Addition Properties worksheet with examples and exercises for identifying properties and solving equations.

Problem Analysis:

The worksheet focuses on identifying and applying the properties of addition. The properties mentioned are:

1. Commutative Property of Addition: The order of numbers being added does not affect the sum.
- Example: \( 3 + 5 = 5 + 3 \)

2. Associative Property of Addition: The grouping of numbers being added does not affect the sum.
- Example: \( (2 + 3) + 4 = 2 + (3 + 4) \)

3. Identity Property of Addition: Adding zero to any number leaves the number unchanged.
- Example: \( 7 + 0 = 7 \)

We need to solve each problem, find the value of the variables, and identify which property is used.

---

Problem 1:

\[
6 + 3 + 7 = a
\]
\[
3 + 6 + b = 18
\]

#### Step 1: Solve for \( a \)
\[
6 + 3 + 7 = a
\]
\[
9 + 7 = a
\]
\[
a = 16
\]

#### Step 2: Solve for \( b \)
\[
3 + 6 + b = 18
\]
\[
9 + b = 18
\]
\[
b = 18 - 9
\]
\[
b = 9
\]

#### Step 3: Identify the property
The first equation (\( 6 + 3 + 7 = a \)) demonstrates the Associative Property of Addition because the numbers are grouped differently but yield the same result.

#### Final Answer for Problem 1:
\[
a = 16, \quad b = 9, \quad \text{property: Associative Property of Addition}
\]

---

Problem 2:

\[
10 + [10 + 5] = c
\]
\[
[10 + 10] + 5 = d
\]

#### Step 1: Solve for \( c \)
\[
10 + [10 + 5] = c
\]
\[
10 + 15 = c
\]
\[
c = 25
\]

#### Step 2: Solve for \( d \)
\[
[10 + 10] + 5 = d
\]
\[
20 + 5 = d
\]
\[
d = 25
\]

#### Step 3: Identify the property
Both equations demonstrate the Associative Property of Addition because the grouping of numbers being added does not affect the sum.

#### Final Answer for Problem 2:
\[
c = 25, \quad d = 25, \quad \text{property: Associative Property of Addition}
\]

---

Problem 3:

\[
(12 + e) + 7 = 21
\]
\[
12 + (e + 7) = f
\]

#### Step 1: Solve for \( e \)
From the first equation:
\[
(12 + e) + 7 = 21
\]
\[
12 + e + 7 = 21
\]
\[
19 + e = 21
\]
\[
e = 21 - 19
\]
\[
e = 2
\]

#### Step 2: Solve for \( f \)
Using the value of \( e \):
\[
f = 12 + (e + 7)
\]
\[
f = 12 + (2 + 7)
\]
\[
f = 12 + 9
\]
\[
f = 21
\]

#### Step 3: Identify the property
The equations demonstrate the Associative Property of Addition because the grouping of numbers being added does not affect the sum.

#### Final Answer for Problem 3:
\[
e = 2, \quad f = 21, \quad \text{property: Associative Property of Addition}
\]

---

Problem 4:

\[
102 + g = 102
\]
\[
h + 0 = 102
\]

#### Step 1: Solve for \( g \)
\[
102 + g = 102
\]
\[
g = 102 - 102
\]
\[
g = 0
\]

#### Step 2: Solve for \( h \)
\[
h + 0 = 102
\]
\[
h = 102
\]

#### Step 3: Identify the property
Both equations demonstrate the Identity Property of Addition because adding zero to any number leaves the number unchanged.

#### Final Answer for Problem 4:
\[
g = 0, \quad h = 102, \quad \text{property: Identity Property of Addition}
\]

---

Final Answers:

1. \( a = 16, \, b = 9, \, \text{property: Associative Property of Addition} \)
2. \( c = 25, \, d = 25, \, \text{property: Associative Property of Addition} \)
3. \( e = 2, \, f = 21, \, \text{property: Associative Property of Addition} \)
4. \( g = 0, \, h = 102, \, \text{property: Identity Property of Addition} \)

\boxed{
\begin{aligned}
1. & \, a = 16, \, b = 9, \, \text{property: Associative Property of Addition} \\
2. & \, c = 25, \, d = 25, \, \text{property: Associative Property of Addition} \\
3. & \, e = 2, \, f = 21, \, \text{property: Associative Property of Addition} \\
4. & \, g = 0, \, h = 102, \, \text{property: Identity Property of Addition}
\end{aligned}
}