ABSTRACT
People seem to have different approaches to solving problems involving division with fractions. Fractions are often considered the most complex numbers in elementary school mathematics. Division by fractions, the most complicated operation with the most complex numbers, can be considered as a topic at the summit of arithmetic. “Dividing by a number is equivalent to multiplying by its reciprocal” is used in Chinese textbooks to justify the division by fractions algorithm. The interview question reminded the teachers that “people seem to have different approaches to solving problems involving division with fractions.” The Chinese teachers, however, proposed at least three other approaches: dividing by fractions using decimals, applying the distributive law, and dividing a fraction without multiplying by the reciprocal of the divisor. A popular alternative way of dividing by fractions used by the Chinese teachers was to compute with decimals.
