### Theory:

Changing the order of the integers does not change the value of the result or the sum. This is called the commutative property of integers.
While adding two integers, changing the order of the integers will not change the result.
Consider $$a$$ and  $$b$$ are two integers then:

$\left(\phantom{\rule{0.147em}{0ex}}a+b\phantom{\rule{0.147em}{0ex}}\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\left(\phantom{\rule{0.147em}{0ex}}b+a\phantom{\rule{0.147em}{0ex}}\right)$
Example:
i) $\left(10+5\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\left(5+10\right)\phantom{\rule{0.147em}{0ex}}=15$.

ii) $$100 + 2 = 2 + 100 = 102$$.

iii) $\left(\left(-10\right)+\left(-5\right)\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\left(\left(-5\right)+\left(-10\right)\right)=-15$
Thus addition operation satisfies the commutative property.

Therefore the commutative property of integers states that while operating addition with two or more integers, and by changing the order of number does not change the result of the operation.