Pearson's Square is a method used to determine the proportions of feeds needed to produce a ration with a specific quantity and crude protein percentage. It involves drawing a square, labeling feeds and their protein percentages on sides, subtracting smaller from larger numbers along diagonals, dividing parts of each feed by the total parts to find its percentage in the ration. An example shows using it to mix soybean meal and corn to make 1200 lbs of 25% crude protein hog feed.