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$a)$ $6$ $.$ $63$ $=$ $9$ $.$ $42$
$→$ $\dfrac{6}{9}$ $=$ $\dfrac{42}{63}$
$→$  $\dfrac{9}{6}$ $=$ $\dfrac{63}{42}$ 
$→$  $\dfrac{42}{6}$ $=$ $\dfrac{63}{9}$
$→$  $\dfrac{6}{21}$ $=$ $\dfrac{9}{63}$
$b)$ $0,241$ $.$ $6,1$ $=$ $0,84$ $.$ $0,46$
$→$ $\dfrac{0,241}{0,84}$ $=$ $\dfrac{0,46}{6,1}$
$→$ $\dfrac{0,84}{0,241}$ $=$ $\dfrac{6,1}{0,46}$
$→$ $\dfrac{0,46}{0,241}$ $=$ $\dfrac{6,1}{0,84}$
$→$ $\dfrac{0,241}{0,84}$ $=$ $\dfrac{0,46}{6,1}$