Question

check commutative property under subtraction for a=-8÷9, b=-4÷7 take LHS and RHS.
$\frac{ - 8}{9} - \frac{ - 4}{7}$
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Answer 1

Given :

• LHS : $\tt{ \dfrac{-8}{9}}$<- a

• RHS : $\tt{\dfrac{-4}{7}}$<- b

To Find :

• Difference between LHS and RHS using commutative property.

Commutative property :

$\large{\boxed{\tt{ a + b = b + a}}}$

Solution :

a = $\tt{ \dfrac{-8}{9}}$

b = $\tt{\dfrac{-4}{7}}$

So according to the property : (a + b = b + a)

The given property is of Addition. For finding the commutative property of Subtraction ; we will replace the Addition sign with Subtraction sign.

Let us check if commutative property works for subtraction :

$\longrightarrow{\tt{a - b = b - a}}$

$\longrightarrow{\tt{\dfrac{-8}{9} - \dfrac{-4}{7} = \dfrac{-4}{7} - \dfrac{-8}{9}}}$

Now we will Subtract both the terms on both the sides by taking LCM and simplifying them. We get :

$\longrightarrow{\tt{ \dfrac{-20}{63} = \dfrac{20}{63}}}$

$\large{\boxed{\implies{\tt{\dfrac{-20}{63} \ne \dfrac{20}{63}}}}}$

Thus , we can conclude that commutative property is not closed under Subtraction.