Here is how I solved it: First, I divided the whole square into sixteenths, so I wouldn't have to divide that much. Next, I divided one sixteenth into half, so I got one thirty-second. Then, I divided the one thirty-second into half, so I got one sixty-fourth. I continued on dividing each fraction in half until I got to one five hundred-twelfth. I noticed that one five hundred-twelfth was the same size as the small colored in triangle. Therefore the fraction of the smallest triangle is five hundred-twelfth.
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