Question

choose the property of real numbers that justifies the equation.

$1 \cdot a = a$	select
$-m + m = 0$	select
$5 \cdot (7 \cdot c) = (5 \cdot 7) \cdot c$	select

Explanation:

For the equation \( 1 \cdot a = a \)

Step1: Recall Identity Property of Multiplication

The Identity Property of Multiplication states that the product of any real number and 1 is the number itself, i.e., \( 1 \cdot x = x \) for any real number \( x \). Here, \( x = a \), so \( 1 \cdot a = a \) is justified by the Identity Property of Multiplication.

For the equation \( (8 + d) \cdot 4 = 8 \cdot 4 + d \cdot 4 \)

Step1: Recall Distributive Property

The Distributive Property states that for real numbers \( a \), \( b \), and \( c \), \( a \cdot (b + c)=a \cdot b + a \cdot c \) (or \( (b + c)\cdot a = b\cdot a + c\cdot a \)). Here, \( a = 4 \), \( b = 8 \), \( c = d \), so \( (8 + d)\cdot 4 = 8\cdot 4 + d\cdot 4 \) is justified by the Distributive Property.

For the equation \( -m + m = 0 \)

Step1: Recall Inverse Property of Addition

The Inverse Property of Addition states that for any real number \( x \), there exists an additive inverse \( -x \) such that \( x + (-x)=0 \) (or \( -x + x = 0 \)). Here, \( x = m \), so \( -m + m = 0 \) is justified by the Inverse Property of Addition.

For the equation \( 5 \cdot (7 \cdot c)=(5 \cdot 7) \cdot c \)

Answer:

Step1: Recall Associative Property of Multiplication

The Associative Property of Multiplication states that for real numbers \( a \), \( b \), and \( c \), \( (a \cdot b)\cdot c=a \cdot (b \cdot c) \). Here, \( a = 5 \), \( b = 7 \), \( c = c \), so \( 5 \cdot (7 \cdot c)=(5 \cdot 7) \cdot c \) is justified by the Associative Property of Multiplication.

Final Answers for Each Equation:

• \( 1 \cdot a = a \): Identity Property of Multiplication
• \( (8 + d) \cdot 4 = 8 \cdot 4 + d \cdot 4 \): Distributive Property
• \( -m + m = 0 \): Inverse Property of Addition
• \( 5 \cdot (7 \cdot c)=(5 \cdot 7) \cdot c \): Associative Property of Multiplication