Question
Add the following rational numbers. $\frac{7}{-18}\ \text{and}\ \frac{8}{27}$
✓
Answer
We will first write each of the given numbers with positive denominators.
$\frac{7}{-18}=\frac{7\times(-1)}{-18\times(-1)}=\frac{-7}{18}$
The denominators of the given rational number are $18$ and $27.$
$LCM$ of $18, 27$ is $54$
Now,
$\frac{-7}{18}=\frac{-7\times3}{18\times3}$
$=\frac{-21}{54}$
and $\frac{8}{27}=\frac{8\times2}{27\times2}$
$=\frac{16}{54}$
$\therefore\frac{7}{-18}+\frac{8}{27}$
$\frac{-7}{18}+\frac{8}{27}$
$=\frac{-21+16}{54}$
$=\frac{-5}{54}$
$\frac{7}{-18}=\frac{7\times(-1)}{-18\times(-1)}=\frac{-7}{18}$
The denominators of the given rational number are $18$ and $27.$
$LCM$ of $18, 27$ is $54$
Now,
$\frac{-7}{18}=\frac{-7\times3}{18\times3}$
$=\frac{-21}{54}$
and $\frac{8}{27}=\frac{8\times2}{27\times2}$
$=\frac{16}{54}$
$\therefore\frac{7}{-18}+\frac{8}{27}$
$\frac{-7}{18}+\frac{8}{27}$
$=\frac{-21+16}{54}$
$=\frac{-5}{54}$
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