Question

Using appropriate properties (commutative, associative, distributive), find the value of the expression:
$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

• A. $\frac{2}{3}$
• B. $-\frac{3}{2}$
• C. $\frac{2}{1}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{2}{1}$

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