A34H Chapter 1 Review Classifying Numbers AND Identifying Properties

Classifying Numbers Imaginary Numbers Real Numbers Irrational Rational Integers Whole Numbers Natural Numbers

Classifying Numbers Real or Imaginary? Imaginary numbers: All other numbers are Real

Classifying Numbers If Imaginary – You’re done classifying If Real – Keep going

Classifying Real Numbers Irrational VS Rational? Irrational Decimals: Don’t terminate. Don’t repeat. Usually represented by a symbol like or Irrational Square Roots: When simplified, All other numbers are Rational

Classifying Real Numbers If Irrational – You’re done classifying If Rational – Keep going

Classifying Rational Numbers Integer VS Whole VS Natural?...Simplify first, then check Integers: Number line numbers…negatives, zero, positives Whole Numbers: Positive number line numbers and zero Natural Numbers: Positive number line numbers

YOU TRY… Classify each number Real, Irrational Imaginary Real, Rational, Integer Real, Rational, Integer, Whole, Natural

YOU TRY… Classify each number Real, Rational Real, Rational, Integer Whole, Natural Real, Rational Real, Irrational

YOU TRY… Classify each number Real, Rational, Integer Whole, Natural Real, Rational, Integer, Whole

Identifying Properties Closure Property + IF a, b, c are Real Numbers THEN ( a + b + c ) is a Real Number Closure Property X IF a, b, c are Real Numbers THEN ( a )( b )( c ) is a Real Number If you add or multiply real numbers together, your answer is a real number

Identifying Properties Identity Property + a + 0 = a 0 + a = a Identity Property X ( a )1 = a 1( a ) = a You get back what you start with.

Identifying Properties Commutative Property + a + b = b + a Commutative Property X ( a )( b ) = ( b )( a ) You commute (move) the numbers

Identifying Properties Associative Property + a + ( b + c ) = ( a + b ) + c Associative Property X a ( bc ) = ( ab ) c You associate (group) numbers differently…NOTICE you don’t commute them.

Identifying Properties Distributive Property a ( b + c ) = ab + ac ( b + c ) a = ab + ac NOTICE this property is not specific to just addition or just multiplication

YOU TRY… Name the Property Commutative + Distributive Associative +

YOU TRY… Name the Property Closure X Identity X Commutative X

YOU TRY… Name the Property Associative X Distributive Identity +