Question

Add the following rational numbers \[\dfrac{{ - 5}}{7}\] and \[\dfrac{3}{7}\].

Answer 1

Hint: Whenever we have given a rational number in \[\dfrac{p}{q}\] form first we have to check denominator if denominator is same in both the numbers then we perform simple addition and subtraction in numerator.

Complete step-by-step answer:
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 \[ - 2\]
= \[\dfrac{{ - 2}}{7}\]

Additional Information:
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.

Note: If denominator is not same we have to take L.C.M and make the denominator same . After that perform an addition and subtraction in the numerator.
In case of multiplication we simply multiply the numerator to numerator and denominator to denominator and write it in \[\dfrac{p}{q}\] form .