To determine which expressions demonstrate the commutative property, we need to recall that the commutative property allows us to change the order of the numbers in addition or multiplication without changing the result. Here is a step-by-step verification of each expression:
1. [tex]\(13 + 2 + 9 = 2 + 13 + 9\)[/tex]:
- By applying the commutative property of addition, we can rearrange the terms:
[tex]\( (13 + 2) + 9 = 13 + (2 + 9) \)[/tex]
which can be reordered as:
[tex]\( 2 + 13 + 9 \)[/tex].
This expression demonstrates the commutative property as we can reorder the numbers in addition.
2. [tex]\(8 + 0 = 8\)[/tex]:
- This expression simply shows that adding zero to a number does not change the number. It demonstrates the identity property of addition rather than the commutative property.
3. [tex]\(9(8 + 45) = 9(8) + 9(45)\)[/tex]:
- This expression demonstrates the distributive property of multiplication over addition, not the commutative property.
4. [tex]\([29(14)] + 45 = [14(29)] + 45\)[/tex]:
- On the left side, 29 is multiplied by 14, and on the right side, 14 is multiplied by 29. This shows multiplication is commutative. However, the additional operation involving 45 complicates it, and the entire expression does not straightforwardly showcase the commutative property in a clear manner that matches definition given in the simple context required.
5. [tex]\(29(14 + 45) = 14(29) + 45\)[/tex]:
- This expression does not demonstrate the commutative property. It mixes distribution and addition in a single step, neither displaying a direct commutative swap in a straightforward or pure form.
Based on the provided step-by-step analysis, the only expression that fully exemplifies the commutative property is:
[tex]\[ 13 + 2 + 9 = 2 + 13 + 9 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
