ABSTRACT
One of the goals of this chapter is to show that the rules for manipulating fractions are not random or arbitrarily imposed by authority figures. Such patterns are natural consequences of our 7 basic axioms for counting/numbers. I go through the details of deducing these patterns from the 7 axioms because a number of my students who had dutifully memorized correct patterns would sometimes for a variety of reasons imagine new patterns for dealing with fractions. How is one to tell if a new pattern that someone proposes is “OK” or it is wrong?1
