<s>[INST] Solving $\frac{4}{3} = \frac{3.2}{y}$ This is what I've tried.
$\frac{1}{3.2} \cdot \frac{4}{3} = \frac{3.2}{y} \cdot \frac{1}{3.2}$ to isolate $y$ via product and quotient identity.
When simplified this gives me $\frac{4}{9.6} = y$ so $y = 0.41\overline{6}$
However, the textbook gives an answer of $y=2.4$ and in the example they used the cross-product method which does follow, but what I did should also give me the same answer.
 [/INST] If you multiply $\dfrac{1}{3.2}$ both side:
$$\dfrac{1}{3.2}\times\dfrac{4}{3}=\dfrac{3.2}{y}\times\dfrac{1}{3.2}\\\dfrac{4}{9.6}=\dfrac{1}{y}\\\dfrac{1}{2.4}=\dfrac{1}{y}\\y=\boxed{2.4}$$
Another way to do this is to use cross method:
$$\dfrac{4}{3}=\dfrac{3.2}{y}\\ 4y=3.2\times 3 \\4y=9.6 \\ y=\boxed{2.4}$$
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