Question

Verify the following and identify the property for the given:
$\left[ \left( -51 \right)+\left( -26 \right) \right]+\left( -13 \right)=\left( -51 \right)+\left[ \left( -26 \right)+\left( -13 \right) \right]$

Answer 1

Hint: We should solve this type of questions by considering L.H.S and R.H.S.And find the L.H.S part value and R.H.S part value.According to that we have to find the property.We know that the commutative property over addition is $(a+b)+c=a+(b+c)$.

Complete step-by-step solution:
From the problem we have given that,
$\left[ \left( -51 \right)+\left( -26 \right) \right]+\left( -13 \right)=\left( -51 \right)+\left[ \left( -26 \right)+\left( -13 \right) \right]$....................equation(1)
Let us consider the L.H.S (Left.Hand.Side)part of the equation(1)
$\Rightarrow \left[ \left( -51 \right)+\left( -26 \right) \right]+\left( -13 \right)$
[Adding and multiplying combinations of positive and negetive numbers can cause confusion and so two ‘pluses’ make a plus ,two ‘minuses’ make a plus .A plus and a minus make a plus.That is (−)×(−)=(+) and (−)×(+)=(−) and (+)×(+)=(+)]
$\Rightarrow \left[ -51-26 \right]+\left( -13 \right)$
$\Rightarrow \left( -77 \right)-(13)$
On simplifying this arthmetic expression we get as follows
$\Rightarrow -90$
Hence the L.H.S part value of the equation(1) is $-90$
Let us consider the R.H.S(Right.Hand.Side) part of the equation(1)
$\Rightarrow \left( -51 \right)+\left[ \left( -26 \right)+\left( -13 \right) \right]$
[Adding and multiplying combinations of positive and negetive numbers can cause confusion and so two ‘pluses’ make a plus ,two ‘minuses’ make a plus .A plus and a minus make a plus.That is $(−)\times (−)=(+)$ and $(−)\times (+)=(−)$ and $(+)\times (+)=(+)$
$\Rightarrow \left( -51 \right)-(26)-\left( -13 \right)$
$\Rightarrow \left( -77 \right)-(13)$
On simplifying this arthmetic expression we get as follows
$\Rightarrow -90$
Hence the R.H.S part value of the equation(1) is $-90$
Therefore,R.H.S=L.H.S
Here, as R.H.S=L.H.S the property is commutative property of addition $(a+b)+c=a+(b+c)$

Note: In mathematics, An operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many mathematical proofs depends on it.But it is not applicable for division and multiplication operations and such operations are called non-commutative operations.