Question

which property of multiplication is shown?
(9 × 1) × 3 = 9 × (1 × 3)
identity zero commutative associative
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Explanation:

To determine the property, we analyze each option:

• Identity Property: States that \(a\times1 = a\) or \(1\times a = a\). The given equation doesn't show this (it's about grouping, not multiplying by 1 to keep the number the same).
• Zero Property: States that \(a\times0 = 0\) or \(0\times a = 0\). The equation has no zero, so this is not it.
• Commutative Property: States that \(a\times b = b\times a\) (order of multiplication changes, but product remains same). The given equation doesn't change the order of 9, 1, 3; it changes the grouping.
• Associative Property: States that \((a\times b)\times c = a\times(b\times c)\). In the equation \((9\times1)\times3 = 9\times(1\times3)\), we can see that the grouping of the factors (which two we multiply first) is changed, but the product remains the same. This matches the associative property of multiplication.

Answer:

associative