Math worksheet for identifying commutative and associative properties.

I will solve this problem by identifying whether each equation demonstrates the Commutative or Associative property. I'll go through each one step-by-step.

First, let me recall what these properties mean:
- Commutative Property: The order of numbers can be changed without affecting the result (e.g., a + b = b + a or a × b = b × a).
- Associative Property: The grouping of numbers can be changed without affecting the result (e.g., (a + b) + c = a + (b + c) or (a × b) × c = a × (b × c)).

Now, let me analyze each equation:

A) 3 + (8+2) = (3+8) + 2
This shows changing the grouping of addition: (3 + (8+2)) vs ((3+8) + 2). This is the Associative Property.

B) (9+7) + 4 = 7 + (9+4)
This shows both a change in grouping and order. The 9 and 7 have switched places, and the grouping has changed. Since the commutative property allows for order changes, and this involves switching the order of 9 and 7, this is primarily demonstrating the Commutative Property.

C) (5+8) + 2 = (8+5) + 2
Here, only the order within the first parentheses has changed: (5+8) became (8+5). The grouping remains the same. This is the Commutative Property.

D) 2 + (5+8) = (5+8) + 2
The entire group (5+8) has switched places with the 2. This is a change in order, not grouping. This is the Commutative Property.

E) (8×7) × 3 = 8 × (7×3)
This shows changing the grouping of multiplication: ((8×7) × 3) vs (8 × (7×3)). This is the Associative Property.

F) 11 × (6×5) = 11 × (5×6)
Within the parentheses, the order of 6 and 5 has changed: (6×5) became (5×6). The grouping remains the same. This is the Commutative Property.

G) (17×3) × 6 = 17 × (3×6)
This shows changing the grouping of multiplication: ((17×3) × 6) vs (17 × (3×6)). This is the Associative Property.

H) 12 × (9×1) = (12×9) × 1
This shows changing the grouping of multiplication: (12 × (9×1)) vs ((12×9) × 1). This is the Associative Property.

I) 2 × (3×6) = (3×6) × 2
The entire group (3×6) has switched places with the 2. This is a change in order, not grouping. This is the Commutative Property.

J) (8×9) × 14 = 8 × (9×14)
This shows changing the grouping of multiplication: ((8×9) × 14) vs (8 × (9×14)). This is the Associative Property.

Now I will write out the complete solution.

The completed worksheet should look like this:

A) 3 + (8+2) = (3+8) + 2 → A (Associative)
B) (9+7) + 4 = 7 + (9+4) → C (Commutative)
C) (5+8) + 2 = (8+5) + 2 → C (Commutative)
D) 2 + (5+8) = (5+8) + 2 → C (Commutative)
E) (8×7) × 3 = 8 × (7×3) → A (Associative)
F) 11 × (6×5) = 11 × (5×6) → C (Commutative)
G) (17×3) × 6 = 17 × (3×6) → A (Associative)
H) 12 × (9×1) = (12×9) × 1 → A (Associative)
I) 2 × (3×6) = (3×6) × 2 → C (Commutative)
J) (8×9) × 14 = 8 × (9×14) → A (Associative)