Refresher Course in Mathematics - Properties of Number
Number Properties
Property
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Definition
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Examples
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Closure
Property
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§ When we add or multiply any element in a set of numbers, the sum or product is a unique real number which belongs to that same set.
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14 + 25 + 44 + 52 = 135
23 x 14 x 10 = 3 220
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Commutative Property
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§ states that changing the position of the addends or the factors does not affect the sum or the product
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33 + 10 = 10 + 33
18 x 9 = 9 x 18
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Associative Property
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§ states that changing the grouping of addends in a sum or the grouping of factors in a product does not change the resulting sum or product
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(5 + 6) + 7 = 5 + (6 + 7)
2 x (4 x 6) = (2 x 4) x 6
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Identity Property
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Addition
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§ The sum of any number and zero is the same number.
§ 0 is the identity.
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512 + 0 = 512
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Multiplication
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§ The product of any number and one is the same number.
§ 1 is the identity
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512 x 1 = 512
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Distributive Property of Multiplication over Addition / Subtraction
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§ states that multiplication distributes over addition and subtraction
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7(9 + 12) = 7(9) + 7(12)
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