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So we have to add \[\dfrac{{ - 5}}{7}\] and \[\dfrac{3}{7}\] ;

In both the rational number we see the denominator is same i.e. \[7\];

so we perform addition in numerator only and the denominator remain same

therefore

= \[\dfrac{{ - 5}}{7} + \dfrac{3}{7}\]

=\[\dfrac{{ - 5 + 3}}{7}\]

After adding \[ - 5\] and \[3\] we get \[ - 2\]

= \[\dfrac{{ - 2}}{7}\]

As in this question the denominator is same , let us take some other example in which denominator is not same ;

Like we have to subtract \[\dfrac{1}{2}\] from \[\dfrac{4}{5}\]

So first we make the denominator same for this we take L.C.M and change the rational number according to that

So L.C.M of \[2\] and \[5\] (i.e denominator ) is \[10\]

And the rational number converted as given : \[\dfrac{{1 \times 5}}{{2 \times 5}}\] = \[\dfrac{5}{{10}}\] \[\dfrac{{4 \times 2}}{{5 \times 2}}\] = \[\dfrac{8}{{10}}\]

Now it is just like above question

= \[\dfrac{5}{{10}} - \dfrac{8}{{10}}\]

= \[\dfrac{{5 - 8}}{{10}}\]

= \[\dfrac{-3}{{10}}\]

Hence it is your required solution.

In case of multiplication we simply multiply the numerator to numerator and denominator to denominator and write it in \[\dfrac{p}{q}\] form .