Equivalent Equations

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What is an equivalent equation?

Back

An equivalent equation is an equation that has the same solution as another equation, meaning both sides of the equation are equal when the variable is replaced with the solution.

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How do you isolate a variable in an equation?

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To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

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What is the result of adding zero to a number?

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Adding zero to a number does not change the value of that number; it is known as the identity property of addition.

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What is the result of multiplying a number by one?

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Multiplying a number by one does not change the value of that number; it is known as the identity property of multiplication.

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What does it mean to simplify an expression?

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Simplifying an expression means to reduce it to its simplest form by combining like terms and performing any possible operations.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

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What is the commutative property of addition?

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The commutative property of addition states that changing the order of the addends does not change the sum, i.e., a + b = b + a.

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What is the commutative property of multiplication?

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The commutative property of multiplication states that changing the order of the factors does not change the product, i.e., a × b = b × a.

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What is the associative property of addition?

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The associative property of addition states that the way in which numbers are grouped does not change their sum, i.e., (a + b) + c = a + (b + c).

Front

What is the associative property of multiplication?

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The associative property of multiplication states that the way in which numbers are grouped does not change their product, i.e., (a × b) × c = a × (b × c).