Question

Check the commutative property of addition for $\frac{-7}{9},\frac{-18}{19}$

Answer 1

Commutative property of addition for any element $a,b$ is given by $a+b=b+a$
To check, $\frac{-7}{9}+\frac{-18}{19}=\frac{-18}{19}+\frac{-7}{9}$
Consider LHS,
$=\frac{-7}{9}+\frac{-18}{19}$= $\frac{\left[\right(-7)\times 19+(-18)\times 9)]}{9\times 19}$ = $\frac{-133-162}{171}$ = $\frac{-295}{171}$
RHS,
$=\frac{-18}{19}+\frac{-7}{9}=\frac{\left[\right(-18)\times 9+(-7)\times 19)]}{19\times 9}$ = $\frac{-162-133}{171}=\frac{-295}{171}$
$\therefore$ RHS = LHS

Hence, $\frac{-7}{9},\frac{-18}{19}$ are commutative.