Properties of Real Numbers Worksheets - 15 Worksheets Library - Free Printable

To solve the problem, we need to identify the property of real numbers being used in each exercise. Here is the step-by-step solution:

List of Properties of Real Numbers

1. Commutative Property:
- Addition: \(a + b = b + a\)
- Multiplication: \(a \cdot b = b \cdot a\)

2. Associative Property:
- Addition: \((a + b) + c = a + (b + c)\)
- Multiplication: \((a \cdot b) \cdot c = a \cdot (b \cdot c)\)

3. Identity Property:
- Addition: \(a + 0 = a\)
- Multiplication: \(a \cdot 1 = a\)

4. Inverse Property:
- Addition: \(a + (-a) = 0\)
- Multiplication: \(a \cdot \frac{1}{a} = 1\) (for \(a \neq 0\))

5. Distributive Property:
- \(a(b + c) = ab + ac\)

6. Zero Property of Multiplication:
- \(a \cdot 0 = 0\)

7. Reflexive Property:
- \(a = a\)

8. Symmetric Property:
- If \(a = b\), then \(b = a\)

9. Transitive Property:
- If \(a = b\) and \(b = c\), then \(a = c\)

Solutions for Each Exercise

1. Exercise: \((a)(d) = (d)(a)\)
- Property: Commutative Property of Multiplication

2. Exercise: \((8+2)+4 = 8+(2+4)\)
- Property: Associative Property of Addition

3. Exercise: \(8(1) = 8\)
- Property: Identity Property of Multiplication

4. Exercise: \(42 - 6a = 6(7 - a)\)
- Property: Distributive Property

5. Exercise: \(f + 0 = f\)
- Property: Identity Property of Addition

6. Exercise: \(-14 + 14 = 0\)
- Property: Inverse Property of Addition

7. Exercise: \(3a + 2b = 2b + 3a\)
- Property: Commutative Property of Addition

8. Exercise: \(5(7c) = (5 \cdot 7)c\)
- Property: Associative Property of Multiplication

9. Exercise: \(36 + 48 + 14\)
- Property: Associative Property of Addition (though not explicitly shown as an equation, it implies grouping can be done in any order)

10. Exercise: \(xy + 0 = xy\)
- Property: Identity Property of Addition

11. Exercise: \(99 + 0 = 99\)
- Property: Identity Property of Addition

12. Exercise: \(4 + 5 + 6 = 6 + 4 + 5\)
- Property: Commutative Property of Addition

Final Answer

Here is the completed table:

| N° | Exercise | Property |
|----|-------------------------|------------------------------|
| 1 | \((a)(d) = (d)(a)\) | Commutative Property of Multiplication |
| 2 | \((8+2)+4 = 8+(2+4)\) | Associative Property of Addition |
| 3 | \(8(1) = 8\) | Identity Property of Multiplication |
| 4 | \(42 - 6a = 6(7 - a)\)| Distributive Property |
| 5 | \(f + 0 = f\) | Identity Property of Addition |
| 6 | \(-14 + 14 = 0\) | Inverse Property of Addition |
| 7 | \(3a + 2b = 2b + 3a\) | Commutative Property of Addition |
| 8 | \(5(7c) = (5 \cdot 7)c\)| Associative Property of Multiplication |
| 9 | \(36 + 48 + 14\) | Associative Property of Addition |
| 10 | \(xy + 0 = xy\) | Identity Property of Addition |
| 11 | \(99 + 0 = 99\) | Identity Property of Addition |
| 12 | \(4 + 5 + 6 = 6 + 4 + 5\)| Commutative Property of Addition |

Boxed Final Answer

\[
\boxed{
\begin{array}{|c|l|l|}
\hline
\text{N°} & \text{Exercise} & \text{Property} \\
\hline
1 & (a)(d) = (d)(a) & \text{Commutative Property of Multiplication} \\
2 & (8+2)+4 = 8+(2+4) & \text{Associative Property of Addition} \\
3 & 8(1) = 8 & \text{Identity Property of Multiplication} \\
4 & 42 - 6a = 6(7 - a) & \text{Distributive Property} \\
5 & f + 0 = f & \text{Identity Property of Addition} \\
6 & -14 + 14 = 0 & \text{Inverse Property of Addition} \\
7 & 3a + 2b = 2b + 3a & \text{Commutative Property of Addition} \\
8 & 5(7c) = (5 \cdot 7)c & \text{Associative Property of Multiplication} \\
9 & 36 + 48 + 14 & \text{Associative Property of Addition} \\
10 & xy + 0 = xy & \text{Identity Property of Addition} \\
11 & 99 + 0 = 99 & \text{Identity Property of Addition} \\
12 & 4 + 5 + 6 = 6 + 4 + 5 & \text{Commutative Property of Addition} \\
\hline
\end{array}
}
\]