbers solutions to the equation?

    3527\displaystyle \frac{35}{27}

    -3527\displaystyle \text-\frac{35 }{ 27}

Sample Response

  1. positive
  2. yes, 3527\frac{35}{27}

Synthesis

The purpose of this discussion is for students to share their reasoning. Invite students to share their responses, and record them for all to see. 

Standards
Building On
  • 7.NS.2·Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  • 7.NS.A.2·Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Building Toward
  • 7.EE.4.a·Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. <em>For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?</em>
  • 7.EE.B.4.a·Solve word problems leading to equations of the form <span class="math">\(px + q = r\)</span> and <span class="math">\(p(x + q) = r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. <span>For example, the perimeter of a rectangle is <span class="math">\(54\)</span> cm. Its length is <span class="math">\(6\)</span> cm. What is its width?</span>

10 min

10 min