Question

verify the following​

Answer 1

The property used above is associative property.

Associative Property ⇒ (a + b) + c =  a + (b + c)

Associative Property holds for only addition and multiplication in rational numbers.

So we will apply this property and check if it is true.

$(\frac{2}{5} +\frac{-3}{7}) +\frac{-7}{10} = \frac{2}{5} + (\frac{-3}{7} +\frac{-7}{10} )$

LCM of numbers in brackets (LHS) = 35

LCM of numbers in brackets (RHS) = 70

Sum of the numbers in brackets in LHS ⇒

$\frac{14}{35} +\frac{-15}{35} \\\\\frac{14}{35} - \frac{15}{35} \\\\ \frac{-1}{35}$

Sum of the numbers in brackets in RHS ⇒

$\frac{-3}{7} +\frac{-7}{10} \\\\\frac{-30}{70} +\frac{-49}{70} \\\\\frac{-79}{70}$

Let's solve all of them together ⇒

$\frac{-1}{35} + \frac{-7}{10} = \frac{2}{5} +\frac{-79}{70}$

LCM for LHS = 70

LCM for RHS = 70

$\frac{-2}{70} +\frac{-49}{70} = \frac{28}{70}+\frac{-79}{70}$

$\frac{-51}{70} = \frac{-51}{70}$

∴ We can say that Associative property applies for addition in rational numbers.