Question

which equation demonstrates the additive identity property?

a. (7 + 0 = 7)
b. (7 + (-7) = 0)
c. ((7 + 6) + 3 = 7 + (6 + 3))
d. (7 + 6 = 6 + 7)

Explanation:

🆕 New Concept Discovered: Properties of Real Numbers
Rules governing addition and multiplication operations

Step 1: Understand the Additive Identity Property

The additive identity property states that adding zero to any real number does not change its value. In general terms:

$$ a + 0 = a $$

or

$$ 0 + a = a $$

Step 2: Analyze the Options

Let's look at the mathematical statements presented in the image:

1. First Option: \( (7 + 6) + 2 = 7 + (6 + 2) \)

• This demonstrates the associative property of addition (grouping of numbers does not change the sum).

1. Second Option: \( 7 + 0 = 7 \)

• This shows that adding \( 0 \) to \( 7 \) keeps the identity of \( 7 \) unchanged. This is the additive identity property.

1. Third Option: \( 7 + (-7) = 0 \)

• This demonstrates the additive inverse property (adding a number and its opposite results in \( 0 \)).

1. Fourth Option: \( 7 + 6 = 6 + 7 \)

• This demonstrates the commutative property of addition (order of numbers does not change the sum).

Answer:

The equation that demonstrates the additive identity property is:

$$ 7 + 0 = 7 $$