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# 2.6: Division of Rational Numbers

Difficulty Level: At Grade Created by: CK-12

## 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.

## Vocabulary

Terms introduced in this lesson:

multiplicative inverse
reciprocals
invert the fraction
improper fraction
invisible denominator
speed
distance
time

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

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