Question

Which property allows to compute [(-1/5) + (-3/5)] + (1/7) as (-1/5) + [(-3/5) + (1/7)]

Answer 1

Given:

Two expressions are $\left[\left(-\dfrac{1}{5}\right)+\left(-\dfrac{3}{5}\right)\right]+\left(\dfrac{1}{7}\right)$ and $\left(-\dfrac{1}{5}\right)+\left[\left(-\dfrac{3}{5}\right)+\left(\dfrac{1}{7}\right)\right]$.

To find:

The property that allows to compute $\left[\left(-\dfrac{1}{5}\right)+\left(-\dfrac{3}{5}\right)\right]+\left(\dfrac{1}{7}\right)$ as $\left(-\dfrac{1}{5}\right)+\left[\left(-\dfrac{3}{5}\right)+\left(\dfrac{1}{7}\right)\right]$.

Solution:

According to associative property of addition, if a, b and c are real numbers, then

$(a+b)+c=a+(b+c)$

Using the associative property of addition, we get

$\left[\left(-\dfrac{1}{5}\right)+\left(-\dfrac{3}{5}\right)\right]+\left(\dfrac{1}{7}\right)=\left(-\dfrac{1}{5}\right)+\left[\left(-\dfrac{3}{5}\right)+\left(\dfrac{1}{7}\right)\right]$

Therefore, the required property is associative property of addition.