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

To find the hast common denominator place the several fractions in the order of their denominators, increasing toward the right. If the largest denominator be not divisible by each of the others, double it; if the division cannot now be performed, treble it, and so proceed until it is multiplied by some number which will make it divisible by each of the other denominators. This number multiplied by the largest denominator will be the least common denominator. To raise the denominator of each fraction to this, divide the common denominator by the denominator of one of the fractions, the quotient will be the number by which that fraction is to be multiplied, both numerator and denominator, and so proceed with each fraction. For example: What is the sum of the fractions

1/2, 3/4, 10/12, 7/8? One of these, 10/12, may be reduced, by divid-ing by 2, to 5/6. Therefore, the series is 1/2, 3/4, 5/6, 7/8. On trial we find that 8, the largest denominator, is divisible by the first and by the second, but not by the third, therefore the largest denominator is to be doubled: 2x8=16. This is not yet divisible by the third; therefore 3 x 8 = 24. This now is divisible by the third as well as by the first and the second; 24 is therefore the least common denominator.

Now dividing 24 by 2, the first denominator, the quotient 12 is the factor by which the terms of the first fraction are to be raised, or, 1x12= 12. For the second we have

2 X 12 = 24

24÷ 4 = 6, and 3x6=18 = 18. For the third we have 24 ÷ 6 =

4x6 = 24

4, and 5x4=20; and for the fourth, 24 ÷ 8 = 3, and

6 x 4= 24

7x3 =21. Thus the fractions in their reduced form are:

8 x 3 = 24

12/24+18/24+20/ 24+21/24=71/24=2 23/24.

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