# 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, \begin{align*}0\end{align*}, 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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CK.MAT.ENG.TE.1.Algebra-I.2
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Teacher Edition
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whole numbers
inverse
equivalent fractions
distributive property
rational numbers
integers
Improper Fractions
Absolute Value
real numbers
multiplicative inverse
irrational numbers
multiplicative identity
prime
prime factors
additive identity
associative
commutative
denominator
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proper fractions
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Common Misconceptions
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CK.MAT.ENG.TE.1.Algebra-I.2

Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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