Properties of Operations
Math ⇒ Number and Operations
Properties of Operations starts at 6 and continues till grade 12.
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See sample questions for grade 12
Describe the difference between the associative and commutative properties.
Explain why division is not commutative for real numbers.
Explain why the distributive property is important in algebraic simplification.
State the identity property of addition.
If a = 2, b = 5, and c = 7, compute (a + b) + c and a + (b + c) to verify the associative property of addition.
If a = 3, b = 2, and c = 5, use the distributive property to expand a × (b + c).
If a = 6, b = 2, and c = 3, verify the distributive property: a × (b + c) = a × b + a × c.
If a = 7, b = 3, and c = 2, verify the associative property of addition using these values.
Which of the following is an example of the commutative property of addition?
(1) 5 + 7 = 7 + 5
(2) 5 × (7 + 2) = 5 × 7 + 5 × 2
(3) (5 + 7) + 2 = 5 + (7 + 2)
(4) 5 + 0 = 5
Which of the following is an example of the distributive property?
(1) 2 × (3 + 4) = 2 × 3 + 2 × 4
(2) 2 + 3 = 3 + 2
(3) (2 + 3) + 4 = 2 + (3 + 4)
(4) 2 × 1 = 2
Which of the following is NOT a property of operations?
(1) Distributive Property
(2) Commutative Property
(3) Associative Property
(4) Transitive Property
Which of the following properties states that for any real numbers a, b, and c: (a + b) + c = a + (b + c)?
(1) Commutative Property
(2) Associative Property
(3) Distributive Property
(4) Identity Property
Fill in the blank: For any nonzero real number a, the multiplicative inverse is ________.
Fill in the blank: The ________ property of multiplication states that a × b = b × a for all real numbers a and b.
Fill in the blank: The additive inverse of 9 is ________.
Fill in the blank: The multiplicative identity is the number ________.
Does the commutative property apply to subtraction? Answer Yes or No.
State whether the following statement is true or false: For all real numbers a, b, and c, (a × b) × c = a × (b × c).
True or False: The additive inverse of a number a is -a.
True or False: The associative property applies to both addition and multiplication.
