The equation [tex]\( 7 + ((-7) + 2) = (7 + (-7)) + 2 \)[/tex] showcases a particular property of addition. Let's analyze this step-by-step to identify the property it represents.
### Step 1: Understand the Equation
We have the equation [tex]\( 7 + ((-7) + 2) = (7 + (-7)) + 2 \)[/tex].
### Step 2: Grouping Within Parentheses
Notice how the numbers are grouped within parentheses:
- On the left side: [tex]\( 7 + ((-7) + 2) \)[/tex]
- On the right side: [tex]\( (7 + (-7)) + 2 \)[/tex]
### Step 3: Evaluating Each Side Separately
Left Side:
1. Evaluate the expression inside the inner parentheses: [tex]\( -7 + 2 = -5 \)[/tex]
2. Then, add the result to 7: [tex]\( 7 + (-5) = 2 \)[/tex]
Right Side:
1. Evaluate the expression inside the inner parentheses: [tex]\( 7 + (-7) = 0 \)[/tex]
2. Then, add the result to 2: [tex]\( 0 + 2 = 2 \)[/tex]
### Step 4: Analyze the Structure of the Equation
In both cases, the sum is still 2 regardless of how the numbers are grouped. This illustrates that the way we group numbers in addition doesn't affect the result.
### Conclusion
The property demonstrated by this equation is the associative property. The associative property states that the grouping of numbers does not affect the sum or product, which is what we observed here:
[tex]\[ (a + b) + c = a + (b + c) \][/tex]
Therefore, the equation [tex]\( 7 + ((-7) + 2) = (7 + (-7)) + 2 \)[/tex] represents the associative property of addition.
