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If a fraction is multiplied by itself and the product is divided by its reciprocal, the resulting fraction is $18\frac{3}{4}$. The fraction is:

1. 27/8
2. 3/2
3. 2 1/2
4. 5/4

Correct answer: 3/2

Solution

If the fraction is $x$, then multiplying it by itself gives $x^2$. Dividing by its reciprocal means multiplying by $x$, so the result is $x^3$. Since $18\frac{3}{4}=\frac{75}{4}$, we get $x^3=\frac{75}{4}$, which gives $x=\frac{3}{2}$.

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