Properties of Operations
Math ⇒ Number and Operations
Properties of Operations starts at 6 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Properties of Operations.
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See sample questions for grade 7
If 0 + x = x, what is the name of the property shown?
If a = 2, b = 3, and c = 4, show that a × (b + c) = a × b + a × c.
If a = 3, b = 5, and c = 7, use the distributive property to expand a × (b + c).
If a = 4, b = 6, and c = 2, use the commutative property of addition to write a + b in another way.
If a = 5, b = 2, and c = 3, use the associative property of addition to show (a + b) + c = a + (b + c).
If a = 6, b = 4, and c = 2, verify the associative property of multiplication for these values.
If x + 0 = x, what property does this equation show?
A student claims that (4 + 5) × 2 = 4 × 2 + 5 × 2. Which property justifies the student's claim?
Which of the following demonstrates the commutative property of multiplication?
(1) 3 × 4 = 4 × 3
(2) 3 × (4 × 5) = (3 × 4) × 5
(3) 3 × 1 = 3
(4) 3 × 0 = 0
Which of the following equations demonstrates the associative property of addition?
(1) 2 + (3 + 4) = (2 + 3) + 4
(2) 2 + 3 = 3 + 2
(3) 2 × (3 + 4) = 2 × 3 + 2 × 4
(4) 2 + 0 = 2
Which of the following is an example of the commutative property of addition?
(1) 7 + 3 = 3 + 7
(2) 7 + (3 + 2) = (7 + 3) + 2
(3) 7 × (3 + 2) = 7 × 3 + 7 × 2
(4) 7 + 0 = 7
Which of the following is an example of the distributive property?
(1) 6 × (2 + 3) = 6 × 2 + 6 × 3
(2) 6 + 2 = 2 + 6
(3) (6 + 2) + 3 = 6 + (2 + 3)
(4) 6 × 1 = 6
Fill in the blank: The ________ property states that a × (b + c) = a × b + a × c.
Fill in the blank: The associative property of addition states that (a + b) + c = ________.
Fill in the blank: The commutative property of addition states that a + b = ________.
Fill in the blank: The commutative property of multiplication states that a × b = ________.
True or False: The associative property applies to division.
True or False: The associative property of addition states that (a + b) + c = a + (b + c).
True or False: The commutative property applies to multiplication but not to division.
True or False: The commutative property applies to subtraction.
