Addition Worksheets: Associative, Commutative Properties - Free Printable

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: \( 7 + 0 = 7 \)

The task is to solve for the variables in each problem and identify which property is used.

---

Solution:

#### Problem 1:
\[
6 + 3 + a = b
\]
\[
3 + 6 + b = 18
\]

- Step 1: Solve for \( b \) using the second equation.
\[
3 + 6 + b = 18
\]
Simplify:
\[
9 + b = 18
\]
Subtract 9 from both sides:
\[
b = 9
\]

- Step 2: Substitute \( b = 9 \) into the first equation to solve for \( a \).
\[
6 + 3 + a = 9
\]
Simplify:
\[
9 + a = 9
\]
Subtract 9 from both sides:
\[
a = 0
\]

- Step 3: Identify the property used.
- The equations show that the order of addition does not matter, which is the Commutative Property of Addition.

- Final Answer for Problem 1:
\[
a = 0, \quad b = 9, \quad \text{property: Commutative Property of Addition}
\]

---

#### Problem 2:
\[
10 + [10 + 5] = c
\]
\[
[10 + 10] + 5 = d
\]

- Step 1: Solve for \( c \) using the first equation.
\[
10 + [10 + 5] = c
\]
Simplify inside the brackets:
\[
10 + 15 = c
\]
Add:
\[
c = 25
\]

- Step 2: Solve for \( d \) using the second equation.
\[
[10 + 10] + 5 = d
\]
Simplify inside the brackets:
\[
20 + 5 = d
\]
Add:
\[
d = 25
\]

- Step 3: Identify the property used.
- The equations show that the grouping of numbers being added does not affect the sum, which is the Associative Property of Addition.

- 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 \( e \) using the first equation.
\[
(12 + e) + 7 = 21
\]
Simplify:
\[
12 + e + 7 = 21
\]
Combine like terms:
\[
19 + e = 21
\]
Subtract 19 from both sides:
\[
e = 2
\]

- Step 2: Solve for \( f \) using the second equation.
\[
12 + (e + 7) = f
\]
Substitute \( e = 2 \):
\[
12 + (2 + 7) = f
\]
Simplify inside the parentheses:
\[
12 + 9 = f
\]
Add:
\[
f = 21
\]

- Step 3: Identify the property used.
- The equations show that the grouping of numbers being added does not affect the sum, which is the Associative Property of Addition.

- 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 \( g \) using the first equation.
\[
102 + g = 102
\]
Subtract 102 from both sides:
\[
g = 0
\]

- Step 2: Solve for \( h \) using the second equation.
\[
h + 0 = 102
\]
Since adding zero does not change the number:
\[
h = 102
\]

- Step 3: Identify the property used.
- Both equations involve adding zero, which is the Identity Property of Addition.

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

---

Final Answers:

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

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