This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

By an operation the reverse of that in the last article, we may reduce several equal fractions to one of equal value. Thus, if in each we divide the numerator and denominator by the same number, we reduce it to a fraction of equal value, but with smaller factors.

For example, taking the fractions of the last article, 2/6,3/9 , 4/12, 5/15, let eac be divided by a number which will divide both numerator and denominator without a remainder.*

Thus,

2 | ÷ | 2 | = | 1 |

6 | ÷ | 2 | = | 3 |

3 | ÷ | 3 | = | 1 |

9 | ÷ | 3 | = | 3 |

4 | ÷ | 4 | = | 1 |

12 | ÷ | 4 | = | 3 |

5 | ÷ | 5 | = | 1 |

15 | ÷ | 5 | = | 3 |

As these fractions are shown (Art. 380) to be equal, and as the operation of dividing each factor by a common number produces quotients which in each case form the same fraction, 1/3, we therefore conclude that the numerator and denominator of a fraction may be divided by a common number without changing the value of the fraction.

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