Which expression correctly uses the associative property of addition to simplify the sum $(-3)\; +\; [(-7)\; +\; 5]$ without changing its value?

The distributive property allows you to multiply an integer by a sum of integers by multiplying the integer separately by each addend and then adding the products, regardless of whether the integers are positive or negative, such as in the expression $a(b\; +\; c)\; =\; ab\; +\; ac$ where $a$, $b$, and $c$ can be any integers.

Using the associative property, simplify the expression ($-3\; +\; 5$) + $-7$ without changing the order of the integers. What is the simplified result?

Match each mathematical property of integer operations with its correct explanation or representative expression.

Place the following steps in the correct order to simplify the expression $3\; +\; (-5)\; +\; (-7)\; +\; 9$ using properties of operations with integers.

Sort each item into the correct category based on properties of operations with integers.

Arrange the terms to show the correct sequence for applying properties of operations to simplify integer expressions.

Unscramble the letters to find the term that describes a property used when adding or multiplying integers regardless of how they are grouped.

Which of the following statements correctly illustrate the use of the Distributive Property and the Additive Inverse Property when working with integers? (Select all that apply)

Consider the expression $(-3)\; +\; [4\; +\; (-2)]$. Using the properties of operations with integers, which of the following justifications correctly explains simplifying this expression while showing mastery of these properties?