12.2: Properties of Real Numbers

Elementary Algebra · LibreTexts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Commutative Property

    Addition

    \(a + b = b + a\)

    \(3 + 4 = 4 + 3\)

    Multiplication

    \(ab = ba\)

    \(4 \cdot 3 = 3 \cdot 4\)

    Associative Property

    Addition

    \(a+(b+c)=(a+b)+c\)

    \(4+(3+5)=(4+3)+5\)

    Multiplication

    \(a(bc)=(ab)c\)

    \(4(3⋅5)=(4⋅3)5\)

    Distributive Property

    \(a(b+c)=ab+ac\)

    \(4(x+3)=4x+12\)

    \((b+c)a=ab+bc\)

    \((x+3)4=4x+12\)

    Properties of Zero

    \(a \cdot 0 = 0\)

    \(0 \cdot a = 0\)

    If \(a =\not = 0\), then \(\dfrac{0}{a} = 0\) and \(\dfrac{a}{0} = 0\) is undefined.

    Double Negative Property

    \(-(-a) = a\)

    This page titled 12.2: Properties of Real Numbers was last modified on Sat, 12 Jun 2021 05:18:44 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski and Wade Ellis, Jr. (OpenStax CNX) .