Check the commutative property of addition for $\frac{-8}{13},\frac{23}{27}$

We know that the commutative property of Addition states that changing the order of addends does not change the sum. i.e., if $a$ and $b$ are two real numbers, then $a+b=b+a$.

Let $a=\frac{-8}{13}$ and$b=\frac{23}{27}$.

Let us first find $a+b$ as follows:

$a+b=\frac{-8}{13}+\frac{23}{27}=\frac{-8\times 27}{13\times 27}+\frac{23\times 13}{27\times 13}=\frac{-216}{351}+\frac{299}{351}=\frac{83}{351}........\left(1\right)$

Now, we find $b+a$ as follows:

$b+a=\frac{23}{27}+\left(\frac{-8}{13}\right)=\frac{23\times 13}{27\times 13}-\frac{8\times 27}{13\times 27}=\frac{299}{351}-\frac{216}{351}=\frac{83}{351}.......\left(2\right)$

Since equation $\left(1\right)$ is equal to equation $\left(2\right)$,

$\therefore$ $a+b=b+a$ i.e.

$\frac{-8}{13}+\frac{23}{27}=\frac{23}{27}+\frac{-8}{13}$

Hence, the given numbers $\frac{-8}{13}$ and $\frac{23}{27}$ satisfies the commutative property of addition.