Fraction times fraction

Number Theory Level pending

Yogika was learning multiplication of fractions and have determined the following equations:

\[\dfrac{1}{2} \times \dfrac{3}{4} =\dfrac{3}{8} \\ \dfrac{1}{3} \times \dfrac{1}{2}=\dfrac{1}{6} \\ \dfrac 32 \times \dfrac 54=\dfrac{15}{8} . \]

With these results, she concluded that the product of two non-integer rational numbers is always a non-integer rational number. Is she correct?

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