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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
• 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