9 answers
According to the Associative Property of Addition, the way in which numbers are grouped when adding does not change the sum.
For the expression \((7 + 8) + 6\), we can regroup the numbers. For example, we can group \(8\) and \(6\) instead:
\[ 7 + (8 + 6) \]
So, using the Associative Property of Addition, the equivalent expression is:
\[ 7 + (8 + 6) \]
Using the Associative Property of Addition, we can regroup the terms in the expression \(3x + (2y + z)\).
We can choose to group \(3x\) and \(2y\) together instead:
\[ (3x + 2y) + z \]
So, the expression \(3x + (2y + z)\) can be rewritten as:
\[ (3x + 2y) + z \]
Both expressions are equivalent due to the Associative Property of Addition.
Using the Associative Property of Multiplication, which states that the way in which factors are grouped does not change the product, we can rewrite the expression \( p \cdot (q \cdot r) \).
We can regroup the factors by changing the grouping to \( (p \cdot q) \cdot r \).
Thus, the expression \( p \cdot (q \cdot r) \) can be rewritten as:
\[ (p \cdot q) \cdot r \]
Both expressions are equivalent due to the Associative Property of Multiplication.
To use the Associative Property of Addition to simplify the expression \(3x + (x + 2)\), we can regroup the expression.
We rewrite it as:
\[ (3x + x) + 2 \]
Then, we can combine the like terms \(3x + x\):
\[ (4x) + 2 \]
So the simplified equivalent form is:
\[ 4x + 2 \]
This expression is in its simplest form.
Using the Associative Property to group like terms together in the expression \(9x + (2x + 3)\), we can rearrange the grouping to emphasize the like terms.
We can group \(9x\) and \(2x\) together, while keeping \(3\) separate:
\[ (9x + 2x) + 3 \]
So, the expression \(9x + (2x + 3)\) can be regrouped as:
\[ (9x + 2x) + 3 \]
This groups the like terms \(9x\) and \(2x\) together without simplifying them.
