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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The **reciprocal** of a rational number is found by switching the numerator and denominator of the number.

Number | Reciprocal |
---|---|

$2$ | $21 $ |

$75 $ | $57 $ |

$ba $ | $ab $ |

The reciprocal of a number is also known as its *multiplicative inverse*, since the product of any rational number and its reciprocal is equal to $1.$
$ba ⋅ab =1 $
A similar identity to this one is the additive inverse.

The negative reciprocal of a number is the reciprocal with changed sign.

Number | Negative Reciprocal |
---|---|

$2$ | $-21 $ |

$75 $ | $-57 $ |

$ba $ | $-ab $ |

An example of this is perpendicular lines where their slopes are negative reciprocals of each other.