HA2T Math Prop.
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Created by:
mfurey92 Plus on February 3, 2009
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21 terms
Terms | Definitions |
|---|---|
 Reflexive Property | Any real number us always equal to itself (Refl) a=a |
| Symmetric Property | Answer is the same left to right and right to left - Allows us to read left to right and right to left (Sym) If a=b then b=a |
| Transitive Property | i. If the 1st number is equal to a 2nd and the 2nd is equal to the 3rd then the 1st is equal to the 3rd (Trans) If a=b and b=c, then a=c |
| Closure Property | If 2 numbers are real their sum/product is real (Clos +/X) a+b/ab is a real number |
| Communicative Property | When adding/multiplying if the variable order is changed it doesn't change the sum/product (Comm +/X) a+b=b+a / ab=ba |
| Associative Property | regrouping of the addends or factors does not change the outcome of the operation (Assoc +/X) (a+b)+c=a+(b+c) / (ab)c=a(bc) |
| Identity Property of Addition | i. When adding a number and zero, the sum is always that number (Iden +) a+0=a and 0+a=a |
| Identity Property of Multiplication | When multiplying a number by one, the product is always that number (Iden X) a x 1=a and 1 x a =a |
| Inverse Property of Addition | Every number has an opposite and when adding a number and its opposite, the sum is 0 (Inv +) a + (-a) = 0 |
| Inverse Property of Multiplication | All real numbers have a reciprocal and when multiplying any real number by its inverse, the product is 1 (Inv X) 1/a is a real number and a x 1/a = 1 |
| Distributive Property | When multiplying a term by a sum of numbers each term of the sum is multiplied by the 1st term a(b+c) = (ab) + (ac) |
| Substitution Principle | an expression may be replaced by another expression that has the same value; In sums and products, equals may be substituted for equals |
| Additive/Multiplicative Property of Equality | If 2 numbers are equal, adding or multiplying by the same term on both sides of the equal sign does not effect the sum/product (Add Prop =) If a=b, then a+c=b+c / (Mult Prop =) If a=b, then ac=bc |
| Cancellation Property | If 2 numbers are equal and share the same term on both sides of the equal sign, that shared term can be canceled out (Canc +) If a+c=b+c, then a=b / (Canc X) if ac=bc, then a=b |
| Property of the Opposite of the Sum | The opposite of the sum is equal to the sum of the opposites (Opp Sum) -(a+b) = (-a) + (-b) |
| Property of Reciprocal of the Product | The reciprocal of the product is equal to the product of the reciprocals (Rec Prod) 1/ab = 1/a x 1/b |
| Property of (-1) | Any real number multiplied -1 is its opposite (Prop -1) (-a) = (-1)a |
| Property of Zero | Any number multiplied by 0 is 0 (Prop 0) a x 0=0 and 0 x a=0 |
| Cancellation Property of Additive Inverse | The opposite of the opposite of any number is equal to it self (Canc + Inv) -(-a)=a |
| Definition of Subtraction | Subtracting a number means adding by its opposite (Def -) a-b=a+(-b) |
| Definition of Division | Dividing by a number means multiplying by its reciprocal (Def /) a/b = a x 1/b |
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