Question

Answer the questions below about Line 1 and Line 2 shown below.
left parenthesis, 6, dot, 2, right parenthesis, dot, 7
(6⋅2)⋅7
Line 1
6, dot, left parenthesis, 2, dot, 7, right parenthesis
6⋅(2⋅7)
Line 2
Answer
Attempt 1 out of 2

The expression was rewritten using the
.
left parenthesis, 6, dot, 2, right parenthesis, dot, 7(6⋅2)⋅7 equals
dot, 7⋅7 which equals
.
6, dot, left parenthesis, 2, dot, 7, right parenthesis6⋅(2⋅7) equals 6, dot6⋅
which equals
.

Answer 1

To evaluate the two expressions given in Line 1 and Line 2 and answer the questions about their equivalences:

**Line 1:** \((6 \cdot 2) \cdot 7\)
**Line 2:** \(6 \cdot (2 \cdot 7)\)

Let's calculate each expression step-by-step:

**For Line 1:**
1. Calculate inside the parentheses: \(6 \cdot 2 = 12\).
2. Then multiply by 7: \(12 \cdot 7 = 84\).

So, \((6 \cdot 2) \cdot 7 = 84\).

**For Line 2:**
1. Calculate inside the parentheses: \(2 \cdot 7 = 14\).
2. Then multiply by 6: \(6 \cdot 14 = 84\).

So, \(6 \cdot (2 \cdot 7) = 84\).

Both expressions evaluate to the same result, which is 84.

Now, substituting back into your structured answer for clarification:

1. The expression was rewritten using the **associative property of multiplication**.
2. \((6 \cdot 2) \cdot 7\) equals \(12 \cdot 7\) which equals **84**.
3. \(6 \cdot (2 \cdot 7)\) equals \(6 \cdot 14\) which equals **84**.

Thus, both expressions are indeed equal and follow the associative property of multiplication.