Contemporary Mathematics

Formula Review

3.4Rational Numbers

• $ac±bc=a±bcac±bc=a±bc$
• $ab×cd=a×cb×dab×cd=a×cb×d$
• $ab×cd=a×cb×dab÷cd=ad×dc=a×db×cab×cd=a×cb×dab÷cd=ad×dc=a×db×c$

3.5Irrational Numbers

• $a×b=a×ba×b=a×b$
• $a×x±b×x=(a±b)×xa×x±b×x=(a±b)×x$
• $a÷b=ab=aba÷b=ab=ab$
• $a2−b2=(a−b)(a+b)a2−b2=(a−b)(a+b)$

3.6Real Numbers

• $a×(b+c)=a×b+a×ca×(b+c)=a×b+a×c$
• $a+b=b+aa+b=b+a$
• $a×b=b×aa×b=b×a$
• $a+(b+c)=(a+b)+ca+(b+c)=(a+b)+c$
• $a×(b×c)=(a×b)×ca×(b×c)=(a×b)×c$
• $a+0=aa+0=a$
• $a×1=aa×1=a$
• $a+(−a)=0a+(−a)=0$
• $a×(1a)=1a×(1a)=1$

3.8Exponents

• $anam=an+manam=an+m$
• $anam=a(n−m)anam=a(n−m)$
• $a0=1a0=1$, provided that $a≠0a≠0$
• $(a×b)n=an×bn(a×b)n=an×bn$
• $(ab)n=anbn(ab)n=anbn$
• $(an)m=a(n×m)(an)m=a(n×m)$
• $a−n=1ana−n=1an$, provided that $a≠0a≠0$

3.10Arithmetic Sequences

• $ai=a1+d×(i−1)ai=a1+d×(i−1)$
• $d=aj−aij−id=aj−aij−i$
• $a1=ai−d(i−1)a1=ai−d(i−1)$
• $sn=n(a1+an2)sn=n(a1+an2)$

3.11Geometric Sequences

• $an=a1rn−1an=a1rn−1$
• $sn=a1(1−rn−11−r)sn=a1(1−rn−11−r)$

3.11Geometric Sequences

$an=a1rn−1an=a1rn−1$

$sn=a1(1−rn−11−r)sn=a1(1−rn−11−r)$

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