Skills to Enhance Learning GED Math

Relationship Among Numbers Real Numbers Relationship Among Numbers − 𝟒 𝟓 ,𝝅,𝟎, 𝟏 𝟏𝟎 , 𝟑 Irrational Numbers Rational Numbers 𝝅, 𝟑 , − 𝟐 1/4 2/3 -15/8 Non-integers 14/15, ½, 6.3 Integers -3, 0, 15 Negative Integers -10, -5, -206 Whole Numbers 0, 1, 2, 3, From: D.Franklin Wright, Introductory Algebra, p.6 Zero Natural Numbers 1, 5, 403

Positive and Negative Integers in the number line Positive Integers { 1, 2, 3, 4, 5, …} Negative Integers { ….. -4, -3, -2, -1 } __________________________________________________ -4 _3 -2 -1 0 1 2 3 4 5 Zero Negative numbers Positive Numbers Note: A distance for corresponding points positive or negative is the same

Number Properties 1- Commutative of Addition – a + b = b + a Commutative of Multiplication -- a . b = b . a 2- Associative of Addition – ( a + b) + c = a + ( b + c) Associative of Multiplication-- ( a . b ) . c = a . ( b . c ) 3– Distributive of Multiplication over Addition a ( b + c ) = a b+ a c 4– Additive Identity a + 0 = a Multiplicative Identity a . 1 = a 5– Closure- The addition of a + b results in a rational number 6– Inverse– For each rational number there is one and only one –a such as a+(-a)=0 In multiplication the double negative results in a positive number. 7– Other properties– Reflexive a = a Symmetric a = b b = a Transitive a = b b = c then a = c

Order of Operations PEMDAS-Please excuse my dear aunt Sally P = Parenthesis E= Exponents M= Multiplication D = Division A= Addition and Subtraction Rules for Computations a)Compute within groups b) Multiply and Divide in order from left to right c) Add and subtract in order from left to right

Properties of Exponents