Math Monks Properties of Addition Worksheet with examples and practice problems for commutative, associative, identity, and inverse properties.

Problem Analysis:

The worksheet focuses on the properties of addition. These properties include:
1. Commutative Property: The order of numbers can be changed without affecting the sum.
- \( a + b = b + a \)
2. Associative Property: The grouping of numbers can be changed without affecting the sum.
- \( (a + b) + c = a + (b + c) \)
3. Identity Property: Adding zero to any number leaves the number unchanged.
- \( a + 0 = a \)
4. Inverse Property: Adding a number to its additive inverse results in zero.
- \( a + (-a) = 0 \)

We will solve the problems step by step.

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Part A: Identify the property of additions for each.

#### 1. \( 7 + 3 = 3 + 7 \)
- Here, the order of the numbers \( 7 \) and \( 3 \) is switched, but the sum remains the same.
- This demonstrates the Commutative Property.
- Answer: Commutative Property

#### 2. \( 8 + (-8) = 0 \)
- Here, a number \( 8 \) is added to its additive inverse \( -8 \), resulting in zero.
- This demonstrates the Inverse Property.
- Answer: Inverse Property

#### 3. \( 4 + 0 = 4 \)
- Here, zero is added to the number \( 4 \), and the sum remains \( 4 \).
- This demonstrates the Identity Property.
- Answer: Identity Property

#### 4. \( (9 + 3) + 6 = 9 + (3 + 6) \)
- Here, the grouping of the numbers is changed, but the sum remains the same.
- This demonstrates the Associative Property.
- Answer: Associative Property

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Part B: Write the answers and the addition properties for the following.

#### 1. \( 9 + 0 = \)
- Adding zero to any number leaves the number unchanged (Identity Property).
- Answer: \( 9 \) (Identity Property)

#### 2. \( 3 + 12 = \)
- This is a straightforward addition problem.
- Answer: \( 15 \) (No specific property highlighted here, but it involves basic addition.)

#### 3. \( 0 + 13 = \)
- Adding zero to any number leaves the number unchanged (Identity Property).
- Answer: \( 13 \) (Identity Property)

#### 4. \( 18 + 3 = \)
- This is a straightforward addition problem.
- Answer: \( 21 \) (No specific property highlighted here, but it involves basic addition.)

#### 5. \( 10 + (-10) = \)
- Adding a number to its additive inverse results in zero (Inverse Property).
- Answer: \( 0 \) (Inverse Property)

#### 6. \( (15 + 2) + 1 = \)
- First, add \( 15 + 2 = 17 \).
- Then, add \( 17 + 1 = 18 \).
- This demonstrates the Associative Property because the grouping of numbers can be changed without affecting the sum.
- Answer: \( 18 \) (Associative Property)

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Final Answers:

Part A:
1. Commutative Property
2. Inverse Property
3. Identity Property
4. Associative Property

Part B:
1. \( 9 \) (Identity Property)
2. \( 15 \)
3. \( 13 \) (Identity Property)
4. \( 21 \)
5. \( 0 \) (Inverse Property)
6. \( 18 \) (Associative Property)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part A:} \\
1. \text{Commutative Property} \\
2. \text{Inverse Property} \\
3. \text{Identity Property} \\
4. \text{Associative Property} \\
\\
\text{Part B:} \\
1. 9 \text{ (Identity Property)} \\
2. 15 \\
3. 13 \text{ (Identity Property)} \\
4. 21 \\
5. 0 \text{ (Inverse Property)} \\
6. 18 \text{ (Associative Property)}
\end{array}
}
\]