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If x and y are real numbers, then… x+y is a unique real number. [CLOSURE PROPERTY OF ADDITION]
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If x and y are real numbers, then… xy is a unique real number. [CLOSURE PROPERTY OF MULTIPLICATION]
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If x and y are real numbers, then… x+y = y+x. [COMMUTATIVE PROPERTY OF ADDITION]
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If x and y are real numbers, then… xy = yx. [COMMUTATIVE PROPERTY OF MULTIPLICATION]
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If x, y and z are real numbers, then… (x+y)+z = x+(y+z). [ASSOCIATIVE PROPERTY OF ADDITION]
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If x, y and z are real numbers, then… (xy)z = x(yz). [ASSOCIATIVE PROPERTY OF MULTIPLICATION]
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Multiplication distributes over addition. If x, y and z are real numbers, then… x(y+z) = xy + xz. [DISTRIBUTIVE PROPERTY]
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The IDENTITY ELEMENT FOR ADDITION is 0, i.e., for any real number x, … x+0 = x. [ADDITION PROPERTY OF 0]
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The IDENTITY ELEMENT FOR MULTIPLICATION is 1, i.e., for any real number x, … x.1 or 1x = x. [MULTIPLICATION PROPERTY OF 1]
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A unique ADDITIVE INVERSE exists for every real number, i.e., for every x the additive inverse is -x such that… x + (-x) = 0.
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A unique MULTIPLICATIVE INVERSE exists for every real number, i.e., for every non-zero x the multiplicative inverse is 1/x such that… x . (1/x) = 1.
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