Algebraic Properties
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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| Transitive Property of Equality | If a=b and b=c then a=c
Ex.) If x+5 = 9 and 9 = 4+5 then x+5 = 4+5
Ex.) If a<b and b<7 then a<7.
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| Symmetric Property of Equality | If a=b then b=a
Ex.) If 2x+9 = 12 then 12 = 2x+9
Ex.) If x+6 = 5 then 5 = x+6
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| Reflexive Property of Equality | For all real numbers a, a = a
Ex.) 8x = 8x
Ex.) x-3 = x-3
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| Addition Property of Equality /Inequality | If the same number is added to both sides of an equation, the two sides remain equal. That is if
x = y, then x+z = y+z
In an inequality,the number does not change the inequality.
if x>y, then x+z > y+z, and
if x<y, then x+z < y+z
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| Substitution Property | If a = b then a can be substituted for b in any equation or inequality.
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| Commutative Property | The order of adding does not change the sum or product.
Ex.) 5x+3y = 3y+5x (Addition)
Ex.) 7x(2) = 2(7x) (Multiplication)
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| Associative Property | Grouping numbers differently does not change the sum or product.
Ex.) 5x+(6x + 3) = (5x + 6x)+3 ( + )
Ex.) 9*(10 * 3) = (9 * 10)*3 ( * )
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| Identity Property | Adding zero to a number does not change its value.
Ex.) 6xy+0 = 6xy
Multiplying a number by one does not change its value.
Ex.) 18a(1) = 18a ( Multiplication )
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| Additive Inverse /Multiplicative Inverse Property | The sum of opposites equals zero. ( + )
Ex.) 8x+( -8x ) = 0
A number times its reciprocal equals one. ( * )
Ex.) 2 * 1/2 = 1
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| Multiplication Property of Zero or (The Zero Property) | Zero times any number equals zero.
Ex.) 3*0 = 0
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| The Distributive Property | a( b + c) = a*b + a*c or (b + c)a = a( b + c) = a*b + a*c
Rainbow method.
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