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2.6: Division of Rational Numbers

Difficulty Level: At Grade Created by: CK-12
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Learning Objectives

At the end of this lesson, students will be able to:

  • Find multiplicative inverses.
  • Divide rational numbers.
  • Solve real-world problems using division.


Terms introduced in this lesson:

multiplicative inverse
invert the fraction
improper fraction
invisible denominator

Teaching Strategies and Tips

Draw an analogy between the division and subtraction of rational numbers.

  • A subtraction problem can be recast as an addition problem using additive inverses (opposites). A division problem can be recast as a multiplication problem using multiplicative inverses (reciprocals).
  • When a number is added to its opposite, the additive identity, , is obtained. When a number is multiplied by its reciprocal, the multiplicative identity, \begin{align*}1\end{align*}, is obtained.

In Example 1c, remind students that a mixed number needs to be converted to an improper fraction before determining the multiplicative inverse.

Error Troubleshooting

In Example 1d, point out that finding the multiplicative inverse of the expression will not affect the negative. See also Example 2d.

  • The reciprocal of \begin{align*}-\frac{x} {y}\end{align*} is \begin{align*}-\frac{y}{x}\end{align*}. (Invert the fraction.)
  • The opposite of \begin{align*}-\frac{x} {y}\end{align*} is \begin{align*}\frac{x}{y}\end{align*}.(Multiply by \begin{align*}-1\end{align*}.)

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