Question
Evaluate: $\frac{-16}{9}+\frac{-5}{12}+\frac{7}{18}$
✓
Answer
$\frac{-16}{9}+\frac{-5}{12}+\frac{7}{18}$
$LCM$ of $9,12,18 = 36$
$\begin{array}{c|c}2&9,12,18\\\hline3 &9,6,9\\\hline3&3,2,3\\\hline&1,2,1\end{array}$ $\therefore\text{LCM}=2\times3\times3\times2=36$
$\frac{-16}{9}=\frac{-16\times4}{9\times4}=\frac{-64}{36}$
$\frac{-5}{12}=\frac{-5\times3}{12\times3}=\frac{-15}{36}$
$\frac{7}{18}=\frac{7\times2}{18\times2}=\frac{14}{36}$
$\therefore \ \frac{-16}{9}+\frac{-5}{12}+\frac{7}{18}$
$=\frac{-64}{36}+\frac{-15}{36}+\frac{14}{36}$
$=\frac{-64+(-15)+14}{36}$
$=\frac{-64-15+14}{36}=\frac{-79+14}{36}$
$=\frac{-65}{36}$
$LCM$ of $9,12,18 = 36$
$\begin{array}{c|c}2&9,12,18\\\hline3 &9,6,9\\\hline3&3,2,3\\\hline&1,2,1\end{array}$ $\therefore\text{LCM}=2\times3\times3\times2=36$
$\frac{-16}{9}=\frac{-16\times4}{9\times4}=\frac{-64}{36}$
$\frac{-5}{12}=\frac{-5\times3}{12\times3}=\frac{-15}{36}$
$\frac{7}{18}=\frac{7\times2}{18\times2}=\frac{14}{36}$
$\therefore \ \frac{-16}{9}+\frac{-5}{12}+\frac{7}{18}$
$=\frac{-64}{36}+\frac{-15}{36}+\frac{14}{36}$
$=\frac{-64+(-15)+14}{36}$
$=\frac{-64-15+14}{36}=\frac{-79+14}{36}$
$=\frac{-65}{36}$
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