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## Main Question or Discussion Point

Give a rigorous proof using the appropriate axioms and the definition ,[tex]\frac{a}{b}=a\frac{1}{b}[/tex] of the following:

[tex]\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}[/tex]

[tex]\frac{a}{b}:\frac{c}{d} =\frac{ad}{bc}[/tex]

[tex]\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}[/tex]

[tex]\frac{a}{b}:\frac{c}{d} =\frac{ad}{bc}[/tex]