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Answer 1 · 2018-02-11T16:00:51

It doesn't?

$\frac{13}{30} = 0.4333$ $13/30 = 0.4333$

$\frac{2}{7} = 0.285714$ $2/7 = 0.285714$

Answer 2 · 2018-02-11T16:02:38

Only with integer division
in which case $\frac{13}{30} = 0$ $13/30=0$ and $\frac{2}{7} = 0$ $2/7=0$

Assuming the numbers are base 10
$\frac{2}{7} = 0 . ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 285714$ $2/7=0.bar(285714)$ and $\frac{13}{30} = 0.4 ¯ 3$ $13/30=0.4bar3$

So they are obviously not equal for base 10 with rational ( $RR$ ) values.

With a bit of manipulation it can be demonstrated that the two ratios are not equal for any positive base.