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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, $0$, is obtained. When a number is multiplied by its reciprocal, the multiplicative identity, $1$, 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 $-\frac{x} {y}$ is $-\frac{y}{x}$. (Invert the fraction.)
• The opposite of $-\frac{x} {y}$ is $\frac{x}{y}$.(Multiply by $-1$.)

Feb 22, 2012

Aug 22, 2014