Question

which equation shows the associative property of addition? 80 + 41 = 41 + 80 80 + 0 = 80 80 × (41 + 95) = (80 × 41) + (80 × 95) 80 + (41 + 95) = (80 + 41) + 95

Explanation:

1. Recall the Associative Property of Addition: For any real numbers \(a\), \(b\), and \(c\), \(a+(b + c)=(a + b)+c\). This property states that the way we group three or more numbers when adding does not change the sum.
2. Analyze each option:

• Option 1: \(80 + 41=41 + 80\) shows the Commutative Property of Addition (\(a + b=b + a\)), not the Associative Property.
• Option 2: \(80+0 = 80\) shows the Identity Property of Addition (adding 0 to a number gives the number itself), not the Associative Property.
• Option 3: \(80\times(41 + 95)=(80\times41)+(80\times95)\) shows the Distributive Property of Multiplication over Addition, not related to addition's associative property.
• Option 4: \(80+(41 + 95)=(80 + 41)+95\) follows the form \(a+(b + c)=(a + b)+c\) where \(a = 80\), \(b = 41\), and \(c = 95\), which is the Associative Property of Addition.

Answer:

\(80+(41 + 95)=(80 + 41)+95\) (the fourth option)