Fractions are one of the most difficult topics for
students to learn in elementary school. In fact,
children often find the topic of fractions to be
nonsensical and mysterious. Consider, for example, the following exposition, which highlights
how senseless fraction operations can appear:
When we add or subtract fractions, we have to
find a common denominator, but not when we
multiply or divide. And once we get a common
denominator, we add or subtract the numerators,
but not the denominators, despite the fact that
when we multiply, we multiply both the numerators and the denominators, and when we
divide, we divide neither the numerators nor the
denominators.
Although no teach

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