Question

Add the following rational numbers $${\displaystyle \frac{-5}{7}}$$ and $${\displaystyle \frac{3}{7}}$$.

Answer 1

Hint: Whenever we have given a rational number in $${\displaystyle \frac{p}{q}}$$ 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 $${\displaystyle \frac{-5}{7}}$$ and $${\displaystyle \frac{3}{7}}$$ ;
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
= $${\displaystyle \frac{-5}{7}}+{\displaystyle \frac{3}{7}}$$
=$${\displaystyle \frac{-5+3}{7}}$$
After adding $$-5$$ and $$3$$ we get $$-2$$
= $${\displaystyle \frac{-2}{7}}$$

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 $${\displaystyle \frac{1}{2}}$$ from $${\displaystyle \frac{4}{5}}$$
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 : $${\displaystyle \frac{1\times 5}{2\times 5}}$$ = $${\displaystyle \frac{5}{10}}$$ $${\displaystyle \frac{4\times 2}{5\times 2}}$$ = $${\displaystyle \frac{8}{10}}$$
Now it is just like above question
= $${\displaystyle \frac{5}{10}}-{\displaystyle \frac{8}{10}}$$
= $${\displaystyle \frac{5-8}{10}}$$
= $${\displaystyle \frac{-3}{10}}$$
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 $${\displaystyle \frac{p}{q}}$$ form .