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Question 1(i)
Using appropriate properties find:

\(-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}\)


Solution

\(=-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}\)
\(=-\frac{2}{3}\times \frac{3}{5}-\frac{3}{5}\times\frac{1}{6} +\frac{5}{2}\\
\text{[Using Commutative property]}\\
=\frac{3}{5}\left ( \frac{-2}{3}-\frac{1}{6} \right )+\frac{5}{2}\\
\text{[Using distributive property]}\\
=\frac{3}{5}\left ( \frac{-4-1}{6} \right )+\frac{5}{2}=\frac{3}{5}\times \frac{-5}{6}+\frac{5}{2}\\
=-\frac{1}{2}+\frac{5}{2}=\frac{-1+5}{2}=\frac{4}{2}=2\)

Mathematics
NCERT Textbook
Standard VIII

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