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 8
Explain the difference between the commutative and associative properties.
Explain why 0 is called the additive identity.
Explain why the distributive property is useful when multiplying large numbers.
State the property: For any nonzero number a, a × (1/a) = 1.
If a = 2, b = 3, and c = 4, use the distributive property to expand a × (b + c).
If a = 4, b = 5, and c = 6, use the associative property to show that (a × b) × c = a × (b × c).
If a = 5, b = 2, and c = 7, use the distributive property to expand 5 × (2 + 7).
If a = 6, b = 0, what is a + b and which property does it illustrate?
Which of the following equations demonstrates the identity property of addition?
(1) 6 + 0 = 6
(2) 6 × 1 = 6
(3) 6 + 1 = 7
(4) 6 × 0 = 0
Which of the following is an example of the commutative property of addition?
(1) 2 + 3 = 3 + 2
(2) 2 × 3 = 6
(3) 2 + 0 = 2
(4) 2 × 1 = 2
Which of the following is an example of the identity property of multiplication?
(1) 7 × 1 = 7
(2) 7 + 0 = 7
(3) 7 × 0 = 0
(4) 7 + 1 = 8
Which of the following is an example of the inverse property of multiplication?
(1) 5 × 1 = 5
(2) 5 × 0 = 0
(3) 5 × (1/5) = 1
(4) 5 + (-5) = 0
Fill in the blank: (a + b) + c = a + (b + c) is an example of the ________ property.
Fill in the blank: The ________ property states that a × (b + c) = a × b + a × c.
Fill in the blank: The ________ property states that a × 0 = 0 for any number a.
Fill in the blank: The ________ property states that a × 1 = a for any number a.
Is the following statement true or false? The associative property applies to subtraction.
True or False: The commutative property holds for division.
True or False: The commutative property of addition means that changing the order of the numbers does not change the sum.
True or False: The distributive property allows you to multiply a number by a sum by multiplying each addend separately and then adding the products.
