Question

choose the property of addition that justifies the equation.
7 + 5 = 5 + 7 \tselect

y = y + 0 \tselect

• a + a = 0 \tselect

Explanation:

Step1: Analyze \( 7 + 5 = 5 + 7 \)

The Commutative Property of Addition states that \( a + b = b + a \). Here, swapping 7 and 5 doesn't change the sum, so this uses the Commutative Property of Addition.

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

The Identity Property of Addition (or Additive Identity Property) states that adding 0 to a number (or variable) leaves it unchanged, i.e., \( a + 0 = a \) (or \( y + 0 = y \) here). So this uses the Identity Property of Addition.

Step3: Analyze \( -a + a = 0 \)

The Inverse Property of Addition states that the sum of a number and its additive inverse is 0. The additive inverse of \( a \) is \( -a \), so \( a + (-a)=0 \) (or \( -a + a = 0 \) here), which uses the Inverse Property of Addition.

Answer:

• For \( 7 + 5 = 5 + 7 \): Commutative Property of Addition
• For \( y = y + 0 \): Identity Property of Addition (Additive Identity)
• For \( -a + a = 0 \): Inverse Property of Addition (Additive Inverse)