Question

complete the statement below.
illustrates the commutative property of
the expression
multiplication.
11 × w × 3 = 11 × 3 × w
11 × w × 3 = 11 × w × 3
(11 × w) × 3 = 11 × (w × 3)
11 × (w × 3) = (11 × w) + (11 × 3)

Explanation:

Step1: Recall Commutative Property of Multiplication

The commutative property of multiplication states that for any numbers \(a\), \(b\), and \(c\), \(a\times b\times c=a\times c\times b = b\times a\times c=\dots\), i.e., the order of multiplying factors can be changed without changing the product.

Step2: Analyze Each Option

• For \(11\times w\times 3 = 11\times 3\times w\): Here, we have changed the order of \(w\) and \(3\) (the factors being multiplied), which is exactly the commutative property of multiplication.
• The second option \(11\times w\times 3=11\times w\times 3\) is just an identity, not showing the commutative property.
• The third option \((11\times w)\times 3 = 11\times(w\times 3)\) is the associative property of multiplication (grouping of factors is changed, not the order).
• The fourth option \(11\times(w\times 3)=(11\times w)+(11\times 3)\) is incorrect as it misapplies the distributive property (and the right - hand side is a sum, not a product).

Answer:

\(11\times w\times 3 = 11\times 3\times w\)