Given:
Two expressions are [tex]\left[\left(-\dfrac{1}{5}\right)+\left(-\dfrac{3}{5}\right)\right]+\left(\dfrac{1}{7}\right)[/tex] and [tex]\left(-\dfrac{1}{5}\right)+\left[\left(-\dfrac{3}{5}\right)+\left(\dfrac{1}{7}\right)\right][/tex].
To find:
The property that allows to compute [tex]\left[\left(-\dfrac{1}{5}\right)+\left(-\dfrac{3}{5}\right)\right]+\left(\dfrac{1}{7}\right)[/tex] as [tex]\left(-\dfrac{1}{5}\right)+\left[\left(-\dfrac{3}{5}\right)+\left(\dfrac{1}{7}\right)\right][/tex].
Solution:
According to associative property of addition, if a, b and c are real numbers, then
[tex](a+b)+c=a+(b+c)[/tex]
Using the associative property of addition, we get
[tex]\left[\left(-\dfrac{1}{5}\right)+\left(-\dfrac{3}{5}\right)\right]+\left(\dfrac{1}{7}\right)=\left(-\dfrac{1}{5}\right)+\left[\left(-\dfrac{3}{5}\right)+\left(\dfrac{1}{7}\right)\right][/tex]
Therefore, the required property is associative property of addition.
