Properties of REAL Properties of REAL NumbersNumbers

OppositesOpposites

Two real numbers that are the same distance from the origin of the real number line are

opposites of each other.

EXAMPLESEXAMPLES-100 AND 100

2 AND -2

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ReciprocalsReciprocals

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Absolute ValueAbsolute Value

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Commutative Property of AdditionCommutative Property of Addition

a + b = b + aa + b = b + aWhen adding two numbers, the order of the

numbers does not matter.

EXAMPLESEXAMPLES2 + 3 = 3 + 2

(-5) + 4 = 4 + (-5)

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Commutative Property of MultiplicationCommutative Property of Multiplication

a × b = b × aa × b = b × aWhen multiplying two numbers, the order of the

numbers does not matter.

EXAMPLESEXAMPLES2 × 3 = 3 × 2

(-3) × 24 = 24 × (-3)

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Associative Property of AdditionAssociative Property of Addition

a + (b + c) = (a + b) + ca + (b + c) = (a + b) + cWhen three numbers are added, it makes no

difference which two numbers are added first.

EXAMPLESEXAMPLES2 + (3 + 5) = (2 + 3) + 5(4 + 2) + 6 = 4 + (2 + 6)

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Associative Property of MultiplicationAssociative Property of Multiplication

a(bc) = (ab)ca(bc) = (ab)cWhen three numbers are multiplied, it makes no

difference which two numbers are multiplied first.

EXAMPLESEXAMPLES2 × (3 × 5) = (2 × 3) × 5(4 × 2) × 6 = 4 × (2 × 6)

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Distributive PropertyDistributive Property

a(b + c) = ab + aca(b + c) = ab + acMultiplication distributes over addition.

EXAMPLESEXAMPLES2 (3 + 5) = (2 × 3) + (2 × 5)

(4 + 2) × 6 = (4 × 6) + (2 × 6)

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Additive Identity PropertyAdditive Identity Property

The additive identity property states that if 0 is added to a number, the result is that number.

EXAMPLEEXAMPLE3 + 0 = 0 + 3 = 3

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Multiplicative Identity PropertyMultiplicative Identity Property

The multiplicative identity property states that if a number is multiplied by 1, the result is that

number.

EXAMPLEEXAMPLE5 1 = 1 5 = 5

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Additive Inverse PropertyAdditive Inverse Property

The additive inverse property states that opposites add to zero.

EXAMPLEEXAMPLE7 + (-7) = 0 and -4 + 4 = 0

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Multiplicative Inverse PropertyMultiplicative Inverse Property

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PRACTICE EXERCISESPRACTICE EXERCISES

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Identify which property justifies each of the following:

4 × (8 × 2) = (4 × 8) × 2

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Identify which property justifies each of the following:

6 + 8 = 8 + 6

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Identify which property justifies each of the following:

12 + 0 = 12

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Identify which property justifies each of the following:

5(2 + 9) = (5 × 2) + (5 × 9)

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Identify which property justifies each of the following:

5 × 24 = 24 × 5

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Identify which property justifies each of the following:

18 + (-18) = 0

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Identify which property justifies each of the following:

-34 × 1 = -34

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