Question

choose the property of addition that justifies the equation.
2 + (a + 5) = (2 + a) + 5 select
0 + b = b select
(4 + y) + 3 = 3 + (4 + y) select

Explanation:

Step1: Analyze \( 2 + (a + 5) = (2 + a) + 5 \)

The associative property of addition states that \( (x + y) + z = x + (y + z) \) (or vice - versa). Here, we are regrouping the addends \( 2\), \(a\), and \(5\). So this equation is justified by the associative property of addition.

Step2: Analyze \( 0 + b = b \)

The identity property of addition states that the sum of any number and \(0\) is the number itself, i.e., \(x+0 = x\) (or \(0 + x=x\)). In the equation \(0 + b=b\), we are adding \(0\) to \(b\) and getting \(b\) back. So this is justified by the identity property of addition.

Step3: Analyze \( (4 + y)+3 = 3+(4 + y) \)

The commutative property of addition states that \(x + y=y + x\) (or for more than two terms, the order of addition can be changed). Here, we are changing the order of \((4 + y)\) and \(3\) in the addition. So this equation is justified by the commutative property of addition.

Answer:

• For \( 2+(a + 5)=(2 + a)+5 \): Associative Property of Addition
• For \( 0 + b=b \): Identity Property of Addition
• For \( (4 + y)+3 = 3+(4 + y) \): Commutative Property of Addition