Question
Simplify: $\frac{-7}{10}+\frac{13}{-15}+\frac{27}{20}$
✓
Answer
$\frac{-7}{10}+\frac{13}{-15}+\frac{27}{20}$
$\frac{13}{-15}=\frac{13\times(-1)}{-15\times(-1)}=\frac{-13}{15}$
Now $LCM$ of $10, 15, 20 = 60$
$\begin{array}{c|c}2&10,15,20\\\hline5&5,15,10\\\hline&1,3,2\end{array}$
$\therefore\text{LCM}=2\times5\times3\times2=60$
$\frac{-7}{10}=\frac{-7\times6}{10\times6}=\frac{-42}{60}$
$\frac{-13}{15}=\frac{-13\times4}{15\times4}=\frac{-52}{60}$
$\frac{27}{20}=\frac{27\times3}{20\times3}=\frac{81}{60}$
$\therefore\frac{-7}{10}+\frac{-13}{15}+\frac{27}{20}$
$=\frac{-42}{60}+\frac{-52}{60}+\frac{81}{60}$
$=\frac{-42+(-52)+81}{60}$
$=\frac{-42-52+81}{60}=\frac{-94+81}{60}$
$=\frac{-13}{60}$
$\frac{13}{-15}=\frac{13\times(-1)}{-15\times(-1)}=\frac{-13}{15}$
Now $LCM$ of $10, 15, 20 = 60$
$\begin{array}{c|c}2&10,15,20\\\hline5&5,15,10\\\hline&1,3,2\end{array}$
$\therefore\text{LCM}=2\times5\times3\times2=60$
$\frac{-7}{10}=\frac{-7\times6}{10\times6}=\frac{-42}{60}$
$\frac{-13}{15}=\frac{-13\times4}{15\times4}=\frac{-52}{60}$
$\frac{27}{20}=\frac{27\times3}{20\times3}=\frac{81}{60}$
$\therefore\frac{-7}{10}+\frac{-13}{15}+\frac{27}{20}$
$=\frac{-42}{60}+\frac{-52}{60}+\frac{81}{60}$
$=\frac{-42+(-52)+81}{60}$
$=\frac{-42-52+81}{60}=\frac{-94+81}{60}$
$=\frac{-13}{60}$
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