Test Questions for Commutative and Associative Properties in Algebra

📚 Quick Study Guide

🔢 Commutative Property: This property states that the order of operands does not change the result.
• ➕ For addition: $a + b = b + a$
• ✖️ For multiplication: $a \times b = b \times a$
🧮 Associative Property: This property states that the grouping of operands does not change the result.
• ➕ For addition: $(a + b) + c = a + (b + c)$
• ✖️ For multiplication: $(a \times b) \times c = a \times (b \times c)$

Practice Quiz

1. Question 1: Which property is demonstrated by the equation $5 + 3 = 3 + 5$?
   1. A) Associative Property of Addition
   2. B) Commutative Property of Addition
   3. C) Distributive Property
   4. D) Identity Property of Addition
2. Question 2: Which of the following equations demonstrates the associative property of multiplication?
   1. A) $7 \times 1 = 7$
   2. B) $4 \times (2 \times 3) = (4 \times 2) \times 3$
   3. C) $6 \times 5 = 5 \times 6$
   4. D) $8 + 0 = 8$
3. Question 3: Identify the property illustrated in the equation $(2 + 4) + 6 = 2 + (4 + 6)$.
   1. A) Commutative Property of Multiplication
   2. B) Associative Property of Addition
   3. C) Commutative Property of Addition
   4. D) Distributive Property
4. Question 4: Which equation exemplifies the commutative property of multiplication?
   1. A) $9 \times (2 \times 1) = (9 \times 2) \times 1$
   2. B) $10 \times 1 = 10$
   3. C) $11 \times 8 = 8 \times 11$
   4. D) $12 + 0 = 12$
5. Question 5: Which property allows you to rearrange the terms in the expression $a + c + b$ to $a + b + c$ without changing the result?
   1. A) Associative Property of Addition
   2. B) Identity Property of Addition
   3. C) Commutative Property of Addition
   4. D) Distributive Property
6. Question 6: What property is being used in the equation $3 \times (x \times y) = (3 \times x) \times y$?
   1. A) Commutative Property of Multiplication
   2. B) Associative Property of Multiplication
   3. C) Distributive Property
   4. D) Identity Property of Multiplication
7. Question 7: Which of the following does NOT demonstrate either the commutative or associative property?
   1. A) $p + q = q + p$
   2. B) $(m \times n) \times o = m \times (n \times o)$
   3. C) $r \times 1 = r$
   4. D) $s + (t + u) = (s + t) + u$