Fraction division as a grouping model

A classroom model starts with four and one half meters of ribbon. Each identical piece must be three quarters of a meter long. A learner divides by three quarters but reverses the first fraction instead of the divisor. Another adds the numerator and denominator as though the task concerned a count of written digits. A third converts the mixed number, finds the number of groups and checks the result by multiplication. The problem supplies the whole length and piece size; no cutting loss, knot allowance or extra ribbon is included. The task asks how many complete pieces can be made under these explicit ideal conditions. A valid explanation should connect reciprocal arithmetic to the actual grouping question rather than present a memorized instruction without a check.