## 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, , 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 is . (Invert the fraction.)
- The opposite of is .(Multiply by .)

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## Date Created:

Feb 22, 2012## Last Modified:

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