# Delightful Division 3: Reciprocals of Half-Integers

y = 1/x or x^{-1}

## This function gives you a number's reciprocal. If *x* is equal to a half-integer...

x | y |

½ | 2/1(or simply 2) |

1½ | 2/3 |

2½ | 2/5 |

3½ | 2/7 |

4½ | 2/9 |

5½ | 2/11 |

6½ | 2/13 |

7½ | 2/15 |

8½ | 2/17 |

9½ | 2/19 |

10½ | 2/21 |

11½ | 2/23 |

W + ½ | 2/(2W + 1) |

#### {You understand how I used the variable *W* in the bottom row, do you?}

## All the fractions in the *y* column have a common numerator: 2, but have you noticed that the denominators are consecutive odd numbers? Interesting, isn't it?

Note: *x*/1 = *x* since **1** is the number of *multiplicative identity. *Whenever the number **1** is a denominator of a fraction, the fraction technically turns into an integer! (Algebra, calculus & wacky irrational numbers as numerators are not considered)

## By the way, this same math trick happens on the __negative__ side of the number line, if you get what I mean! It'll also work with imaginary numbers, but only real numbers are allowed in function tables.

Back to Index Page Back to Math Trick Menu

© Derek Cumberbatch