1. A34H Chapter 1 Review Classifying Numbers AND Identifying Properties

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

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

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

5. 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

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

7. 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

8. YOU TRY… Classify each number 1. 2. 3. 4. Real, Irrational Imaginary Real, Rational, Integer Real, Rational, Integer, Whole, Natural

9. YOU TRY… Classify each number 1. 2. 3. 4. Real, Rational Real, Rational, Integer Whole, Natural Real, Rational Real, Irrational

10. YOU TRY… Classify each number 1. 2. 3. Real, Rational, Integer Whole, Natural Real, Rational, Integer, Whole

11. 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

12. 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.

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

14. 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.

15. 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

16. YOU TRY… Name the Property 1. 2. 3. Commutative + Distributive Associative +

17. YOU TRY… Name the Property 1. 2. 3. Closure X Identity X Commutative X

18. YOU TRY… Name the Property 1. 2. 3. Associative X Distributive Identity +