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

In the example given in the last article it will be observed that the product of the denominators of the two given fractions equals the area of the whole figure (A B CD), while the product of the numerators equals the area of the rectangle (E F A G), the sides of which are equal respectively to the given fractions. From this we obtain for the product of fractions this -

RULE. - Multiply together the denominators for the new denominator, and the numerators for a new numerator.

For example: what is the product of 13/21 and 7/20? Here we have 20x21=420 for the new denominator, and

7 x 13 = 91 for the new numerator; therefore the product of -

13/21x7/20=91/420;

or, of a rectangular area divided one way into 20 parts and the other way into 21 parts, thus containing 420 rectangles, the product of the two fractions 13/21 and 7/20 is equal to 91 of these rectangles, or91/420of the whole.

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