Question

Is the associative property to this demonstrate that expression one is equivalent to expression 2 25r - 15 20R + (5r - 3) - 12

Answer 1

To determine if the expression \(25r - 15 + 20r + (5r - 3) - 12\) is equivalent to the expression \(25r - 15 + 20r - 12 + (5r - 3)\), we can use the associative property of addition. The associative property states that the way in which numbers are grouped in addition does not change their sum.

First, let's simplify both expressions step-by-step, applying the associative property where necessary.

**Expression 1:**
\[ 25r - 15 + 20r + (5r - 3) - 12 \]

1. Combine the terms inside the parentheses:
\[ 25r - 15 + 20r + 5r - 3 - 12 \]

2. Now combine all the \(r\) terms together:
\[ (25r + 20r + 5r) + (-15 - 3 - 12) \]
\[ 50r - 30 \]

**Expression 2:**
\[ 25r - 15 + 20r - 12 + (5r - 3) \]

1. Combine the terms inside the parentheses:
\[ 25r - 15 + 20r - 12 + 5r - 3 \]

2. Now combine all the \(r\) terms together:
\[ (25r + 20r + 5r) + (-15 - 12 - 3) \]
\[ 50r - 30 \]

Since both expressions simplify to \(50r - 30\), we have demonstrated that they are equivalent.

Thus, both expressions are equivalent, and this can indeed be shown using the associative property of addition to regroup the terms.