Properties of Equality Notes worksheet for students to learn and fill in definitions and examples of algebraic properties.

Problem Overview:

The task is to fill in the blanks in the table that outlines the Properties of Equality. Each property has a definition and an example provided, and we need to complete the missing parts based on our understanding of these properties.

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Solution:

#### 1. Addition Property
- Definition: You can add a number to both sides of an equation.
- Example: \( x - 3 = 10 \)

#### 2. Subtraction Property
- Definition: You can subtract a number from both sides of an equation.
- Example: \( x + 4 = 6 \)

#### 3. Multiplication Property
- Definition: You can multiply both sides of an equation by the same number.
- Example: \( \frac{x}{2} = 5 \)

#### 4. Division Property
- Definition: You can divide both sides of an equation by the same number.
- Example: \( 3x = 12 \)

#### 5. Reflexive Property
- Definition: A number or variable equals itself.
- Example: \( 10 = 10 \), \( a = a \)

#### 6. Symmetric Property
- Definition: If \( a = b \), then \( b = a \).
- Example: \( x = 3 \) is the same as \( 3 = x \)

#### 7. Transitive Property
- Definition: If \( a = b \) and \( b = c \), then \( a = c \).
- Example: If \( x + 2 = 10 \) and \( 10 = y \), then \( x + 2 = y \)

#### 8. Substitution Property
- Definition: If \( a = b \), then you can substitute \( a \) with \( b \).
- Example: If \( a = b \) and \( a + c = d \), then \( b + c = d \)

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Completed Table:

| PROPERTY | DEFINITION | EXAMPLE |
|------------------------|---------------------------------------------------------------------------|--------------------------|
| Addition Property | You can add a number to both sides of an equation. | \( x - 3 = 10 \) |
| Subtraction Property | You can subtract a number from both sides of an equation. | \( x + 4 = 6 \) |
| Multiplication Property| You can multiply both sides of an equation by the same number. | \( \frac{x}{2} = 5 \) |
| Division Property | You can divide both sides of an equation by the same number. | \( 3x = 12 \) |
| Reflexive Property | A number or variable equals itself. | \( 10 = 10 \), \( a = a \)|
| Symmetric Property | If \( a = b \), then \( b = a \). | \( x = 3 \) is the same as \( 3 = x \) |
| Transitive Property | If \( a = b \) and \( b = c \), then \( a = c \). | If \( x + 2 = 10 \) and \( 10 = y \), then \( x + 2 = y \) |
| Substitution Property | If \( a = b \), then you can substitute \( a \) with \( b \). | If \( a = b \) and \( a + c = d \), then \( b + c = d \) |

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Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{PROPERTY} & \text{DEFINITION} & \text{EXAMPLE} \\
\hline
\text{Addition Property} & \text{You can add a number to both sides of an equation.} & x - 3 = 10 \\
\hline
\text{Subtraction Property} & \text{You can subtract a number from both sides of an equation.} & x + 4 = 6 \\
\hline
\text{Multiplication Property} & \text{You can multiply both sides of an equation by the same number.} & \frac{x}{2} = 5 \\
\hline
\text{Division Property} & \text{You can divide both sides of an equation by the same number.} & 3x = 12 \\
\hline
\text{Reflexive Property} & \text{A number or variable equals itself.} & 10 = 10, \, a = a \\
\hline
\text{Symmetric Property} & \text{If } a = b, \text{ then } b = a. & x = 3 \text{ is the same as } 3 = x \\
\hline
\text{Transitive Property} & \text{If } a = b \text{ and } b = c, \text{ then } a = c. & \text{If } x + 2 = 10 \text{ and } 10 = y, \text{ then } x + 2 = y \\
\hline
\text{Substitution Property} & \text{If } a = b, \text{ then you can substitute } a \text{ with } b. & \text{If } a = b \text{ and } a + c = d, \text{ then } b + c = d \\
\hline
\end{array}
}
\]