question_answer

Simplify : \[\frac{16}{39}+\frac{9}{-26}\]

Answer:

We have         \[\frac{16}{39}+\frac{9}{(-26)}=\frac{16}{39}+\frac{-9}{26}\]

Now, the LCM of 39 and 26 is 78.

\[\therefore \] Rewritine \[\frac{16}{39}\] and \[\frac{-9}{26}\] in such a manner they have the same denominator 78.

\[\frac{16}{39}=\frac{16\times 2}{39\times 2}=\frac{32}{78}\]

\[\frac{-9}{26}=\frac{-9\times 3}{26\times 3}=\frac{-27}{78}\]

\[\frac{16}{39}+\frac{-9}{26}=\frac{32}{78}+\frac{(-27)}{78}\]

\[=\frac{32+(-27)}{78}\]

\[=\frac{32-27}{78}=\frac{5}{78}\]