Chapter R Review of Basic Algebra R 1

Chapter R: Review of Basic Algebra • R. 1 The Set of Real Numbers • R. 2 Operations with Real Numbers • R. 3 Exponential Notation and Order of Operations • R. 4 Intro to Algebraic Expressions • R. 5 Equivalent Algebraic Expressions • R. 6 Simplifying Algebraic Expressions • R. 7 Properties of Exponents and Scientific Notation R Math 120 - KM 1

A Map of the Number Sets REAL NUMBERS Irrationals: pi, e, 3, 2. 12212222… Rational Numbers: a/b with b 0 Integers: …-2, -1, 0, 1, 2, … Whole Numbers: 0, 1, 2, 3, … Natural Numbers: 1, 2, 3, … R Math 120 - KM 2

Identifying Numbers 1. Name the: a) Natural Numbers b) Whole Numbers c) Integers d) Rational Numbers e) Irrational Numbers f) Real Numbers R Math 120 - KM 3

ROSTER Notation for a SET 2. Use ROSTER Notation to name the set of all odd numbers between 2 and 8. R Math 120 - KM 4

SET-BUILDER Notation 3. Use SET-BUILDER Notation to name the set of all Real Numbers greater than -7. R Math 120 - KM 5

ORDER for the Real Numbers smaller -7 0 BIGGER -2 4 a. Insert > or < to make a true sentence. R Math 120 - KM 6

ORDER for the Real Numbers smaller -99 0 BIGGER 0 4 b. Insert > or < to make a true sentence. R Math 120 - KM 7

ORDER for the Real Numbers smaller BIGGER 0 1/2 3/5 4 c. Insert > or < to make a true sentence. R Math 120 - KM 8

Another Way to Write 5. Write a different inequality with the same meaning: R Math 120 - KM 9

TRUE or FALSE ? 6. Is the sentence TRUE or FALSE? R Math 120 - KM 10

Graphs on the Number Line 7. Graph each inequality: -2 3 4 R Math 120 - KM 11

Absolute Value 8. Find the following : R Math 120 - KM 12

Additive Inverse or Opposite 9. Find the Opposite. The opposite of -13 is 13. The opposite of 0 is 0. The opposite of 4 is -4. The opposite of x is -x. The opposite of –x+3 is x – 3. R Math 120 - KM 13

Operations with Real Numbers 10. Add, Subtract, Multiply, or Divide, if possible. R Math 120 - KM 14

Exponential Notation 11. Evaluate (Rewrite without exponents. ) R Math 120 - KM 15

Negative Exponents 12. Evaluate (Rewrite without exponents. ) R Math 120 - KM 16

Order of Operations: PEMDAS 13. Simplify: R Math 120 - KM 17

Translating English into an Algebraic Expression 14. Translate the phrase into algebra. 5 more than the product of 3 and x or 2 less than the quotient of x and 7 The distance traveled by a bike going 30 miles per hour for t hours. D R r t Math 120 - KM 18

Evaluate an Algebraic Expression 16. Evaluate. when x = 4 -25 when x = -2 and z = 3 -15 when r = -1 and s = 4 0 R Math 120 - KM 19

Equivalent Algebraic Expressions 17. a) Find an equivalent expression with a denomiator of 24 x. b) Simplify. R Math 120 - KM 20

The Commutative Law 18. Use the Commutative Law to write an equivalent expression. a) b) c) R or Math 120 - KM 21

The Associative Law 19. Use the Associative Law to write an equivalent expression. a) b) R Math 120 - KM 22

The Distributive Law of Multiplication over Addition and Subtraction 20. Use the Distributive Law to write an equivalent expression. a) b) R Math 120 - KM 23

Factor (Rewrite as a Product) 21. Factor. a) b) R Math 120 - KM 24

Simplify 22. Simplify as much as possible. a) b) c) d) R Math 120 - KM 25

Properties of Exponents 23. Simplify as much as possible. a) b) c) d) R Math 120 - KM 26

Scientific Notation 24. Write in Scientific Notation. a) b) R Math 120 - KM 27

Scientific Notation 25. Simplify and then write the answer in Scientific Notation. a) b) R Math 120 - KM 28

“Gage” – Puppy In Training 26. Gage had 5 cookies and ate x of them. How may cookies does Gage Have left? R Math 120 - KM 29

That’s All For Now! R Math 120 - KM 30