Formula Review

3.4 Rational 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

3.5 Irrational Numbers

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

3.6 Real 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

3.8 Exponents

• 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

3.10 Arithmetic 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)

3.11 Geometric Sequences

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

3.11 Geometric Sequences

an=a1rn−1an=a1rn−1

sn=a1(1−rn−11−r)