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# Add the following rational numbers $\dfrac{{ - 5}}{7}$ and $\dfrac{3}{7}$.

Last updated date: 20th Jun 2024
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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.

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.

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 .