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

In Fig. 277 let A B equal 8 feet and A C equal 5 feet; then the rectangle A BCD contains 5 x 8 = 40 feet. The interior lines divide the space included within A BCD into 40 equal squares of one foot each. Let A E equal 3 feet or - of A C. Let A G equal 7 feet or 7/8 of A B. Then the rectangle

Fig. 277.

EFAG contains 3/5x 7/8 = 21/40 or twenty-one fortieths of the whole area ABCD. Thus, while the factor fractions 3/5 and 7/8 represent lines, it is shown that the product fraction 21/40 represents surface. Thus 21/40 is a fraction, E FA G, of the whole surface, CD A B.

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