Question

properties & relationships
properties of operations
properties of operations are useful for solving and better understanding
equations.
the identity property states that any number multiplied by 1 keeps its
identity. it also states that any number plus or minus 0 remains the same,
and any number divided by 1 remains the same.
the commutative property states that changing the order of numbers while
adding or multiplying them does not change the end result. for example, 5 +
4 = 4 + 5.
the associative property states that when three or more numbers are
added or multiplied, the product or sum remains the same regardless of the
position of the parentheses.
the distributive property is used to solve expressions in the form a(b + c).
under normal circumstances, b and c would be added together. however,
distributive property states that a can be multiplied by b and c before
adding to achieve the same result.

Explanation:

Since no specific question is provided about these properties (like identifying a property, applying it, etc.), it's not possible to give a targeted answer. If you want to identify a property for a given expression, or apply one of these properties to simplify an expression, or have another type of question related to these operation properties, please provide more details. For example, if you have an expression like \(3\times(2 + 5)\) and want to apply the distributive property, we can solve it as follows:

Step1: Recall the distributive property

The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b = 2\), and \(c = 5\).

Step2: Apply the distributive property

\(3\times(2 + 5)=3\times2+3\times5\)

Step3: Calculate the products

\(3\times2 = 6\) and \(3\times5=15\)

Step4: Add the results

\(6 + 15=21\)

Answer:

\(21\)

But without a specific question, please clarify what you need help with regarding these operation properties (e.g., identify the property in a statement, apply a property to an expression, etc.).