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The algorithm is A/B * C/D = AB/CD.
Dividing by a non-zero rational number is the same as multiplying by its reciprocal.
By dividing
It the two rational numbers have different signs, then the answer will be negative, otherwise it will be positive.
It the signs of the two numbers that you are multiplying or dividing is the same, then the answer is positive, otherwise the answer is negative. Remember though, that division by 0 is not defined.