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Rational numbers & Equivalent fractions

How many equivalent fractions does any rational number have? All of the fractions equivalent to the rational number p/q line on the line y = (p/q)x. The point {0,0} lies on all lines of the form y = (p/q)x. Does this mean that the "fraction" 0/0 is equivalent to all rational numbers? How can and/or do you make sense of this? What questions could/would you pose to your students based on this applet?