Properties of Numbers & Equality Notes and Worksheets - Lindsay Bowden - Free Printable

Problem Analysis:

The task involves filling in the blanks in a table about the Properties of Numbers. Each row describes a property, its definition, and an example. The goal is to complete the missing information in the "DEFINITION" and "EXAMPLE" columns.

Solution:

#### 1. Commutative Property
- Definition: When adding or multiplying, the order does not matter.
- Example:
- \( 2 + 3 = 5 \)
- \( 3 + 2 = 5 \)
- \( 4 \cdot 5 = 20 \)
- \( 5 \cdot 4 = 20 \)

#### 2. Associative Property
- Definition: When adding or multiplying, it doesn’t matter how the numbers are grouped.
- Example:
- \( 3 + (2 + 1) = 6 \)
- \( (3 + 2) + 1 = 6 \)
- \( 2 \cdot (4 \cdot 6) = 48 \)
- \( (2 \cdot 4) \cdot 6 = 48 \)

#### 3. Distributive Property
- Definition: When multiplying by a sum, you can multiply each term separately and add.
- Example:
- \( 3(2 + 4) = 3 \cdot 2 + 3 \cdot 4 = 6 + 12 = 18 \)

#### 4. Identity Property
- Definition:
- The sum of any number and zero is that number.
- The product of any number and one is that number.
- Example:
- \( 4 + 0 = 4 \)
- \( 8 \cdot 1 = 8 \)

#### 5. Inverse Property
- Definition:
- Additive Inverse: The sum of any number and the negative of that number is zero.
- Multiplicative Inverse: The product of any number and its reciprocal is one.
- Example:
- \( 7 + (-7) = 0 \)
- \( 3 \cdot \frac{1}{3} = 1 \)

Final Completed Table:

| PROPERTY | DEFINITION | EXAMPLE |
|------------------------|---------------------------------------------------------------------------|-------------------------------------------------------------------------|
| Commutative Property | When adding or multiplying, the order does not matter. | \( 2 + 3 = 5 \)<br> \( 3 + 2 = 5 \)<br> \( 4 \cdot 5 = 20 \)<br> \( 5 \cdot 4 = 20 \) |
| Associative Property | When adding or multiplying, it doesn’t matter how the numbers are grouped. | \( 3 + (2 + 1) = 6 \)<br> \( (3 + 2) + 1 = 6 \)<br> \( 2 \cdot (4 \cdot 6) = 48 \)<br> \( (2 \cdot 4) \cdot 6 = 48 \) |
| Distributive Property | When multiplying by a sum, you can multiply each term separately and add. | \( 3(2 + 4) = 3 \cdot 2 + 3 \cdot 4 = 6 + 12 = 18 \) |
| Identity Property | The sum of any number and zero is that number.<br>The product of any number and one is that number. | \( 4 + 0 = 4 \)<br> \( 8 \cdot 1 = 8 \) |
| Inverse Property | Additive Inverse: The sum of any number and the negative of that number is zero.<br>Multiplicative Inverse: The product of any number and its reciprocal is one. | \( 7 + (-7) = 0 \)<br> \( 3 \cdot \frac{1}{3} = 1 \) |

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{PROPERTY} & \text{DEFINITION} & \text{EXAMPLE} \\
\hline
\text{Commutative Property} & \text{When adding or multiplying, the order does not matter.} & 2 + 3 = 5, \, 3 + 2 = 5, \, 4 \cdot 5 = 20, \, 5 \cdot 4 = 20 \\
\hline
\text{Associative Property} & \text{When adding or multiplying, it doesn’t matter how the numbers are grouped.} & 3 + (2 + 1) = 6, \, (3 + 2) + 1 = 6, \, 2 \cdot (4 \cdot 6) = 48, \, (2 \cdot 4) \cdot 6 = 48 \\
\hline
\text{Distributive Property} & \text{When multiplying by a sum, you can multiply each term separately and add.} & 3(2 + 4) = 3 \cdot 2 + 3 \cdot 4 = 6 + 12 = 18 \\
\hline
\text{Identity Property} & \text{The sum of any number and zero is that number. The product of any number and one is that number.} & 4 + 0 = 4, \, 8 \cdot 1 = 8 \\
\hline
\text{Inverse Property} & \text{Additive Inverse: The sum of any number and the negative of that number is zero. Multiplicative Inverse: The product of any number and its reciprocal is one.} & 7 + (-7) = 0, \, 3 \cdot \frac{1}{3} = 1 \\
\hline
\end{array}
}
\]