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 .

The problem asks about the property used to rewrite the expression \( (6+9) + 5 \) as \( 6 + (9+5) \). 

### Step 1: Recognize the Property
In the expressions:
- **Line 1**: \( (6+9) + 5 \)
- **Line 2**: \( 6 + (9+5) \)

The grouping of numbers (parentheses) changes from \( (6+9) + 5 \) in Line 1 to \( 6 + (9+5) \) 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:
\[
(a + b) + c = a + (b + c)
\]
Here:
- \( (6+9) + 5 \) was rewritten as \( 6 + (9+5) \), 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:

1. How does the Associative Property differ from the Commutative Property?
2. Can the Associative Property be used with subtraction or only addition?
3. What is the result of calculating both expressions: \( (6+9) + 5 \) and \( 6 + (9+5) \)?
4. How does the Associative Property apply to multiplication?
5. 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!

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 .

Explore how to apply the Associative Property of Addition to rewrite expressions like (6+9)+5 as 6+(9+5). This step-by-step solution is suitable for Grades 5-7 and focuses on key mathematical concepts like grouping in addition.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation