Question

Simplify using commutative and associative property :

$\frac{2}{9}+\frac{-3}{5}+\frac{1}{3}$

• A. $\frac{10}{18}$
• B. $\frac{-2}{45}$
• C. $\frac{2}{45}$
• D. $\frac{2}{27}$

Answer 1

The correct option is B $\frac{-2}{45}$

$\frac{2}{9}+\frac{-3}{5}+\frac{1}{3}=\frac{2}{9}+(\frac{-3}{5}+\frac{1}{3})$

$=\frac{2}{9}+(\frac{1}{3}+\frac{-3}{5})$ (commutative property)

$=(\frac{2}{9}+\frac{1}{3})+\frac{-3}{5}$ (associative property)

$=\frac{2+3}{9}+\frac{-3}{5}$

$=\frac{5}{9}+\frac{-3}{5}$

$=\frac{25-27}{45}$

$=\frac{-2}{45}$