Certainly! Here are the detailed properties for each equation:
### 8. [tex]\(4 + 0 = 4\)[/tex]
This is an example of the Identity Property of Addition. The identity property states that any number plus zero is the number itself. In this case, adding 0 to 4 leaves 4 unchanged.
### 9. [tex]\(5 + 2 = 2 + 5\)[/tex]
This illustrates the Commutative Property of Addition. The commutative property states that the order in which two numbers are added does not affect the sum. Thus, 5 + 2 is equal to 2 + 5.
### 10. [tex]\((3 + 2) + 6 = 2 + (3 + 6)\)[/tex]
This showcases the Associative Property of Addition. The associative property states that when three or more numbers are added, the way in which they are grouped does not change the sum. Here, [tex]\((3 + 2) + 6\)[/tex] is equivalent to [tex]\(2 + (3 + 6)\)[/tex].
### 11. [tex]\((4 \times 8) + (4 \times 6) = 4 (8 + 6)\)[/tex]
This demonstrates the Distributive Property. The distributive property states that a single term multiplied by a sum of two terms is the same as the sum of that single term multiplied by each of the terms individually. So, [tex]\((4 \times 8) + (4 \times 6)\)[/tex] is the same as [tex]\(4 \times (8 + 6)\)[/tex].
In summary:
1. [tex]\(4 + 0 = 4\)[/tex] - Identity Property of Addition
2. [tex]\(5 + 2 = 2 + 5\)[/tex] - Commutative Property of Addition
3. [tex]\((3 + 2) + 6 = 2 + (3 + 6)\)[/tex] - Associative Property of Addition
4. [tex]\((4 \times 8) + (4 \times 6) = 4(8 + 6)\)[/tex] - Distributive Property
