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\begin{tabular}{|c|c|c|}
\hline
\multicolumn{3}{|c|}{Properties of Real Numbers} \\
\hline
Property & Addition Example & Multiplication Example \\
\hline
\multicolumn{3}{|l|}{Commutative} \\
\hline
\multicolumn{3}{|l|}{Associative} \\
\hline
\multicolumn{3}{|l|}{Identity} \\
\hline
\multicolumn{3}{|l|}{Inverse} \\
\hline
Distributive & & \\
\hline
\end{tabular}

Name that Property!

13. [tex]$5 \cdot(2 \cdot 8)=(5 \cdot 2) \cdot 8$[/tex]

14. [tex]$6(3-7)=6 \cdot 3-6 \cdot 7$[/tex]

15. [tex][tex]$7y+(-7y)=0$[/tex][/tex]

16. [tex]$3a+2b=2b+3a$[/tex]

17. [tex]$\left(x^2+8x\right)+1=x^2+(8x+1)$[/tex]

18. [tex][tex]$\frac{1}{5} \cdot 5=1$[/tex][/tex]

19. [tex]$3m+3n=3(m+n)$[/tex]

20. [tex]$9c+0=9c$[/tex]



Answer :

GinnyAnswer
Let's identify each property of real numbers based on the given expressions.

1. Statement: [tex]\(5 \cdot(2 \cdot 8)=(5 \cdot 2) \cdot 8\)[/tex]
- Property: Associative Property of Multiplication
- This property states that the way in which numbers are grouped in multiplication does not change their product.

2. Statement: [tex]\(6(3-7)=6 \cdot 3-6 \cdot 7\)[/tex]
- Property: Distributive Property
- This property allows us to multiply a single term across a sum or difference inside parentheses.

3. Statement: [tex]\(7y+(-7y)=0\)[/tex]
- Property: Inverse Property of Addition
- This property states that every number has an additive inverse (opposite) that sums to zero.

4. Statement: [tex]\(3a + 2b = 2b + 3a\)[/tex]
- Property: Commutative Property of Addition
- This property states that the order of addition does not affect the sum.

5. Statement: [tex]\((x^2 + 8x) + 1 = x^2 + (8x + 1)\)[/tex]
- Property: Associative Property of Addition
- This property states that the way in which numbers are grouped in addition does not change their sum.

6. Statement: [tex]\(\frac{1}{5} \cdot 5 = 1\)[/tex]
- Property: Identity Property of Multiplication
- This property states that any number multiplied by 1 remains the same.

7. Statement: [tex]\(3m + 3n = 3(m + n)\)[/tex]
- Property: Distributive Property
- This property allows us to factor out a common factor from the terms in addition.

8. Statement: [tex]\(9c + 0 = 9c\)[/tex]
- Property: Identity Property of Addition
- This property states that any number added to zero remains the same.

Summarized, the properties corresponding to the problems are:

- 13: Associative Property of Multiplication
- 14: Distributive Property
- 15: Inverse Property of Addition
- 16: Commutative Property of Addition
- 17: Associative Property of Addition
- 18: Identity Property of Multiplication
- 19: Distributive Property
- 20: Identity Property of Addition

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