Question

1. which equation demonstrates the associative property of multiplication?

(9 + 8)+2 = 9+(8 + 2)
9(8 + 2)=72 + 18
(9·8)·2 = 9·(8·2)
9+8 + 2=2 + 9+8

Explanation:

Step1: Recall associative property of multiplication

The associative property of multiplication states that for any real - numbers \(a\), \(b\), and \(c\), \((a\times b)\times c=a\times(b\times c)\).

Step2: Analyze each option

• Option 1: \((9 + 8)+2=9+(8 + 2)\) is the associative property of addition, not multiplication.
• Option 2: \(9(8 + 2)=72+18\) is the distributive property of multiplication over addition (\(a(b + c)=ab+ac\)).
• Option 3: \((9\cdot8)\cdot2=9\cdot(8\cdot2)\) follows the form \((a\times b)\times c=a\times(b\times c)\) for \(a = 9\), \(b = 8\), and \(c = 2\), which is the associative property of multiplication.
• Option 4: \(9 + 8+2=2+9+8\) is the commutative property of addition.

Answer:

\((9\cdot8)\cdot2=9\cdot(8\cdot2)\)