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

When the denominators are not divisible by one another, then to obtain a common denominator, it is requisite to multiply to-get her all of the denominators which will not divide any of the other denominators. For example: What is the sum of the tractions1/3,2/5,3/7, and 4/9?

In this case the first denominator will divide the last, but the others are prime to each other. Therefore, for the common denominator, multiply, together all but the first; or -

5x7x9 = 315 the common denominator; and -

315 | ÷ | 3 | = | 105, | common factor for the first fraction; |

315 | ÷ | 5 | = | 63, | common factor for the second fraction; |

315 | ÷ | 7 | = | 45, | common factor for the third; . |

315 | ÷ | 9 | = | 35, | common factor for the fourth. |

And, then -

1 x 105 = 105; 2 x 63 = 126 ; 3 x 45 = 135; 4 x 35 = 140; 3x 105 = 315' 5x63=315 7 x 45 = 315' 9 x 35 = 315

105 + 126 + 135 + 140 = 506 = 1 191

315 315 315 315 315 315

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