Properties of Operations

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What is the Associative Property of Multiplication?

Back

The Associative Property of Multiplication states that the way in which numbers are grouped in multiplication does not change their product. For example, x(yz) = (xy)z.

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What is the Distributive Property?

Back

The Distributive Property states that a number multiplied by a sum is equal to the sum of the individual products. For example, a(b + c) = ab + ac.

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What is the Identity Property of Addition?

Back

The Identity Property of Addition states that adding zero to any number does not change the value of that number. For example, 100 + 0 = 100.

Front

What is the Distributive Property of Multiplication?

Back

The Distributive Property of Multiplication states that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products. For example, 3(5+y) = 15 + 3y.

Front

What is the Commutative Property of Addition?

Back

The Commutative Property of Addition states that changing the order of the addends does not change the sum. For example, 10 + 4 = 4 + 10.

Front

What is the Commutative Property of Multiplication?

Back

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. For example, ab = ba.

Front

What is the Identity Property of Multiplication?

Back

The Identity Property of Multiplication states that multiplying any number by one does not change the value of that number. For example, 7 × 1 = 7.

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What is an example of the Associative Property of Addition?

Back

An example of the Associative Property of Addition is (2 + 3) + 4 = 2 + (3 + 4).

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What is the difference between the Distributive Property and the Associative Property?

Back

The Distributive Property involves distributing a multiplication over addition, while the Associative Property involves changing the grouping of numbers in addition or multiplication without changing the result.

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How does the Commutative Property apply to subtraction?

Back

The Commutative Property does not apply to subtraction; changing the order of the numbers in subtraction changes the result. For example, 5 - 3 ≠ 3 - 5.