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Chapter 1, Section 1&2

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Chapter 1, Sections 1 and 2, Expressions and Order of Operations.

Chapter 1, Sections 1 and 2, Expressions and Order of Operations.

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  • 1. Pre-Algebra Review Chapter 1, Sections 1 and 2 By Ms. Dewey-Hoffman, 2009 http://msdhpowerpoints.blogspot.com/
  • 2. Section 1: Variables and Expressions
    • Variables
      • Are letters or symbols that act as placeholders for numbers.
      • One letter = One number.
    • Simplify
      • To replace a variable with a number.
    • Expressions: Numerical and Variable
      • Expressions don’t have an equal sign. 50 + 10  Expression
      • Equations do have an equal sign. 50 + 10 = 60  Equation
    • Numerical Expressions
      • Only have numbers: 50 + 10  No Variables
    • Variable Expressions
      • Have at least 1 Variable: 75 + g + 25  At least 1 Variable
      • 3x + y  At least 1 Variable
  • 3. Language of Math: Operations
    • Addition: Total , Sum , Altogether , Increase , and Combine .
    • Subtraction: Difference , Less Than , More Than , and Decrease .
    • Multiplication: Product , Times , and Each .
    • Division: Quotient , Share , and Each .
    Operations and their Parts: Addition & Subtraction
    • Two numbers being added are called ADDENDS.
    • The answer to an addition problem is called the SUM.
    • The number being subtracted is the SUBTRAHEND and the number from which we are subtracting is called the MINUEND.
    • (First Number  Minuend) – (Second Number  Subtrahend) = Difference.
    • The answer to a subtraction problem is called the DIFFERNCE.
  • 4. Operations and their Parts: Multiplication & Division
    • Two numbers in a multiplication problem are called the FACTORS .
    • The answer to a multiplication problem is the PRODUCT .
    • The number being divided is called the DIVIDEND . The number we are dividing by is called the DIVISOR .
    • The answer to a division problem is the QUOTIENT .
    • (Top Number  Dividend ) / ( Divisor  Bottom Number) = Quotient
  • 5. Writing Variable Expressions: Example Problems
    • Nine more than number y  y + 9
    • A number z times three  z x 3 , z • 3 , z3
    • 5 times the quantity 4 plus a number c  5 • (4 + c) , 5(4 + c)
    • Try These:
    • The product of x and y, plus 5 
    • The sum of t and u, divided by 4 
    • R divided by 5, minus 3, equals 2. 
    • Y fewer than 27 
    • Daniel has 14 more than Sam. 
    • The total of Tommy’s marbles and 13 
    • 55 subtracted from 105, divided by 5 equals 10. 
    Challenge problems are in purple.
  • 6. Section 2: The Order of Operations
    • Simplify an Expression
      • To replace the expression with the simplest name for its value…
      • or solve as far as possible!
      • What does 36 + 25 ÷ 5 simplify to?
    • The Order of Operations
      • 36 + 25 ÷ 5
    Division first! 25 ÷ 5 = 5 Rewrite. 36 + 5 Addition second! 36 + 5 = 41 41 is the simplified expression for 36 + 25 ÷ 5
  • 7. The Order of Operations: PEMDAS
    • P : Do operations inside PARENTHESES (or other delimiters/grouping symbols, like [BRACKETS] and division bars).
      • Work from the inside of the Parentheses/Brackets to the outside.
      • Division Bars: Simplify the top and bottom first, then divide!
    • E : Evaluate terms with EXPONENTS .
      • The exponent ONLY effects the NUMBERS/VARIABLES/PARENTHESES in front of the little number (to the left). Example: 5 10 , x 2 , (5 + 8) 3 .
    • D M : Do MULTIPLICATION and DIVISION .
      • In order from LEFT to RIGHT .
      • 5 • 10 ÷ 2  5 • 10 = 50, 50 ÷ 2 = 25, 5•10÷2=25
    • A S : ADD and SUBTRACT terms .
      • In order from LEFT to RIGHT .
      • 8 + 7 – 5  8 + 7 = 15, 15 – 5 = 10, 8+7-5=10
    PEDMAS is where order REALLY matters!
  • 8. Example Problems: Show each Step of PEMDAS
    • 2[(13 – 4) ÷ 3] =
    • 1 + 10 – 2 =
    • 4
    • 4 – 1 • 2 + 6 ÷ 3 =
    • 5 + 6 • 4 ÷ 3 – 1 =
    6 3 4 12
    • Example of Showing Steps: PEMDAS
    • 2[(13 – 4) ÷ 3] = Copy Problem
    • 2[(9) ÷ 3] = Simplify Parentheses
    • 2[3] = Simplify Brackets
    • 2[3] = 6, Multiply
    • 6, Answer, Always Boxed!
  • 9. Assignment #1
    • Pages 6-7: 10-44 even. (Show answers only)
    • Page 11: 10-30 even. (Copy problem and show each step of PEMDAS)
    • Extra Credit: Page 11: 36-39 all. (Show problem and answer)
    • Start your homework!
    • Fold a lined piece of paper in half. (Holes on the Left Side!)
    • Top right: Name, Class, Assignment Number, Assignment.
    • Start on the left side of the fold and show all work.
    • Remember to box your answers!
    • Print out of pages 3, 4, 5, and 7 should be pasted in with your notes!