Properties of Equality

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What is the Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a number by a sum by distributing the multiplication over each addend.

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What is the Commutative Property?

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The Commutative Property states that the order in which two numbers are added or multiplied does not change the result. For addition: a + b = b + a; for multiplication: ab = ba.

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What is the Identity Property of Addition?

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

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What is the Identity Property of Multiplication?

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

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What is the Associative Property?

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The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. For addition: (a + b) + c = a + (b + c); for multiplication: (ab)c = a(bc).

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What is the Addition Property of Equality?

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The Addition Property of Equality states that if you add the same number to both sides of an equation, the two sides remain equal. For example, if a = b, then a + c = b + c.

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What is the Subtraction Property of Equality?

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The Subtraction Property of Equality states that if you subtract the same number from both sides of an equation, the two sides remain equal. For example, if a = b, then a - c = b - c.

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What is the Multiplication Property of Equality?

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The Multiplication Property of Equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. For example, if a = b, then ac = bc.

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What is the Division Property of Equality?

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The Division Property of Equality states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. For example, if a = b, then a/c = b/c.

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How do you combine like terms?

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Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 3x + 4x = 7x.