$$9p+16q:13p+2q$$
$\frac{16pq}{13}+2q+9p$
$$9p+\frac{16qp}{13}+2q$$
$$\frac{13\left(9p+2q\right)}{13}+\frac{16qp}{13}$$
$$\frac{13\left(9p+2q\right)+16qp}{13}$$
$$\frac{117p+26q+16qp}{13}$$
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$\frac{16pq+117p+26q}{13}$
$$\frac{117p+16qp+26q}{13}$$
