a sugar cane farmer harvested only 1/4 of his crop. he sold 2/3 of his harvest to the mill. what fraction of the total crop did he sell.

darens recipe for florida fudge calls for 5/8 cup of sugar. if he wants to make only 1/2 of the recipe how much sugar should he use.


Imagine that the farmer's sugar cane crop is in one large square field and he harvested 1/4 of it.

He then sold 2/3 of the amount harvested so divide the harvested region into 3 equal sized rectangles and mark two of them as sold.

The question now is "What fraction of the large square is sold?"

To see the answer, divide each of the unharvested quarters as you divided the harvested quarter and now you have the entire crop divided into 12 equal sized pieces.

Two of them are sold so 2/12 of the entire crop is sold. But 2/12 = 1/6 so 1/6 of the crop is sold.

You can, of course, do this without the diagrams. The farmer sold two-thirds of the one-quarter he harvested, and 2/3  of 1/4 is 2/3 x 1/4 = (2 x 1)/(3 x 4) = 2/12 = 1/6.

Now try the second problem.

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