The fractions

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Such pairs of number are referred to as reciprocals.

### Reciprocal

The mutual of the fraction

Here are some instances of reciprocals:

Original numberReciprocalProductTo uncover the mutual of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. You have the right to think of it as switching the numerator and denominator: swap the

Make sure that if it’s a an unfavorable fraction, the mutual is likewise negative. This is since the product of two an adverse numbers will give you the hopeful one the you space looking for. To acquire a positive an outcome when multiplying two numbers, the numbers must have the same sign. Therefore reciprocals must have the very same sign.

To uncover the reciprocal, store the exact same sign and invert the fraction.

### Example

Find the reciprocal of every number. Then examine that the product of each number and also its reciprocal is

Solution:To find the reciprocals, we store the sign and also invert the fractions.

1. | |

Find the mutual of | The reciprocal of |

Check: | |

Multiply the number and its reciprocal. | |

Multiply numerators and also denominators. | |

Simplify. |

2. | |

Find the mutual of | |

Simplify. | |

Check: | |

3. | |

Find the reciprocal of | |

Check: | |

4. | |

Find the mutual of | |

Write | |

Write the reciprocal of | |

Check: | |

In the following video clip we will show an ext examples of exactly how to discover the reciprocal of integers, fractions and also mixed numbers.

Caution! department by zero is undefined and so is the reciprocal of any fraction that has a zero in the numerator. For any type of real number a,

## Division through Zero

You recognize what it way to division by

We have the right to read it as, “zero separated by eight.” due to the fact that multiplication is the train station of division, we can rewrite this as a multiplication problem. What number time

We can infer the the unknown have to be

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Now let’s consider the reciprocal of

This doesn’t make any sense. There are no numbers the you have the right to multiply by zero to get a result of 8. In fact, any kind of number divided by