p/q * r/s = (p*r)/(q*s)
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The question has no sensible answer because its proposition is not true. Multiplication is commutative, division is not, so the rules are NOT the same.
Dividing by a non-zero rational number is the same as multiplying by its reciprocal.
It the two rational numbers have different signs, then the answer will be negative, otherwise it will be positive.
The algorithm is A/B * C/D = AB/CD.
The product of two rational numbers, X and Y, is smaller than either of them if both are between 0 and 1.