ATYP Math - Algebra 1 - Exam 1 Vocabulary and Definitions

Natural Number

Natural Number

{1,2,3...}

Whole Number

{0,1,2,3...}

Integer

{-3,-2,-1,0,1,2,3...}

Real Number

All of the numbers

Rational Number

Any number that can be expressed in the form a/b

Irrational Number

Any number that can't be expressed in the form a/b

Commutative Property of Addition

a+b=b+a

Commutative Property of Multiplication

ab=ba

Associative Property of Addition

(a+b)+c=a+(b+c)

Associative Property of Multiplication

(ab)c=a(bc)

Inverse Property of Multiplication

For every a, if a does not equal 0, there is a multiplicative inverse 1/a such that a(1/a) = 1.

Multiplicative Inverse

one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7

Additive Inverse

one of a pair of numbers whose sum is zero; the additive inverse of -5 is +5

Inverse Property of Addition

For every a, there is an additive inverse -a such that a + (-a) = 0

Identity Property of Addition

a+0=a

Identity Property of Multiplication

a*1=a

Symmetric Property

If a = b, then b = a

Distributive Property

a(b+c)=ab+ac or a(b-c)=ab-ac

Multiplication Property of 0

For every real number n, n*0=0.

Multiplication Property of -1

For every real number n, -1*n=-n

Addition Property of Equality

For all real numbers a, b, and c, if a=b, then a+c = b+c

Subtraction Property of Equality

For all real numbers a, b, and c, if a=b, then a-c = b-c

Multiplication Property of Equality

For all real numbers a, b, and c, if a=b, then ac = bc

Division Property of Equality

For all real numbers a, b, and c, if a=b, then a/c = a/b

Reflexive Property

a = a

Symmetric Property

If a = b, then b = a

Transitive Property

If a = b and b=c, then a=c

Transitive Property of Inequality

If a<b and b<c, then a<c