Question

complete the expressions and select the missing properties. write each answer as a number, a variable, or the product of a number and a variable. 8(w·9) = 8(9·□) = (8·□)w = □w multiply

Explanation:

Step1: Apply Commutative Property of Multiplication

The commutative property of multiplication states that \(a \cdot b = b \cdot a\). So for \(8(w \cdot 9)\), we can rewrite \(w \cdot 9\) as \(9 \cdot w\). So the first blank is \(w\), and the property is the Commutative Property of Multiplication.
\[8(w \cdot 9)=8(9 \cdot w)\]

Step2: Apply Associative Property of Multiplication

The associative property of multiplication states that \((a \cdot b) \cdot c = a \cdot (b \cdot c)\). Here, we can group \(8\) and \(9\) together. So \(8(9 \cdot w)=(8 \cdot 9)w\). The second blank is \(9\), and the property is the Associative Property of Multiplication.
\[8(9 \cdot w)=(8 \cdot 9)w\]

Step3: Multiply 8 and 9

Calculate \(8 \cdot 9 = 72\). So the third blank is \(72\).
\[(8 \cdot 9)w = 72w\]

Answer:

First blank: \(w\) (Property: Commutative Property of Multiplication)
Second blank: \(9\) (Property: Associative Property of Multiplication)
Third blank: \(72\)