Let's match each equation to the mathematical property it demonstrates:
1. [tex]$(4+5)+2=4+(5+2)$[/tex]
- This equation demonstrates the associative property of addition. The associative property states that the way in which numbers are grouped when adding or multiplying does not change their sum or product. Here, [tex]$(4 + 5) + 2$[/tex] is equivalent to [tex]$4 + (5 + 2)$[/tex].
2. [tex]$2(2x+4)=4x+8$[/tex]
- This equation uses the distributive property. The distributive property states that multiplying a number by a sum is the same as doing each multiplication separately. Here, [tex]$2(2x + 4)$[/tex] expands to [tex]$2 \cdot 2x + 2 \cdot 4$[/tex], which equals [tex]$4x + 8$[/tex].
3. [tex]$(7 \cdot x) \cdot 3=7 \cdot (x \cdot 3)$[/tex]
- This equation exemplifies the associative property of multiplication. The associative property indicates that the way numbers are grouped in multiplication doesn't change the product. So, [tex]$(7 \cdot x) \cdot 3$[/tex] is the same as [tex]$7 \cdot (x \cdot 3)$[/tex].
4. [tex]$(8 \cdot x \cdot 2)=(x \cdot 8 \cdot 2)$[/tex]
- This equation shows the commutative property of multiplication. The commutative property of multiplication states that the order in which two numbers are multiplied does not affect the product. Therefore, [tex]$(8 \cdot x \cdot 2)$[/tex] is the same as [tex]$(x \cdot 8 \cdot 2)$[/tex].
5. [tex]$(7+3)+1=1+(7+3)$[/tex]
- This equation uses the commutative property of addition. The commutative property of addition states that the order in which two numbers are added does not affect the sum. Thus, [tex]$(7 + 3) + 1$[/tex] is equivalent to [tex]$1 + (7 + 3)$[/tex].
To summarize the matches:
- [tex]$(4+5)+2=4+(5+2)$[/tex]: Associative property of addition
- [tex]$2(2x+4)=4x+8$[/tex]: Distributive property
- [tex]$(7 \cdot x) \cdot 3=7 \cdot (x \cdot 3)$[/tex]: Associative property of multiplication
- [tex]$(8 \cdot x \cdot 2)=(x \cdot 8 \cdot 2)$[/tex]: Commutative property of multiplication
- [tex]$(7+3)+1=1+(7+3)$[/tex]: Commutative property of addition
