Math Problem Statement
Answer the questions below about Line 1 and Line 2 shown below.
left parenthesis, 6, plus, 9, right parenthesis, plus, 5
(6+9)+5
Line 1
6, plus, left parenthesis, 9, plus, 5, right parenthesis
6+(9+5)
Line 2
Answer
Attempt 1 out of 2
The expression was rewritten using the Commutative Property of AdditionCommutative Property of MultiplicationAssociative Property of MultiplicationAssociative Property of AdditionDistributive Property. left parenthesis, 6, plus, 9, right parenthesis, plus, 5(6+9)+5 equals plus, 5+5 which equals .6, plus, left parenthesis, 9, plus, 5, right parenthesis6+(9+5) equals 6, plus6+ which equals .
Solution
The problem asks about the property used to rewrite the expression as .
Step 1: Recognize the Property
In the expressions:
- Line 1:
- Line 2:
The grouping of numbers (parentheses) changes from in Line 1 to in Line 2. Since only the grouping of numbers has changed without altering the order of numbers themselves, the Associative Property of Addition is being applied.
Step 2: Explanation
The Associative Property of Addition states that changing the grouping of the numbers being added does not change their sum. In symbols, it is expressed as: Here:
- was rewritten as , so we are applying this property.
Final Answer:
The expression was rewritten using the Associative Property of Addition.
Would you like further clarification or details on this explanation?
Here are 5 related questions to expand your understanding:
- How does the Associative Property differ from the Commutative Property?
- Can the Associative Property be used with subtraction or only addition?
- What is the result of calculating both expressions: and ?
- How does the Associative Property apply to multiplication?
- Can the Distributive Property change the order of addition like the Associative Property?
Tip: When dealing with parentheses in addition, always check whether changing their grouping affects the result—it often leads to using the Associative Property!
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Math Problem Analysis
Mathematical Concepts
Associative Property
Addition
Formulas
(a + b) + c = a + (b + c)
Theorems
Associative Property of Addition
Suitable Grade Level
Grades 5-7
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