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# Algebraic Properties

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.
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
Reflexive Property of Equality For all real numbers a, a = a Ex.) 8x = 8x Ex.) x-3 = x-3
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
Substitution Property If a = b then a can be substituted for b in any equation or inequality.
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)
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 ( * )
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 )
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
Multiplication Property of Zero or (The Zero Property) Zero times any number equals zero. Ex.) 3*0 = 0
The Distributive Property a( b + c) = a*b + a*c or (b + c)a = a( b + c) = a*b + a*c Rainbow method.
Created by: 3119244