Question
Simplify: $-1+\frac{7}{9}+\frac{11}{12}$
✓
Answer
$-1+\frac{7}{9}+\frac{11}{12}$
$\frac{7}{-9}=\frac{7\times(-1)}{-9\times(-1)}=\frac{-7}{9}$
$LCM$ of $9$ and $12 = 36$
$\begin{array}{c|c}3&9,12\\\hline&3,4\end{array}$
$\text{LCM}=3\times3\times4=36$
$\frac{-1}{1}=\frac{-1\times36}{1\times36}=\frac{-36}{36}$
$\frac{-7}{9}=\frac{-7\times4}{9\times4}=\frac{-28}{36}$
$\frac{11}{12}=\frac{11\times3}{12\times3}=\frac{33}{36}$
$\therefore\frac{-1}{1}+\frac{-7}{9}+\frac{11}{12}$
$=\frac{-36}{36}+\frac{-28}{36}+\frac{33}{36}$
$=\frac{-36+(-28)+33}{36}$
$=\frac{-36-28+33}{36}$
$=\frac{-64+33}{36}$
$=\frac{-31}{36}$
$\frac{7}{-9}=\frac{7\times(-1)}{-9\times(-1)}=\frac{-7}{9}$
$LCM$ of $9$ and $12 = 36$
$\begin{array}{c|c}3&9,12\\\hline&3,4\end{array}$
$\text{LCM}=3\times3\times4=36$
$\frac{-1}{1}=\frac{-1\times36}{1\times36}=\frac{-36}{36}$
$\frac{-7}{9}=\frac{-7\times4}{9\times4}=\frac{-28}{36}$
$\frac{11}{12}=\frac{11\times3}{12\times3}=\frac{33}{36}$
$\therefore\frac{-1}{1}+\frac{-7}{9}+\frac{11}{12}$
$=\frac{-36}{36}+\frac{-28}{36}+\frac{33}{36}$
$=\frac{-36+(-28)+33}{36}$
$=\frac{-36-28+33}{36}$
$=\frac{-64+33}{36}$
$=\frac{-31}{36}$
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