Question

Simplify using commutative and associative property :

$[\frac{2}{5}+\frac{5}{7}+\frac{-12}{5}]$

• A. $-2\frac{5}{7}$
• B. $\frac{9}{7}$
• C. $\frac{-7}{9}$
• D. $\frac{-9}{7}$

Answer 1

The correct option is D $\frac{-9}{7}$

$\frac{2}{5}+\frac{5}{7}+\frac{-12}{5}=\frac{2}{5}+(\frac{5}{7}+\frac{-12}{5})$

$=\frac{2}{5}+(\frac{-12}{5}+\frac{5}{7})$ (commutative property)

$=(\frac{2}{5}+\frac{-12}{5})+\frac{5}{7}$ (associative property)

$=\frac{2-12}{5}+\frac{5}{7}$

$=\frac{-10}{5}+\frac{5}{7}$

$=\frac{-70+25}{35}$

$=-\frac{45}{35}$

$=\frac{-9}{7}$
Or
$=-2+\frac{5}{7}$

$=\frac{-14+5}{7}$

$=\frac{-9}{7}$