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

Division is the reverse of multiplication; or, while multiplication requires the product of two given factors, division requires one of the factors when the other and the product are given. Or (referring to Fig. 277) in division we have the area of the rectangle, EFA G, and one side, EA; given, to find the other side, A G.

Now it is required to find the number of times E A is contained in E FA G. By inspection of the figure we perceive the answer to be, A G times; for E A x A G = E FA G, the given area. Or, when E A FG is given as 21/40 and E A

as 3/5, we have as the given problem -

21/40÷3/5.

Since division is the reverse of multiplication, instead of multiplying we divide the factors, and have -

21 ÷ 3 = 7

40 ÷ 5 8.

Thus, to divide one fraction by another, for the numerator of the required factor, divide the numerator of the product by the numerator of the given factor, and for the denominator of the required factor divide the denominator of the product by the denominator of the given factor. For example:

Divide 10/63 by 2/3 Answer, 5/7. Divide 28/27 by 4/9. Answer, 7/3.

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