properties of algebra
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| commutative property | Arithmetic: 5+3=3+5 or 5(3)=3(5)
Algebraic: x+y=y+x or ab=ba
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| additive identity | arithmetic: 5+0=5, anything added to 0 is itself
Algebraic: x+0=x, abc+0=abc
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| associative property | arithmetic: (5+2)+3=5+(2+3)
Algebraic: (mn)z=m(nz)
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| multiplicative property of zero | arithmetic: 6*0=0, any numbwer times 0=0
Algebraic: ab*0=0
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| multiplicative identity | arithmetic: a*1=a, any number times 1=the number
Algebraic: xy*1=xy
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| distributive property | arithmetic: 5(7+3)=5(7)+5(3)
Algebraic: x(y+z)=x(y)+x(z)
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| additive inverse | arithmetic: 5-9=5+(-9) or -3-9=-3+(-9)
Algebraic: a-b=a+(-b)
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| comparison property | algebraic: given any two numbers a and b, either a>b, a
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| density property | algebraic: the number line is forever dense. there are infinate numbers between any two numbers
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| reflexive property | algebraic: x=x, 5=5, 2x-3=2x-3
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| symetric property | arithmetic: if 5+2=7 then 7=5+2
Algebraic: if a=b then b=a, if 2x+3=13 then 13=2x+3
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| transitive property | arithmetic: if 5+3=8 and 8=4*2, then 5+3=4*2
Algebraic: if a=b and b
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| transitive property of order | algebraic: if a>b and b>c, then a>c
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| substitution property | arithmetic: if a=b, then b may replace a
Algebraic: 5(2)+3=10+3
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