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A34H Chapter 1 Review Classifying Numbers AND Identifying Properties
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Classifying Numbers Imaginary Numbers Real Numbers Irrational Rational Integers Whole Numbers Natural Numbers
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Classifying Numbers Real or Imaginary? Imaginary numbers: All other numbers are Real
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Classifying Numbers If Imaginary – You’re done classifying If Real – Keep going
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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
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Classifying Real Numbers If Irrational – You’re done classifying If Rational – Keep going
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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
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YOU TRY… Classify each number 1. 2. 3. 4. Real, Irrational Imaginary Real, Rational, Integer Real, Rational, Integer, Whole, Natural
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YOU TRY… Classify each number 1. 2. 3. 4. Real, Rational Real, Rational, Integer Whole, Natural Real, Rational Real, Irrational
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YOU TRY… Classify each number 1. 2. 3. Real, Rational, Integer Whole, Natural Real, Rational, Integer, Whole
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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
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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.
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Identifying Properties Commutative Property + a + b = b + a Commutative Property X ( a )( b ) = ( b )( a ) You commute (move) the numbers
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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.
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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
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YOU TRY… Name the Property 1. 2. 3. Commutative + Distributive Associative +
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YOU TRY… Name the Property 1. 2. 3. Closure X Identity X Commutative X
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YOU TRY… Name the Property 1. 2. 3. Associative X Distributive Identity +
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