Questions: (a) Write the commutative property of multiplication using the variables m and n. mn = nm (b) Write the associative property of multiplication using the variables x, y, and z. (xy)z = x(yz)

Solution Steps

To solve the given problem, we need to identify and write the properties of multiplication using the provided variables. Specifically, we need to:

1. Write the commutative property of multiplication using the variables \( m \) and \( n \).
2. Write the associative property of multiplication using the variables \( x \), \( y \), and \( z \).

1. Commutative Property of Multiplication: This property states that the order of multiplication does not affect the result. For variables \( m \) and \( n \), it can be written as \( m \cdot n = n \cdot m \).
2. Associative Property of Multiplication: This property states that the way in which factors are grouped in multiplication does not affect the result. For variables \( x \), \( y \), and \( z \), it can be written as \( (x \cdot y) \cdot z = x \cdot (y \cdot z) \).

The commutative property of multiplication states that for any two numbers \( m \) and \( n \), the equation \( m \cdot n = n \cdot m \) holds true. Given \( m = 5 \) and \( n = 3 \):

\[ 5 \cdot 3 = 3 \cdot 5 \]

Both sides of the equation equal 15, confirming the commutative property.

The associative property of multiplication states that for any three numbers \( x \), \( y \), and \( z \), the equation \( (x \cdot y) \cdot z = x \cdot (y \cdot z) \) holds true. Given \( x = 2 \), \( y = 4 \), and \( z = 6 \):

\[ (2 \cdot 4) \cdot 6 = 2 \cdot (4 \cdot 6) \]

Calculating both sides:

\[ (8) \cdot 6 = 2 \cdot (24) \]

Both sides of the equation equal 48, confirming the associative property.

Final Answer