Question

Which of the following correctly demonstrates the Commutative Property of Addition?(1 point) Responses 0+5z9=5z90+5z9=5z9 0 plus 5 z superscript 9 baseline equals 5 z superscript 9 baseline 5z9+8a=8a+5z95z9+8a=8a+5z9 5 z superscript 9 baseline plus 8 a equals 8 a plus 5 z superscript 9 baseline 5+8=4+95+8=4+9 5 plus 8 equals 4 plus 9 z9⋅5=5z9

Answer 1

The Commutative Property of Addition states that changing the order of the addends does not change the sum. In other words, for any numbers \(a\) and \(b\), \(a + b = b + a\).

Let's analyze the options provided:

1. \(0 + 5z^9 = 5z^9 + 0\)
2. \(5z^9 + 8a = 8a + 5z^9\)
3. \(5 + 8 = 4 + 9\)
4. \(z^9 \cdot 5 = 5z^9\)

The first two options correctly demonstrate the Commutative Property of Addition:

• The first option shows that \(0 + 5z^9\) equals \(5z^9 + 0\).
• The second option shows that \(5z^9 + 8a\) equals \(8a + 5z^9\).

The third option is incorrect for demonstrating the Commutative Property since it is an equation that is not true. The fourth option demonstrates multiplication, not addition.

Thus, the correct responses demonstrating the Commutative Property of Addition are:

1. \(0 + 5z^9 = 5z^9 + 0\)
2. \(5z^9 + 8a = 8a + 5z^9\)