Multiplication of algebraic fractions: $\LARGE \frac{a}{b} \cdot \LARGE \frac{c}{d} = \LARGE \frac{ac}{bd}$

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$\LARGE \frac{a}{2b} \cdot \LARGE \frac{b}{a} =$ $\LARGE \frac{ab}{2ab} = \LARGE \frac{1}{2}$
$\LARGE \frac{a}{6b} \cdot \LARGE \frac{3b}{4} =$ $\LARGE \frac{3ab}{24b} = \LARGE \frac{a}{8}$
$\LARGE \frac{a}{4a^2 - 25b^2} \cdot \LARGE \frac{5b - 2a}{2a} =$ $\LARGE \frac{a}{2a + 5b)(2a - 5b)}\cdot \LARGE (-\frac{2a - 5b}{2a}) = -\frac{1}{4a + 10b} $
$ (6x - 2) \cdot \LARGE \frac{4}{1 - 3x} =$ $\LARGE \frac{8(3x - 1)}{1 - 3x}$ = $-8 $
$\LARGE \frac{4x^2 - 6xy}{5x} \cdot \LARGE \frac{10x}{6x - 9y} =$ $\LARGE \frac{2x(2x - 3y)}{5x}\cdot \LARGE \frac{10x}{3(2x - 3y)} = \frac{4x}{3} $