Properties of Real Numbers worksheet for identifying mathematical properties in equations.

The task involves identifying the properties of real numbers used in each given exercise. Below is the solution with explanations for each exercise:

List of Properties of Real Numbers

1. Commutative Property of Addition: $a + b = b + a$
2. Commutative Property of Multiplication: $a \cdot b = b \cdot a$
3. Associative Property of Addition: $(a + b) + c = a + (b + c)$
4. Associative Property of Multiplication: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$
5. Identity Property of Addition: $a + 0 = a$ (0 is the additive identity)
6. Identity Property of Multiplication: $a \cdot 1 = a$ (1 is the multiplicative identity)
7. Inverse Property of Addition: $a + (-a) = 0$
8. Inverse Property of Multiplication: $a \cdot \frac{1}{a} = 1$ (for $a \neq 0$)
9. Distributive Property: $a(b + c) = ab + ac$
10. Zero Property of Multiplication: $a \cdot 0 = 0$

Solutions to Each Exercise

1. Exercise: $(4 + 3) + 1 = 4 + (3 + 1)$
Property: Associative Property of Addition

2. Exercise: $xy + 0 = xy$
Property: Identity Property of Addition

3. Exercise: $8 \cdot 1 = 8$
Property: Identity Property of Multiplication

4. Exercise: $-3 + 3 = 0$
Property: Inverse Property of Addition

5. Exercise: $-9 \cdot 0 = 0$
Property: Zero Property of Multiplication

6. Exercise: $15 \cdot 0 = 0$
Property: Zero Property of Multiplication

7. Exercise: $99 + 0 = 99$
Property: Identity Property of Addition

8. Exercise: $8 \cdot 11 = 11 \cdot 8$
Property: Commutative Property of Multiplication

9. Exercise: $(2 + 5) + 3 = 2 + (5 + 3)$
Property: Associative Property of Addition

10. Exercise: $3 \cdot 9 = 9 \cdot 3$
Property: Commutative Property of Multiplication

11. Exercise: $4 + 5 + 6 = 6 + 4 + 5$
Property: Commutative Property of Addition

12. Exercise: $a(0) = 0$
Property: Zero Property of Multiplication

Final Answer

\[
\boxed{
\begin{array}{|c|l|l|}
\hline
\text{N°} & \text{Exercise} & \text{Property} \\
\hline
1 & (4 + 3) + 1 = 4 + (3 + 1) & \text{Associative Property of Addition} \\
2 & xy + 0 = xy & \text{Identity Property of Addition} \\
3 & 8 \cdot 1 = 8 & \text{Identity Property of Multiplication} \\
4 & -3 + 3 = 0 & \text{Inverse Property of Addition} \\
5 & -9 \cdot 0 = 0 & \text{Zero Property of Multiplication} \\
6 & 15 \cdot 0 = 0 & \text{Zero Property of Multiplication} \\
7 & 99 + 0 = 99 & \text{Identity Property of Addition} \\
8 & 8 \cdot 11 = 11 \cdot 8 & \text{Commutative Property of Multiplication} \\
9 & (2 + 5) + 3 = 2 + (5 + 3) & \text{Associative Property of Addition} \\
10 & 3 \cdot 9 = 9 \cdot 3 & \text{Commutative Property of Multiplication} \\
11 & 4 + 5 + 6 = 6 + 4 + 5 & \text{Commutative Property of Addition} \\
12 & a(0) = 0 & \text{Zero Property of Multiplication} \\
\hline
\end{array}
}
\]