# 2.6: Division of Rational Numbers

Difficulty Level:

**At Grade**Created by: CK-12Turn In

## 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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Tags:

Absolute Value
Activities
additive identity
(45 more)
Answer Key
Answers
Assessment
associative
CK.MAT.ENG.TE.1.Algebra-I.2
Common Misconceptions
commutative
Concept Check and Troubleshooting
denominator
Differentiated Instruction
distributive property
Enrichment
equivalent fractions
Improper Fractions
Inquiry Process
integers
inverse
irrational numbers
LCD
lowest common denominator
multiplicative identity
multiplicative inverse
numerator
opposites
Pacing
prime
prime factors
Problem Sets
Problem Solving
proper fractions
Quizzes
rational numbers
real numbers
reducing a fraction
Science Inquiry
simplest form
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Teaching Strategies and Tips
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Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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