Let's analyze the given equation step-by-step:
The original equation is:
[tex]\[ 3 + ((-5) + 6) = (3 + (-5)) + 6 \][/tex]
We observe that the numbers are grouped differently on each side of the equation but both expressions include addition operations:
1. On the left-hand side: [tex]\( 3 + ((-5) + 6) \)[/tex]
2. On the right-hand side: [tex]\( (3 + (-5)) + 6 \)[/tex]
To determine which property is illustrated, let's look at the options:
- Commutative property of addition: This property states that changing the order of the addends does not change the sum, for example, [tex]\( a + b = b + a \)[/tex]. However, this property is not about changing the order of numbers here.
- Identity property of multiplication: This property states that any number multiplied by 1 remains the same, for example, [tex]\( a \times 1 = a \)[/tex]. This property is not relevant here since our equation deals with addition, not multiplication.
- Associative property of addition: This property states that the way numbers are grouped when adding does not affect the sum, for example, [tex]\( a + (b + c) = (a + b) + c \)[/tex]. This matches our scenario, where the grouping of 3, -5, and 6 changes, but the overall sum remains the same.
- Commutative property of multiplication: This property states that changing the order of factors does not change the product, for example, [tex]\( a \times b = b \times a \)[/tex]. Since our equation is about addition, this property doesn't apply.
Given the detailed analysis, the property demonstrated by the equation
[tex]\[ 3 + ((-5) + 6) = (3 + (-5)) + 6 \][/tex]
is the associative property of addition.
