Question

fill in the blanks. then, choose the property of multiplication you used.
(a) \\( 7 \times 9 = 9 \times 7 \\)
(b) \\( 0 \times 6 = 0 \\)
(c) \\( 1 \times 6 = 6 \\)
(d) \\( 4 \times (3 \times 8) = (4 \times 3) \times 8 \\)
options: associative property, commutative property, identity property, zero property

Explanation:

Step1: Analyze part (a)

The equation is \(7\times9 = 9\times7\). The Commutative Property of Multiplication states that \(a\times b = b\times a\) for any numbers \(a\) and \(b\). Here, \(a = 7\) and \(b = 9\), so this follows the Commutative Property.

Step2: Analyze part (b)

The equation is \(0\times6 = 0\). The Zero Property of Multiplication states that any number multiplied by 0 is 0, i.e., \(a\times0 = 0\) for any number \(a\). Here, \(a = 6\), so this follows the Zero Property.

Step3: Analyze part (c)

The equation is \(1\times6 = 6\). The Identity Property of Multiplication states that any number multiplied by 1 is the number itself, i.e., \(a\times1 = a\) for any number \(a\). Here, \(a = 6\), so this follows the Identity Property.

Step4: Analyze part (d)

The equation is \(4\times(3\times8)=(4\times3)\times8\). The Associative Property of Multiplication states that \((a\times b)\times c = a\times(b\times c)\) for any numbers \(a\), \(b\), and \(c\). Here, \(a = 4\), \(b = 3\), and \(c = 8\), so this follows the Associative Property.

Answer:

(a) Commutative Property
(b) Zero Property
(c) Identity Property
(d) Associative Property