Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2.
Expression 1: 22r−13
Expression 2: 19r+(3r−2)−11
Expression 1: 22r−13
Expression 2: 19r+(3r−2)−11
To use the associative property, we need to group the terms in Expression 2 differently. Let's regroup the terms inside the parentheses:
Expression 2: 19r+3r−2−11
Now, we can use the associative property to rearrange the terms:
Expression 2: (19r+3r)−2−11
Simplifying the terms inside the parentheses:
Expression 2: 22r−2−11
Combining like terms:
Expression 2: 22r−13
As we can see, both Expression 1 and Expression 2 simplify to 22r−13, demonstrating that they are equivalent.
To use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2, we need to rearrange the terms in Expression 2 so that we can group like terms together.
Expression 2: 19r + (3r − 2) − 11
First, we'll work within the parentheses by distributing the 3r to the terms inside:
Expression 2: 19r + 3r − 2 − 11
Next, we'll combine like terms. The like terms are the ones with the same variable, which in this case is 'r':
22r − 2 − 11
To simplify further, we'll combine the -2 and -11:
22r − 13
Now, we can see that Expression 2 simplifies to 22r − 13, which is exactly the same as Expression 1. This demonstrates that using the Associative Property, Expression 1 is indeed equivalent to Expression 2.
To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we need to show that the grouping of terms in Expression 2 doesn't affect the final result when simplified.
Let's simplify Expression 2 step-by-step:
Expression 2: 19r + (3r - 2) - 11
First, simplify the expression inside the parentheses:
3r - 2.
Expression 2 becomes:
19r + 3r - 2 - 11
Next, combine like terms:
(19r + 3r) - 2 - 11
Simplify:
22r - 2 - 11
Combine like terms:
22r - 13
After simplifying Expression 2, we get the same result as Expression 1, which is 22r - 13. This demonstrates that Expression 1 is equivalent to Expression 2 using the Associative Property.