Question

4. Which property of addition satisfies the statement?
[(-5) + (-2)] + (-7) = (-5) + [(-2) + (-7)]
(A) Closure
(B) Commutative
(C) Associative
(D) Identity​

Answer 1

Answer:

Commutative property .. always remember it for similar LHS - RHS ( Same )

Answer 2

Concept

This problem is based on the properties of integers.There are five main properties of operation namely:

Closure Property, Associative Property, Commutative Property, Distributive Property, and Identity Property.

Given

We have a statement $[(-5) + (-2)] + (-7) = (-5) + [(-2) + (-7)]$

To Find

We have to find which property of addition satisfies the given statement:

(A) Closure

(B) Commutative

(C) Associative

(D) Identity​

Solution

(A) The closure property of addition and subtraction states that the sum or difference of any two integers will always be an integer. Let x and y are any two integers, then x + y and x − y will also be an integer.

(B) The commutative property of addition states that the order of terms doesn’t matter, the result will be the same i.e swapping of terms will not change the sum. Let x and y are any two integers, then

⇒ x + y = y + x

(C) The associative property of addition states that the way of the grouping of integers doesn’t matter, their result will be the same. Let x, y, and z be any three integers, then

⇒ x + (y + z) = (x + y) +z

We have statement

$[(-5) + (-2)] + (-7) = (-5) + [(-2) + (-7)]$

Compare with the associative property of addition statement i.e

x + (y + z) = (x + y) +z

It shows the given statement satisfies the associative property of addition.

(D) The identity property of addition states that when any integer is added to zero it will give the same number where "0" is called additive identity. Let x be any integer then,

x + 0 = x = 0 + x

As a result, the given statement $[(-5) + (-2)] + (-7) = (-5) + [(-2) + (-7)]$  satisfies the associative property of addition i.e option (C)

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