Question

which equation demonstrates the additive identity property?

(7 + 9) - 7 = (7 - 7) + 9
(7 + 9) + 0 = 7 + 9
(7 + 9) = 7 + 9
(7 + 9) + (-7 - 9) = 0

Explanation:

⚡ Using what you learned: Zero and Identity in Operations

Step 1: Identify the property

The additive identity property states that adding \( 0 \) to any number keeps the number's identity unchanged:

$$ a + 0 = a $$

Step 2: Evaluate the options

Looking at the given choices:

1. \( (7 + 9) - 7 = (7 - 7) + 9 = 9 \) (Associative/Commutative properties)
2. \( (7 + 9) - 9 = 7 + 0 \) (Additive inverse property, where \( 9 - 9 = 0 \))
3. \( (7 + 9) \cdot 1 = 7 + 9 \) (Multiplicative identity property)
4. \( (7 + 9) \cdot 0 = 0 \) (Zero product property)

The equation that directly demonstrates the additive identity property is:

$$ (7 + 9) - 9 = 7 + 0 $$

This simplifies the left side to \( 7 \) and shows that it is equal to \( 7 + 0 \), demonstrating that adding \( 0 \) does not change the value.

Answer:

The second option:

$$ (7 + 9) - 9 = 7 + 0 $$