The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

$\displaystyle \left | 135\right |=135$

For this problem, that gives us a final answer of 135.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

$\displaystyle \left | -12\right |=12$

For this problem, that gives us a final answer of 12.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

$\displaystyle \left | 25\right |=25$

For this problem, that gives us a final answer of 25.

The statement shows that two numbers can be added in either order to achieve the same result. This is the commutative property of addition.

The fact that 0 can be added to any number to yield the latter number as the sum is the identity property of addition.

For every real number, there is a number that can be added to it to yield the sum 0. This is the inverse property of addition.

That any number is equal to itself is the reflexive property of equality.

If an equality is true, then it can be correctly stated with the expressions in either order with equal validity. This is the symmetric property of equality.

The statement shows that two numbers can be added in either order to yield the same sum. This is the commutative property of addition.

A set is closed under multiplication if and only the product of any two (not necessarily distinct) elements of that set is itself an element of that set. 

$\displaystyle \left \{ 2, 4, 6, 8, 10...\right \}$ is closed under multiplication since the product of two even numbers is even:

$\displaystyle 2N \cdot 2M = 4MN = 2 (2MN)$

$\displaystyle \left \{ 1, 4, 9, 16, 25,...\right \}$ is closed under multiplication since the product of two perfect squares is a perfect square:

$\displaystyle N^{2} \cdot M^{2} = (NM)^{2}$

$\displaystyle \left \{ \sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \sqrt{5} ... \right \}$ is closed under multiplication since the product of two square roots of positive integers is the square root of a positve integer:

$\displaystyle \sqrt{N} \cdot \sqrt{M} = \sqrt{NM}$

But $\displaystyle \left \{ i, 2i, 3i, 4i, 5i...\right \}$, as can be seen here, is not closed under multiplication:

$\displaystyle 2i \cdot 3i = 2\cdot 3 \cdot i \cdot i = 6 \cdot i^{2} = 6 (-1)= -6 \notin \left \{ i, 2i, 3i, 4i, 5i...\right \}$