# HA2T Math Prop.

## 21 terms

### 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