Question

choose the property of real numbers that justifies the equation.

$(8 + b) + 2 = 8 + (b + 2)$	select
$3 \cdot 1 = 3$	select
$d \cdot 4 = 4 \cdot d$	select
$0 \cdot 6 = 0$	select

Explanation:

For \((8 + b) + 2 = 8 + (b + 2)\)

Step1: Identify the operation and change

The equation involves addition, and the grouping of the addends is changed.

Step2: Recall properties of addition

The Associative Property of Addition states that for any real numbers \(a\), \(b\), and \(c\), \((a + b)+c=a+(b + c)\). Here, \(a = 8\), \(b=b\), and \(c = 2\), so the property is the Associative Property of Addition.

For \(3\cdot1=3\)

Step1: Identify the operation and result

The equation involves multiplication, and multiplying 3 by 1 gives 3.

Step2: Recall properties of multiplication

The Multiplicative Identity Property states that for any real number \(a\), \(a\times1=a\). Here, \(a = 3\), so the property is the Multiplicative Identity Property.

For \(d\cdot4 = 4\cdot d\)

Step1: Identify the operation and change

The equation involves multiplication, and the order of the factors \(d\) and \(4\) is changed.

Step2: Recall properties of multiplication

The Commutative Property of Multiplication states that for any real numbers \(a\) and \(b\), \(a\times b=b\times a\). Here, \(a = d\) and \(b = 4\), so the property is the Commutative Property of Multiplication.

For \(0\cdot6=0\)

Answer:

s:

• \((8 + b) + 2 = 8 + (b + 2)\): Associative Property of Addition
• \(3\cdot1 = 3\): Multiplicative Identity Property
• \(d\cdot4 = 4\cdot d\): Commutative Property of Multiplication
• \(0\cdot6 = 0\): Multiplicative Property of Zero