Which of the following correctly demonstrates the Commutative Property of Addition?

Question

5+8=4+9
5 plus 8 equals 4 plus 9

0+5z9=5z9
0 plus 5 z superscript 9 baseline equals 5 z superscript 9 baseline

z9⋅5=5z9
z superscript 9 baseline times 5 equals 5 z superscript 9 baseline

5z9+8a=8a+5z9

Answer 1

The Commutative Property of Addition states that the order in which numbers are added does not affect the sum. In other words, for any two numbers \( a \) and \( b \), it holds that:

\[ a + b = b + a \]

Now, let's evaluate the options you've provided:

1. 5 + 8 = 4 + 9
   This statement is incorrect and does not demonstrate the Commutative Property.

2. 0 + 5z⁹ = 5z⁹
   This statement is an identity, but it does not demonstrate the Commutative Property.

3. z⁹ ⋅ 5 = 5z⁹
   This is a multiplication statement, not addition, so it does not demonstrate the Commutative Property of Addition.

4. 5z⁹ + 8a = 8a + 5z⁹
   This correctly demonstrates the Commutative Property of Addition because it shows that the order of addition does not change the sum.

Therefore, the option that correctly demonstrates the Commutative Property of Addition is:

5z⁹ + 8a = 8a + 5z⁹