Integers are whole numbers, including positive and negative numbers as well as zero. When working with integers, it's essential to understand their properties, which govern the operations of addition, subtraction, multiplication, and division. Here's a breakdown of these properties:

##### Commutative Property:

**Addition:**a + b = b + a**Multiplication:**a * b = b * a

Think about how the order of numbers doesn't matter in addition and multiplication. Can you come up with examples to illustrate this property?

##### Associative Property:

**Addition:**(a + b) + c = a + (b + c)**Multiplication:**(a * b) * c = a * (b * c)

This property shows how the grouping of numbers doesn't matter in addition and multiplication. Try creating examples that demonstrate this property.

##### Distributive Property:

a * (b + c) = a * b + a * c

The distributive property connects multiplication and addition. Can you create examples where you apply the distributive property to simplify expressions?

##### Identity Property:

**Addition:**a + 0 = a**Multiplication:**a * 1 = a

Identity properties highlight the unique role of 0 in addition and 1 in multiplication. Practice using the identity property by solving equations that involve these special numbers.

##### Inverse Property:

**Addition:**a + (-a) = 0**Multiplication:**a * (1/a) = 1, when a ≠ 0

The inverse property demonstrates how to "undo" an operation. Consider how you might use the inverse property to solve equations that require isolating a variable.

Now that we've covered the main properties of integers, it's your turn! Practice creating and solving problems involving these properties.