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1-3, ALGEBRAIC EXPRESSIONS

1-3, ALGEBRAIC EXPRESSIONS. Objectives: Translate word phrases into algebraic expressions. Simplify algebraic expressions Evaluate algebraic expression using order of operations. 1-3, ALGEBRAIC EXPRESSIONS – Getting Ready!!. By tradition the term containing the variable is written first.

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1-3, ALGEBRAIC EXPRESSIONS

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  1. 1-3, ALGEBRAIC EXPRESSIONS • Objectives: • Translate word phrases into algebraic expressions. • Simplify algebraic expressions • Evaluate algebraic expression using order of operations

  2. 1-3, ALGEBRAIC EXPRESSIONS – Getting Ready!! • By tradition the term containing the variable is written first. • What expression is the same as 20 + 6w and has the term containing the variable first? • What Property permits this?

  3. 1-3 Translating from verbal to algebraic • 10 is equal to 12 minus 2 • The sum of a number and -8 is -9 • A number divided by 6 is equal to that number squared. • The quotient of 4 and a number is 1

  4. Writing an Algebraic Expression to model a stituation Josh and Pam have bought an older home that needs some repair. After budgeting a total of $1685 for home improvements, they started by spending $425 on small improvements. They would like to replace 6 interior doors next. What is the maximum they can spend on each door? $210 Textbook p 22, 1-8 10 minutes

  5. 1-3, Page 19 Algebraic Expressions • Problem 3 • What is the value of the expression for the given variables of the expression? • 7( a + 4) + 3b – 8 for a = -4 and b = 5 • First substitute • When you substitute ALWAYS create a blank parenthesis to receive the substitute number. 7( ( ) + 4) + 3( ) – 8. • Then insert correct number. 7( (-4 ) + 4) + 3( 5 ) – 8

  6. 1-3, Page 19 Algebraic Expressions • Don’t forget the Order of Operations! ORDER OF OPERATIONS • Parentheses • Exponents • Multiply/Divide from left to right • Add/Subtract from left to right • 7( 0 ) + 15 – 8 • 0 + 15 – 8 • 15 – 8 • 7

  7. 1-3, Page 19 Algebraic Expressions • Problem 3B • x/2 + y2 for x = 1 and y = ½. • ½ + ( ½ )2 • = ½ + ¼ • = ¾ • Got 3a: What is the value of the expression 2( x2– y2 ) / 3 for x = 6 and y = -3. • 18 • Got it 3b: Will the value of the expression change if the parenthesis are removed? Explain.

  8. 1-3, Page 20 Algebraic Expressions Organize the data by completing the tables.

  9. 1-3, Page 20 Algebraic Expressions Organize the data by completing the tables.Got it #4: • Let x = the number of 2 point shots, y = the number of three – point shots, z = the number of one point free throws, • 2x + 3y + 1z • 42 points

  10. 1-3, Page 21 Algebraic Expressions Properties for simplifying Algebraic Expressions • Definition of Subtraction a – b = a + ( -b ) • Definition of Division a ÷ b = a/b = a ∙ 1/b, b ≠ 0 • Distributive Property for Subtraction a( b – c) = ab – ac • Multiplication by 0 0 ∙ a = 0 • Multiplication by -1 -1 ∙ a = - a • Opposite of a Sum -(a + b ) = -a + ( -b ) = -a – b • Opposite of a Difference -(a – b ) = -a + b = b - a • Opposite of a Product -(ab) = -a ∙ b = a ∙ ( -b ) • Opposite of an Opposite -(-a) = a

  11. 1-3, Page 21 Algebraic ExpressionsSimplifying Algebraic Expressions • It’s all about combining like terms… • A: 7x2 + 3y2 + 2y2 – 4x27x2+ 3y2 + 2y2– 4x23x2 + 5y2 • B:-(3k + m) + 2(k – 4m) -3k – m + 2k – 8m = -k – 9m • Got it #5: Your Turn! • A: -4j2 – 7k + 5j + j2 = -3j2 -7k +5j • B: -(8a + 3b) + 10(2a – 5b) = -8a – 3b + 20a – 50b =12a – 53b

  12. Let’s look at some questions Lesson 1-3, Page 22. • Lesson Check #1, #2, #6, #8 • Practice #10 – 18 Even • Homework #20 - #24 Even, #30 - #44 Even • Test Practice: #63, #64, #65

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